05-QRE-Calculation-Normalize.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1362f56e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.optimize import minimize\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import copy\n",
    "import os\n",
    "import random\n",
    "import math as math\n",
    "import matplotlib.pylab as plt #Typically matplotlib.pylab is imported as plt (shortened name)\n",
    "import pdb\n",
    "from scipy.optimize import minimize\n",
    "import shutil\n",
    "import csv\n",
    "from MyLatexFunctions_SocialLearning import * \n",
    "from itertools import permutations \n",
    "from itertools import combinations\n",
    "import csv\n",
    "\n",
    "\n",
    "import networkx as nx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "662ad055",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "network = [\"c1\",\"c2\"]\n",
    "Alldata =  pd.DataFrame()\n",
    "for i in range(1,3):\n",
    "    data = pd.read_csv(\"..\\\\ImportedData\\\\network_c\"+str(i)+\".csv\", sep=\",\", header=0)\n",
    "    #data.columns = [ \"from\", \"to\" ]\n",
    "    data[\"network\"] = i\n",
    "    Alldata = Alldata.append(data)\n",
    "\n",
    "    \n",
    "for i in range(1,3):\n",
    "    # Build your graph. Note that we use the DiGraph function to create the graph!\n",
    "    G=nx.from_pandas_edgelist(Alldata[Alldata.network==i], 'from', 'to', create_using=nx.DiGraph() )\n",
    "\n",
    "    # Make the graph\n",
    "    f1 = plt.figure()\n",
    "    plt.title(\"Directed Network_\"+str(i))\n",
    "    nx.draw(G, pos=nx.circular_layout(G), with_labels=True, node_size=1500, alpha=1, arrows=True) \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71685cb3",
   "metadata": {},
   "source": [
    "# Content\n",
    "\n",
    "- [Sequential Probability](#First-method:-sequantial-probability)\n",
    "\n",
    "- [Normal Form](#Method-2:-Agent-Normal-Form-Estimation)\n",
    "    - [Obtain QRE and QRE Figures](#Obtain-QRE-and-QRE-Figures)\n",
    "    - [ Estimate lambda](#Estimate-lambda)\n",
    "\n",
    "- [Extensive Form](#Method-3:-Agent-Extensive-Form-Estimation)\n",
    "    - [ Estimate lambda extensive](#Estimate-lambda-extensive)\n",
    "    \n",
    "- [Extensive Form (linear)](#Method-4:-Agent-Extensive-Form-Estimation-linear)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a33d67c",
   "metadata": {},
   "source": [
    "# First method: sequantial probability\n",
    "\n",
    "- [Return](#Content)\n",
    "\n",
    "First determine the equilibrium at turn 0, since what matters are only A and B's decision probability, once an equilibrium is achieved, can just add the rest of the probabilities in (For node C, D, E) \n",
    "\n",
    "At turn 1, conditional on A and B's decision in turn 1,the payoffs could be different for subjects at different nodes. However, in all cases, the payoff should be fixed and there should be no more strategic consideration.\n",
    "\n",
    "For example, at turn 1, B will know whether A has made a prediction or not. There are 4 cases: AB both decided, A decidedBnot; ... At turn 2, there are more conditions, but no longer has a strategic consideration in it. But the issue is to assure a subject to make a decision at period 4, for example, the likelihood will be (1-p_i0)*(1-p_i1)*(1-p_i2)*p_i3. It may introduce additional problem at the empirical estimation stage. \n",
    "\n",
    "On the other hand if we consider probability at the normal game form, assigning the probabilities as the probability to decide at turn 0,1,2,3,4,5, then my biggest concern is that the decision process doesn't follow what is described in the procedure where a max of future payoffs is considered in the paper and it only considers the probability distribution at turn 0, ignoring the potential information gain from turn 1 and on, when certain information set is not reached or ignore the information updates, but it should give me an underestimated lambda (maybe, or since the method is consistently estimating everything in the expected value term, it is fine/still comparable)\n",
    "\n",
    "Based on my current reading of the QRE book, the above two methods separately correspond to agent normal-form and agent behavioral strategy method. If you can implement both, maybe worth checking the difference? \n",
    "\n",
    "Next step: it is easier to implement the second method (normal form, especially for the latter estimation part) , do that first, after that, can move on to implementing the first method. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c90aee5",
   "metadata": {},
   "source": [
    "## Incomplete for now since it only considers the strategic interaction between A and B at turn 0, ignoring other nodes and other turns. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1cee99b6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Network A, payoff for turn 0\n",
    "\n",
    "# Define the payoff, assuming that the utility depends solely on the payoff\n",
    "# Estimate the prob of decising at turn 0, \n",
    "# Here only focus on A and B\n",
    "# pOther = [A, B< C, D, E] probability of deciding at turn 0\n",
    "# pay has two values, [0] is to decide; [1] is to wait for longer\n",
    "def payoff(pOther,network, cost):\n",
    "    '''This is for network (a)'''\n",
    "    diff_pay = 100\n",
    "    q = 0.7\n",
    "    if cost=='h':\n",
    "        c = 8\n",
    "    elif cost == 'l':\n",
    "        c = 1\n",
    "    \n",
    "    if network == 'a':\n",
    "        #In network a, I only consider the pay for A and B, at turn 0 \n",
    "        pay =  np.empty((5,2),dtype=float)\n",
    "        pay[:,0] = ProbCorrect_Bayesian(1,q)*diff_pay\n",
    "        # indegree = 1, node A or E, (position 0, 4)\n",
    "        pay_1 = ProbCorrect_Bayesian(2,q)*diff_pay - c\n",
    "        pay[0,1] = pay_1 \n",
    "        pay[4,1] = pay_1 \n",
    "        # indegree = 1, node D, (position 3)\n",
    "        pay_2 = pOther[0]*ProbCorrect_Bayesian(2,q)*diff_pay + (1- pOther[0])*ProbCorrect_Bayesian(3,q)*diff_pay - 2*c\n",
    "        pay[3,1] = max(pay_1, pay_2)\n",
    "        # indegree = 3, node B\n",
    "        pay_1 = ProbCorrect_Bayesian(4,q)*diff_pay - c\n",
    "        pay_2 = pOther[0]*ProbCorrect_Bayesian(4,q)*diff_pay + (1- pOther[0])*ProbCorrect_Bayesian(5,q)*diff_pay - 2*c\n",
    "        pay[1,1] = max(pay_1, pay_2)\n",
    "        # indegree = 2, node C\n",
    "        pay_1 = ProbCorrect_Bayesian(3,q)*diff_pay - c\n",
    "        pay_2 = pOther[0]*pOther[1]*ProbCorrect_Bayesian(3,q)*diff_pay \n",
    "        + (pOther[1]*(1- pOther[0])+pOther[0]*(1- pOther[1]))*ProbCorrect_Bayesian(4,q)*diff_pay + (1-pOther[0])*(1-pOther[1])*ProbCorrect_Bayesian(3,q)*diff_pay - 2*c\n",
    "        pay[2,1] = max(pay_1, pay_2)\n",
    "        \n",
    "    if network == 'b':\n",
    "         # We know there are 5 nodes, pay matrix is 5X6 ( 6 period)\n",
    "        pay =  np.empty((5,2),dtype=float)\n",
    "        pay[:,0] = ProbCorrect_Bayesian(1,q)*diff_pay\n",
    "\n",
    "        # Note: since here the payoff is about turn 0,1,2, need to do the max in the \n",
    "        # indegree = 2, node A\n",
    "        pay_1 = pOther[1]* (ProbCorrect_Bayesian(3,q)*diff_pay - c) + (1-pOther[1])* np.max([ProbCorrect_Bayesian(5,q)*diff_pay-2*c, ProbCorrect_Bayesian(3,q)*diff_pay-c])\n",
    "        pay[0,1] = pay_1\n",
    "        \n",
    "        # indegree = 3, node B\n",
    "        pay_1 =  pOther[0]* (ProbCorrect_Bayesian(4,q)*diff_pay - c) + (1- pOther[0])*np.max([ProbCorrect_Bayesian(4,q)*diff_pay - c,ProbCorrect_Bayesian(5,q)*diff_pay - 2*c])\n",
    "        pay[1,1] = pay_1\n",
    "        \n",
    "        #indegree = 1, node C/D/E; not relevant for QRE calculation, but will change based on later decisions\n",
    "        pay_1 = pOther[0]*(ProbCorrect_Bayesian(2,q)*diff_pay - c) + (1-pOther[0])*pOther[1]*(ProbCorrect_Bayesian(3,q)*diff_pay - 2*c)  + (1-pOther[0])*(1-pOther[1])*(ProbCorrect_Bayesian(5,q)*diff_pay - 3*c) \n",
    "        pay[2:5,1] = pay_1\n",
    "\n",
    "    return pay\n",
    "    \n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f64794fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[70.     , 81.2628 ],\n",
       "       [70.     , 81.2628 ],\n",
       "       [70.     , 79.13652],\n",
       "       [70.     , 79.13652],\n",
       "       [70.     , 79.13652]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "payoff([0.1,0.1],'b','l') # payoff for nodes A, B,-E decide vs wait at turn 0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "72e6f04a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Note: My payoff_a has considered the pOthers, the probability of others\n",
    "## Iteration process\n",
    "\n",
    "def policy_iter(l,p_ini,network, waitingcost, tol = 1e-10):\n",
    "    \n",
    "    error = 1\n",
    "    p_1 = np.array(p_ini)\n",
    "    p_2 = np.array(p_ini)\n",
    "    \n",
    "    nrep = 1\n",
    "    while error > tol:\n",
    "        pOthers = np.array([p_1[0], p_2[0]])\n",
    "        mixed_payoff_1 = payoff(pOthers,network, waitingcost)[0] # why I should use p_1? \n",
    "        mixed_payoff_2 = payoff(pOthers,network, waitingcost)[1] \n",
    "        print(mixed_payoff_1)\n",
    "        sigma_1 = np.exp(l*mixed_payoff_1)/np.sum(np.exp(l*mixed_payoff_1))\n",
    "        sigma_2 = np.exp(l*mixed_payoff_2)/np.sum(np.exp(l*mixed_payoff_2))\n",
    "        error_1 = np.sum(np.abs(sigma_1-p_1))\n",
    "        error_2 = np.sum(np.abs(sigma_2-p_2))\n",
    "        \n",
    "        error = max(error_1,error_2)\n",
    "#         print(\"Minimum error\", error)\n",
    "        \n",
    "        p_1 = sigma_1\n",
    "        p_2 = sigma_2\n",
    "        nrep += 1\n",
    "        \n",
    "    print(\"Number of Iterations:\",nrep)\n",
    "    return [p_1,p_2]\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8b1fe500",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Round: 1\n",
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      "Round: 50\n",
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      "Round: 60\n",
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      "Round: 64\n",
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      "Round: 65\n",
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      "Round: 66\n",
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      "Round: 67\n",
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      "Round: 69\n",
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      "Round: 70\n",
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      "Round: 71\n",
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      "Round: 72\n",
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      "Round: 73\n",
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      "Round: 74\n",
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      "Round: 75\n",
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      "Round: 76\n",
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      "Round: 77\n",
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      "Round: 78\n",
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      "Round: 79\n",
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      "Round: 80\n",
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      "Round: 176"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_8056/3109127715.py:17: RuntimeWarning: overflow encountered in exp\n",
      "  sigma_2 = np.exp(l*mixed_payoff_2)/np.sum(np.exp(l*mixed_payoff_2))\n",
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_8056/3109127715.py:17: RuntimeWarning: invalid value encountered in true_divide\n",
      "  sigma_2 = np.exp(l*mixed_payoff_2)/np.sum(np.exp(l*mixed_payoff_2))\n",
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_8056/3109127715.py:16: RuntimeWarning: overflow encountered in exp\n",
      "  sigma_1 = np.exp(l*mixed_payoff_1)/np.sum(np.exp(l*mixed_payoff_1))\n",
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_8056/3109127715.py:16: RuntimeWarning: invalid value encountered in true_divide\n",
      "  sigma_1 = np.exp(l*mixed_payoff_1)/np.sum(np.exp(l*mixed_payoff_1))\n",
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_8056/2405291984.py:34: UserWarning: You have mixed positional and keyword arguments, some input may be discarded.\n",
      "  lgd = ax.legend(handles, labels = labels, loc = 0)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "[70. 69.]\n",
      "Number of Iterations: 2\n",
      "Round: 177\n",
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     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambd = []\n",
    "n = 200\n",
    "for i in range(n):\n",
    "    lambd.append(1.0173182**i - 1)\n",
    "\n",
    "p_1 = np.empty((n,2))\n",
    "p_2 = np.empty((n,2))\n",
    "\n",
    "for i in range(n):\n",
    "    print(\"Round:\", i+1)\n",
    "    Result = policy_iter(lambd[i],[1/2,1/2],'a','l')\n",
    "    p_1[i] = Result[0]\n",
    "    p_2[i] = Result[1]\n",
    "    \n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "ax.set_ylabel('Strategies')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "ax.set_title(\"QRE for game\")\n",
    "ax.set_ylim(0, 1)\n",
    "ax.set_xscale('log')\n",
    "Strategy_names_1 = ['Decide', 'Wait']\n",
    "Strategy_names_2 = ['Decide', 'Wait']\n",
    "\n",
    "# Symmetric Case:\n",
    "\n",
    "for i in range(2):\n",
    "    \n",
    "    ax.plot(lambd,p_1[:,i])\n",
    "    ax.plot(lambd,p_2[:,i],'o',markerfacecolor = \"none\")\n",
    "    labels.append(('A', Strategy_names_1[i]))\n",
    "    labels.append(('B', Strategy_names_2[i]))\n",
    "\n",
    "lgd = ax.legend(handles, labels = labels, loc = 0)         "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d8288681",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "       [5.31884349e-01, 4.68115651e-01],\n",
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       "       [6.43312107e-01, 3.56687893e-01],\n",
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       "       [6.55952697e-01, 3.44047303e-01],\n",
       "       [6.62354263e-01, 3.37645737e-01],\n",
       "       [6.68806189e-01, 3.31193811e-01],\n",
       "       [6.75305370e-01, 3.24694630e-01],\n",
       "       [6.81848502e-01, 3.18151498e-01],\n",
       "       [6.88432085e-01, 3.11567915e-01],\n",
       "       [6.95052423e-01, 3.04947577e-01],\n",
       "       [7.01705625e-01, 2.98294375e-01],\n",
       "       [7.08387606e-01, 2.91612394e-01],\n",
       "       [7.15094091e-01, 2.84905909e-01],\n",
       "       [7.21820622e-01, 2.78179378e-01],\n",
       "       [7.28562558e-01, 2.71437442e-01],\n",
       "       [7.35315086e-01, 2.64684914e-01],\n",
       "       [7.42073227e-01, 2.57926773e-01],\n",
       "       [7.48831846e-01, 2.51168154e-01],\n",
       "       [7.55585660e-01, 2.44414340e-01],\n",
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       "       [8.21620454e-01, 1.78379546e-01],\n",
       "       [8.27945266e-01, 1.72054734e-01],\n",
       "       [8.34195973e-01, 1.65804027e-01],\n",
       "       [8.40366880e-01, 1.59633120e-01],\n",
       "       [8.46452409e-01, 1.53547591e-01],\n",
       "       [8.52447118e-01, 1.47552882e-01],\n",
       "       [8.58345725e-01, 1.41654275e-01],\n",
       "       [8.64143132e-01, 1.35856868e-01],\n",
       "       [8.69834445e-01, 1.30165555e-01],\n",
       "       [8.75414996e-01, 1.24585004e-01],\n",
       "       [8.80880363e-01, 1.19119637e-01],\n",
       "       [8.86226388e-01, 1.13773612e-01],\n",
       "       [8.91449197e-01, 1.08550803e-01],\n",
       "       [8.96545216e-01, 1.03454784e-01],\n",
       "       [9.01511184e-01, 9.84888163e-02],\n",
       "       [9.06344166e-01, 9.36558342e-02],\n",
       "       [9.11041566e-01, 8.89584336e-02],\n",
       "       [9.15601137e-01, 8.43988633e-02],\n",
       "       [9.20020982e-01, 7.99790180e-02],\n",
       "       [9.24299567e-01, 7.57004332e-02],\n",
       "       [9.28435718e-01, 7.15642821e-02],\n",
       "       [9.32428624e-01, 6.75713755e-02],\n",
       "       [9.36277837e-01, 6.37221628e-02],\n",
       "       [9.39983264e-01, 6.00167355e-02],\n",
       "       [9.43545166e-01, 5.64548335e-02],\n",
       "       [9.46964148e-01, 5.30358520e-02],\n",
       "       [9.50241148e-01, 4.97588516e-02],\n",
       "       [9.53377431e-01, 4.66225692e-02],\n",
       "       [9.56374569e-01, 4.36254313e-02],\n",
       "       [9.59234431e-01, 4.07655685e-02],\n",
       "       [9.61959169e-01, 3.80408313e-02],\n",
       "       [9.64551193e-01, 3.54488073e-02],\n",
       "       [9.67013161e-01, 3.29868389e-02],\n",
       "       [9.69347957e-01, 3.06520431e-02],\n",
       "       [9.71558669e-01, 2.84413306e-02],\n",
       "       [9.73648574e-01, 2.63514260e-02],\n",
       "       [9.75621111e-01, 2.43788886e-02],\n",
       "       [9.77479867e-01, 2.25201330e-02],\n",
       "       [9.79228550e-01, 2.07714496e-02],\n",
       "       [9.80870974e-01, 1.91290256e-02],\n",
       "       [9.82411035e-01, 1.75889648e-02],\n",
       "       [9.83852693e-01, 1.61473075e-02],\n",
       "       [9.85199950e-01, 1.48000498e-02],\n",
       "       [9.86456838e-01, 1.35431623e-02],\n",
       "       [9.87627393e-01, 1.23726075e-02],\n",
       "       [9.88715643e-01, 1.12843569e-02],\n",
       "       [9.89725593e-01, 1.02744071e-02],\n",
       "       [9.90661206e-01, 9.33879425e-03],\n",
       "       [9.91526392e-01, 8.47360840e-03],\n",
       "       [9.92324994e-01, 7.67500594e-03],\n",
       "       [9.93060779e-01, 6.93922132e-03],\n",
       "       [9.93737422e-01, 6.26257754e-03],\n",
       "       [9.94358505e-01, 5.64149549e-03],\n",
       "       [9.94927498e-01, 5.07250209e-03],\n",
       "       [9.95447763e-01, 4.55223743e-03],\n",
       "       [9.95922539e-01, 4.07746066e-03],\n",
       "       [9.96354945e-01, 3.64505498e-03],\n",
       "       [9.96747969e-01, 3.25203141e-03],\n",
       "       [9.97104468e-01, 2.89553176e-03],\n",
       "       [9.97427169e-01, 2.57283052e-03],\n",
       "       [9.97718664e-01, 2.28133594e-03],\n",
       "       [9.97981410e-01, 2.01859024e-03],\n",
       "       [9.98217731e-01, 1.78226911e-03],\n",
       "       [9.98429820e-01, 1.57018046e-03],\n",
       "       [9.98619738e-01, 1.38026249e-03],\n",
       "       [9.98789419e-01, 1.21058126e-03],\n",
       "       [9.98940672e-01, 1.05932770e-03],\n",
       "       [9.99075186e-01, 9.24814129e-04],\n",
       "       [9.99194530e-01, 8.05470457e-04],\n",
       "       [9.99300160e-01, 6.99839959e-04],\n",
       "       [9.99393425e-01, 6.06574837e-04],\n",
       "       [9.99475568e-01, 5.24431535e-04],\n",
       "       [9.99547734e-01, 4.52265871e-04],\n",
       "       [9.99610972e-01, 3.89028068e-04],\n",
       "       [9.99666242e-01, 3.33757693e-04],\n",
       "       [9.99714421e-01, 2.85578570e-04],\n",
       "       [9.99756306e-01, 2.43693703e-04],\n",
       "       [9.99792620e-01, 2.07380235e-04],\n",
       "       [9.99824016e-01, 1.75984493e-04],\n",
       "       [9.99851083e-01, 1.48917130e-04],\n",
       "       [9.99874352e-01, 1.25648404e-04],\n",
       "       [9.99894296e-01, 1.05703607e-04],\n",
       "       [9.99911341e-01, 8.86586672e-05],\n",
       "       [9.99925864e-01, 7.41359401e-05],\n",
       "       [9.99938200e-01, 6.18001955e-05],\n",
       "       [9.99948645e-01, 5.13548153e-05],\n",
       "       [9.99957462e-01, 4.25382065e-05],\n",
       "       [           nan, 0.00000000e+00],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan],\n",
       "       [           nan,            nan]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "fbec0215",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Round: 1\n",
      "[70. 62.]\n",
      "Number of Iterations: 2\n",
      "Round: 2\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 3\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 4\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 5\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 6\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 7\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 8\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 9\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 10\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 11\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 12\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 13\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 14\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 15\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 16\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 17\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 18\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 19\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 20\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 21\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 22\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 23\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 24\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 25\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 26\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 27\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 28\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 29\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 30\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 31\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 32\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 33\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 34\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 35\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 36\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 37\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 38\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 39\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 40\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 41\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 42\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 43\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 44\n",
      "[70. 62.]\n",
      "[70. 62.]\n",
      "Number of Iterations: 3\n",
      "Round: 45\n",
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      "Round: 187\n",
      "[70. 62.]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_8056/3109127715.py:16: RuntimeWarning: overflow encountered in exp\n",
      "  sigma_1 = np.exp(l*mixed_payoff_1)/np.sum(np.exp(l*mixed_payoff_1))\n",
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_8056/3109127715.py:16: RuntimeWarning: invalid value encountered in true_divide\n",
      "  sigma_1 = np.exp(l*mixed_payoff_1)/np.sum(np.exp(l*mixed_payoff_1))\n",
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_8056/3109127715.py:17: RuntimeWarning: overflow encountered in exp\n",
      "  sigma_2 = np.exp(l*mixed_payoff_2)/np.sum(np.exp(l*mixed_payoff_2))\n",
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_8056/3109127715.py:17: RuntimeWarning: invalid value encountered in true_divide\n",
      "  sigma_2 = np.exp(l*mixed_payoff_2)/np.sum(np.exp(l*mixed_payoff_2))\n",
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_8056/1600054940.py:34: UserWarning: You have mixed positional and keyword arguments, some input may be discarded.\n",
      "  lgd = ax.legend(handles, labels = labels, loc = 0)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Number of Iterations: 2\n",
      "Round: 188\n",
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     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambd = []\n",
    "n = 200\n",
    "for i in range(n):\n",
    "    lambd.append(1.0173182**i - 1)\n",
    "\n",
    "p_1 = np.empty((n,2))\n",
    "p_2 = np.empty((n,2))\n",
    "\n",
    "for i in range(n):\n",
    "    print(\"Round:\", i+1)\n",
    "    Result = policy_iter(lambd[i],[1/2,1/2],'a','h')\n",
    "    p_1[i] = Result[0]\n",
    "    p_2[i] = Result[1]\n",
    "    \n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "ax.set_ylabel('Strategies')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "ax.set_title(\"QRE for game\")\n",
    "ax.set_ylim(0, 1)\n",
    "ax.set_xscale('log')\n",
    "Strategy_names_1 = ['Decide', 'Wait']\n",
    "Strategy_names_2 = ['Decide', 'Wait']\n",
    "\n",
    "# Symmetric Case:\n",
    "\n",
    "for i in range(2):\n",
    "    \n",
    "    ax.plot(lambd,p_1[:,i])\n",
    "    ax.plot(lambd,p_2[:,i],'o',markerfacecolor = \"none\")\n",
    "    labels.append(('A', Strategy_names_1[i]))\n",
    "    labels.append(('B', Strategy_names_2[i]))\n",
    "\n",
    "lgd = ax.legend(handles, labels = labels, loc = 0)         "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3265e48a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Round: 1\n",
      "[70.    79.546]\n",
      "Number of Iterations: 2\n",
      "Round: 2\n",
      "[70.    79.546]\n",
      "[70.         79.72298496]\n",
      "[70.         79.72625098]\n",
      "[70.         79.72631124]\n",
      "[70.         79.72631236]\n",
      "[70.         79.72631238]\n",
      "[70.         79.72631238]\n",
      "Number of Iterations: 8\n",
      "Round: 3\n",
      "[70.    79.546]\n",
      "[70.         79.90056748]\n",
      "[70.         79.91348282]\n",
      "[70.         79.91395276]\n",
      "[70.         79.91396985]\n",
      "[70.         79.91397048]\n",
      "[70.        79.9139705]\n",
      "[70.        79.9139705]\n",
      "Number of Iterations: 9\n",
      "Round: 4\n",
      "[70.    79.546]\n",
      "[70.         80.07622984]\n",
      "[70.         80.10436837]\n",
      "[70.         80.10585601]\n",
      "[70.         80.10593464]\n",
      "[70.        80.1059388]\n",
      "[70.         80.10593902]\n",
      "[70.         80.10593903]\n",
      "[70.         80.10593903]\n",
      "Number of Iterations: 10\n",
      "Round: 5\n",
      "[70.    79.546]\n",
      "[70.         80.24747833]\n",
      "[70.         80.29487548]\n",
      "[70.         80.29804892]\n",
      "[70.         80.29826126]\n",
      "[70.         80.29827547]\n",
      "[70.         80.29827642]\n",
      "[70.         80.29827648]\n",
      "[70.         80.29827648]\n",
      "[70.         80.29827648]\n",
      "Number of Iterations: 11\n",
      "Round: 6\n",
      "[70.    79.546]\n",
      "[70.         80.41198559]\n",
      "[70.         80.48060845]\n",
      "[70.         80.48594993]\n",
      "[70.        80.4863651]\n",
      "[70.         80.48639736]\n",
      "[70.         80.48639987]\n",
      "[70.         80.48640007]\n",
      "[70.         80.48640008]\n",
      "[70.         80.48640008]\n",
      "Number of Iterations: 11\n",
      "Round: 7\n",
      "[70.    79.546]\n",
      "[70.         80.56771846]\n",
      "[70.         80.65726095]\n",
      "[70.         80.66487194]\n",
      "[70.         80.66551709]\n",
      "[70.         80.66557177]\n",
      "[70.        80.6655764]\n",
      "[70.         80.66557679]\n",
      "[70.         80.66557683]\n",
      "[70.         80.66557683]\n",
      "[70.         80.66557683]\n",
      "Number of Iterations: 12\n",
      "Round: 8\n",
      "[70.    79.546]\n",
      "[70.         80.71303668]\n",
      "[70.         80.82108549]\n",
      "[70.         80.83062538]\n",
      "[70.         80.83146391]\n",
      "[70.         80.83153759]\n",
      "[70.         80.83154406]\n",
      "[70.         80.83154463]\n",
      "[70.         80.83154468]\n",
      "[70.         80.83154468]\n",
      "[70.         80.83154468]\n",
      "Number of Iterations: 12\n",
      "Round: 9\n",
      "[70.    79.546]\n",
      "[70.         80.84675292]\n",
      "[70.         80.96927114]\n",
      "[70.         80.98004873]\n",
      "[70.         80.98099062]\n",
      "[70.         80.98107288]\n",
      "[70.         80.98108007]\n",
      "[70.         80.98108069]\n",
      "[70.         80.98108075]\n",
      "[70.         80.98108075]\n",
      "[70.         80.98108075]\n",
      "Number of Iterations: 12\n",
      "Round: 10\n",
      "[70.    79.546]\n",
      "[70.         80.96815111]\n",
      "[70.         81.10014933]\n",
      "[70.         81.11131453]\n",
      "[70.         81.11225075]\n",
      "[70.         81.11232919]\n",
      "[70.         81.11233577]\n",
      "[70.         81.11233632]\n",
      "[70.         81.11233636]\n",
      "[70.         81.11233637]\n",
      "[70.         81.11233637]\n",
      "Number of Iterations: 12\n",
      "Round: 11\n",
      "[70.    79.546]\n",
      "[70.        81.0769662]\n",
      "[70.         81.21320303]\n",
      "[70.         81.22395171]\n",
      "[70.         81.22479068]\n",
      "[70.        81.2248561]\n",
      "[70.         81.22486121]\n",
      "[70.        81.2248616]\n",
      "[70.         81.22486163]\n",
      "[70.         81.22486164]\n",
      "Number of Iterations: 11\n",
      "Round: 12\n",
      "[70.    79.546]\n",
      "[70.         81.17333369]\n",
      "[70.         81.30891172]\n",
      "[70.         81.31863195]\n",
      "[70.        81.3193202]\n",
      "[70.         81.31936889]\n",
      "[70.         81.31937234]\n",
      "[70.         81.31937258]\n",
      "[70.        81.3193726]\n",
      "[70.        81.3193726]\n",
      "Number of Iterations: 11\n",
      "Round: 13\n",
      "[70.    79.546]\n",
      "[70.         81.25771922]\n",
      "[70.         81.38849869]\n",
      "[70.         81.39683039]\n",
      "[70.         81.39735395]\n",
      "[70.         81.39738682]\n",
      "[70.         81.39738888]\n",
      "[70.         81.39738901]\n",
      "[70.         81.39738902]\n",
      "[70.         81.39738902]\n",
      "Number of Iterations: 11\n",
      "Round: 14\n",
      "[70.    79.546]\n",
      "[70.         81.33083924]\n",
      "[70.         81.45365199]\n",
      "[70.         81.46047227]\n",
      "[70.         81.46084558]\n",
      "[70.       81.460866]\n",
      "[70.         81.46086712]\n",
      "[70.         81.46086718]\n",
      "[70.         81.46086718]\n",
      "Number of Iterations: 10\n",
      "Round: 15\n",
      "[70.    79.546]\n",
      "[70.         81.39358183]\n",
      "[70.         81.50627315]\n",
      "[70.         81.51163887]\n",
      "[70.         81.51189062]\n",
      "[70.         81.51190242]\n",
      "[70.         81.51190298]\n",
      "[70.       81.511903]\n",
      "[70.         81.51190301]\n",
      "Number of Iterations: 10\n",
      "Round: 16\n",
      "[70.    79.546]\n",
      "[70.         81.44693465]\n",
      "[70.        81.5482825]\n",
      "[70.         81.55236097]\n",
      "[70.         81.55252273]\n",
      "[70.         81.55252915]\n",
      "[70.        81.5525294]\n",
      "[70.         81.55252941]\n",
      "[70.         81.55252941]\n",
      "Number of Iterations: 10\n",
      "Round: 17\n",
      "[70.    79.546]\n",
      "[70.         81.49192398]\n",
      "[70.         81.58148802]\n",
      "[70.         81.58449617]\n",
      "[70.         81.58459581]\n",
      "[70.         81.58459911]\n",
      "[70.         81.58459922]\n",
      "[70.         81.58459922]\n",
      "Number of Iterations: 9\n",
      "Round: 18\n",
      "[70.    79.546]\n",
      "[70.        81.5295667]\n",
      "[70.         81.60751051]\n",
      "[70.         81.60967119]\n",
      "[70.         81.60973031]\n",
      "[70.         81.60973192]\n",
      "[70.         81.60973197]\n",
      "[70.         81.60973197]\n",
      "Number of Iterations: 9\n",
      "Round: 19\n",
      "[70.    79.546]\n",
      "[70.         81.56083508]\n",
      "[70.         81.62775192]\n",
      "[70.         81.62926767]\n",
      "[70.         81.62930159]\n",
      "[70.         81.62930235]\n",
      "[70.         81.62930237]\n",
      "[70.         81.62930237]\n",
      "Number of Iterations: 9\n",
      "Round: 20\n",
      "[70.    79.546]\n",
      "[70.         81.58663319]\n",
      "[70.         81.64339264]\n",
      "[70.         81.64443362]\n",
      "[70.        81.6444525]\n",
      "[70.         81.64445285]\n",
      "[70.         81.64445285]\n",
      "Number of Iterations: 8\n",
      "Round: 21\n",
      "[70.    79.546]\n",
      "[70.        81.6077829]\n",
      "[70.         81.65540631]\n",
      "[70.         81.65610752]\n",
      "[70.         81.65611775]\n",
      "[70.        81.6561179]\n",
      "[70.        81.6561179]\n",
      "Number of Iterations: 8\n",
      "Round: 22\n",
      "[70.    79.546]\n",
      "[70.         81.62501763]\n",
      "[70.         81.66458322]\n",
      "[70.         81.66504721]\n",
      "[70.         81.66505261]\n",
      "[70.         81.66505267]\n",
      "[70.         81.66505267]\n",
      "Number of Iterations: 8\n",
      "Round: 23\n",
      "[70.    79.546]\n",
      "[70.         81.63898171]\n",
      "[70.         81.67155678]\n",
      "[70.         81.67185873]\n",
      "[70.         81.67186151]\n",
      "[70.         81.67186154]\n",
      "[70.         81.67186154]\n",
      "Number of Iterations: 8\n",
      "Round: 24\n",
      "[70.    79.546]\n",
      "[70.         81.65023371]\n",
      "[70.         81.67682947]\n",
      "[70.         81.67702292]\n",
      "[70.         81.67702432]\n",
      "[70.         81.67702433]\n",
      "Number of Iterations: 7\n",
      "Round: 25\n",
      "[70.    79.546]\n",
      "[70.         81.65925226]\n",
      "[70.         81.68079658]\n",
      "[70.         81.68091868]\n",
      "[70.         81.68091936]\n",
      "[70.         81.68091937]\n",
      "Number of Iterations: 7\n",
      "Round: 26\n",
      "[70.    79.546]\n",
      "[70.         81.66644339]\n",
      "[70.         81.68376682]\n",
      "[70.         81.68384279]\n",
      "[70.         81.68384312]\n",
      "[70.         81.68384312]\n",
      "Number of Iterations: 7\n",
      "Round: 27\n",
      "[70.    79.546]\n",
      "[70.        81.6721484]\n",
      "[70.        81.6859798]\n",
      "[70.        81.6860264]\n",
      "[70.         81.68602656]\n",
      "[70.         81.68602656]\n",
      "Number of Iterations: 7\n",
      "Round: 28\n",
      "[70.    79.546]\n",
      "[70.         81.67665189]\n",
      "[70.         81.68762038]\n",
      "[70.         81.68764859]\n",
      "[70.         81.68764866]\n",
      "Number of Iterations: 6\n",
      "Round: 29\n",
      "[70.    79.546]\n",
      "[70.         81.68018938]\n",
      "[70.         81.68883048]\n",
      "[70.         81.68884733]\n",
      "[70.         81.68884736]\n",
      "Number of Iterations: 6\n",
      "Round: 30\n",
      "[70.    79.546]\n",
      "[70.         81.68295444]\n",
      "[70.         81.68971845]\n",
      "[70.         81.68972838]\n",
      "[70.        81.6897284]\n",
      "Number of Iterations: 6\n",
      "Round: 31\n",
      "[70.    79.546]\n",
      "[70.         81.68510516]\n",
      "[70.        81.6903666]\n",
      "[70.         81.69037238]\n",
      "[70.         81.69037238]\n",
      "Number of Iterations: 6\n",
      "Round: 32\n",
      "[70.    79.546]\n",
      "[70.        81.6867698]\n",
      "[70.         81.69083714]\n",
      "[70.         81.69084046]\n",
      "[70.         81.69084046]\n",
      "Number of Iterations: 6\n",
      "Round: 33\n",
      "[70.    79.546]\n",
      "[70.         81.68805186]\n",
      "[70.         81.69117684]\n",
      "[70.         81.69117872]\n",
      "[70.         81.69117873]\n",
      "Number of Iterations: 6\n",
      "Round: 34\n",
      "[70.    79.546]\n",
      "[70.         81.68903436]\n",
      "[70.        81.6914207]\n",
      "[70.         81.69142176]\n",
      "[70.         81.69142176]\n",
      "Number of Iterations: 6\n",
      "Round: 35\n",
      "[70.    79.546]\n",
      "[70.        81.6897835]\n",
      "[70.         81.69159475]\n",
      "[70.         81.69159533]\n",
      "Number of Iterations: 5\n",
      "Round: 36\n",
      "[70.    79.546]\n",
      "[70.         81.69035181]\n",
      "[70.         81.69171822]\n",
      "[70.         81.69171854]\n",
      "Number of Iterations: 5\n",
      "Round: 37\n",
      "[70.    79.546]\n",
      "[70.         81.69078072]\n",
      "[70.         81.69180529]\n",
      "[70.         81.69180546]\n",
      "Number of Iterations: 5\n",
      "Round: 38\n",
      "[70.    79.546]\n",
      "[70.         81.69110274]\n",
      "[70.        81.6918663]\n",
      "[70.         81.69186639]\n",
      "Number of Iterations: 5\n",
      "Round: 39\n",
      "[70.    79.546]\n",
      "[70.         81.69134322]\n",
      "[70.         81.69190878]\n",
      "[70.         81.69190883]\n",
      "Number of Iterations: 5\n",
      "Round: 40\n",
      "[70.    79.546]\n",
      "[70.         81.69152184]\n",
      "[70.         81.69193818]\n",
      "[70.        81.6919382]\n",
      "Number of Iterations: 5\n",
      "Round: 41\n",
      "[70.    79.546]\n",
      "[70.        81.6916538]\n",
      "[70.         81.69195838]\n",
      "[70.         81.69195839]\n",
      "Number of Iterations: 5\n",
      "Round: 42\n",
      "[70.    79.546]\n",
      "[70.         81.69175074]\n",
      "[70.         81.69197217]\n",
      "[70.         81.69197218]\n",
      "Number of Iterations: 5\n",
      "Round: 43\n",
      "[70.    79.546]\n",
      "[70.         81.69182156]\n",
      "[70.         81.69198152]\n",
      "[70.         81.69198152]\n",
      "Number of Iterations: 5\n",
      "Round: 44\n",
      "[70.    79.546]\n",
      "[70.         81.69187299]\n",
      "[70.         81.69198782]\n",
      "[70.         81.69198782]\n",
      "Number of Iterations: 5\n",
      "Round: 45\n",
      "[70.    79.546]\n",
      "[70.         81.69191013]\n",
      "[70.         81.69199202]\n",
      "[70.         81.69199202]\n",
      "Number of Iterations: 5\n",
      "Round: 46\n",
      "[70.    79.546]\n",
      "[70.         81.69193679]\n",
      "[70.         81.69199482]\n",
      "[70.         81.69199482]\n",
      "Number of Iterations: 5\n",
      "Round: 47\n",
      "[70.    79.546]\n",
      "[70.         81.69195581]\n",
      "[70.         81.69199666]\n",
      "Number of Iterations: 4\n",
      "Round: 48\n",
      "[70.    79.546]\n",
      "[70.        81.6919693]\n",
      "[70.         81.69199786]\n",
      "Number of Iterations: 4\n",
      "Round: 49\n",
      "[70.    79.546]\n",
      "[70.        81.6919788]\n",
      "[70.         81.69199864]\n",
      "Number of Iterations: 4\n",
      "Round: 50\n",
      "[70.    79.546]\n",
      "[70.         81.69198546]\n",
      "[70.         81.69199914]\n",
      "Number of Iterations: 4\n",
      "Round: 51\n",
      "[70.    79.546]\n",
      "[70.         81.69199009]\n",
      "[70.         81.69199946]\n",
      "Number of Iterations: 4\n",
      "Round: 52\n",
      "[70.    79.546]\n",
      "[70.         81.69199329]\n",
      "[70.         81.69199967]\n",
      "Number of Iterations: 4\n",
      "Round: 53\n",
      "[70.    79.546]\n",
      "[70.         81.69199549]\n",
      "[70.        81.6919998]\n",
      "Number of Iterations: 4\n",
      "Round: 54\n",
      "[70.    79.546]\n",
      "[70.         81.69199699]\n",
      "[70.         81.69199988]\n",
      "Number of Iterations: 4\n",
      "Round: 55\n",
      "[70.    79.546]\n",
      "[70.       81.691998]\n",
      "[70.         81.69199992]\n",
      "Number of Iterations: 4\n",
      "Round: 56\n",
      "[70.    79.546]\n",
      "[70.         81.69199868]\n",
      "[70.         81.69199995]\n",
      "Number of Iterations: 4\n",
      "Round: 57\n",
      "[70.    79.546]\n",
      "[70.         81.69199914]\n",
      "[70.         81.69199997]\n",
      "Number of Iterations: 4\n",
      "Round: 58\n",
      "[70.    79.546]\n",
      "[70.         81.69199944]\n",
      "[70.         81.69199998]\n",
      "Number of Iterations: 4\n",
      "Round: 59\n",
      "[70.    79.546]\n",
      "[70.         81.69199964]\n",
      "[70.         81.69199999]\n",
      "Number of Iterations: 4\n",
      "Round: 60\n",
      "[70.    79.546]\n",
      "[70.         81.69199977]\n",
      "[70.         81.69199999]\n",
      "Number of Iterations: 4\n",
      "Round: 61\n",
      "[70.    79.546]\n",
      "[70.         81.69199985]\n",
      "[70.    81.692]\n",
      "Number of Iterations: 4\n",
      "Round: 62\n",
      "[70.    79.546]\n",
      "[70.         81.69199991]\n",
      "[70.    81.692]\n",
      "Number of Iterations: 4\n",
      "Round: 63\n",
      "[70.    79.546]\n",
      "[70.         81.69199994]\n",
      "[70.    81.692]\n",
      "Number of Iterations: 4\n",
      "Round: 64\n",
      "[70.    79.546]\n",
      "[70.         81.69199996]\n",
      "[70.    81.692]\n",
      "Number of Iterations: 4\n",
      "Round: 65\n",
      "[70.    79.546]\n",
      "[70.         81.69199998]\n",
      "[70.    81.692]\n",
      "Number of Iterations: 4\n",
      "Round: 66\n",
      "[70.    79.546]\n",
      "[70.         81.69199999]\n",
      "[70.    81.692]\n",
      "Number of Iterations: 4\n",
      "Round: 67\n",
      "[70.    79.546]\n",
      "[70.         81.69199999]\n",
      "[70.    81.692]\n",
      "Number of Iterations: 4\n",
      "Round: 68\n",
      "[70.    79.546]\n",
      "[70.    81.692]\n",
      "[70.    81.692]\n",
      "Number of Iterations: 4\n",
      "Round: 69\n",
      "[70.    79.546]\n",
      "[70.    81.692]\n",
      "[70.    81.692]\n",
      "Number of Iterations: 4\n",
      "Round: 70\n",
      "[70.    79.546]\n",
      "[70.    81.692]\n",
      "[70.    81.692]\n",
      "Number of Iterations: 4\n",
      "Round: 71\n",
      "[70.    79.546]\n",
      "[70.    81.692]\n",
      "[70.    81.692]\n",
      "Number of Iterations: 4\n",
      "Round: 72\n",
      "[70.    79.546]\n",
      "[70.    81.692]\n",
      "[70.    81.692]\n",
      "Number of Iterations: 4\n",
      "Round: 73\n",
      "[70.    79.546]\n",
      "[70.    81.692]\n",
      "[70.    81.692]\n",
      "Number of Iterations: 4\n",
      "Round: 74\n",
      "[70.    79.546]\n",
      "[70.    81.692]\n",
      "Number of Iterations: 3\n",
      "Round: 75\n",
      "[70.    79.546]\n",
      "[70.    81.692]\n",
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      "Round: 76\n",
      "[70.    79.546]\n",
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      "Round: 77\n",
      "[70.    79.546]\n",
      "[70.    81.692]\n",
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      "Round: 78\n",
      "[70.    79.546]\n",
      "[70.    81.692]\n",
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      "Round: 79\n",
      "[70.    79.546]\n",
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      "Round: 80\n",
      "[70.    79.546]\n",
      "[70.    81.692]\n",
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      "Round: 81\n",
      "[70.    79.546]\n",
      "[70.    81.692]\n",
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      "Round: 82\n",
      "[70.    79.546]\n",
      "[70.    81.692]\n",
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      "Round: 83\n",
      "[70.    79.546]\n",
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      "Round: 84\n",
      "[70.    79.546]\n",
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      "Round: 85\n",
      "[70.    79.546]\n",
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      "Round: 86\n",
      "[70.    79.546]\n",
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      "Round: 87\n",
      "[70.    79.546]\n",
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      "Round: 88\n",
      "[70.    79.546]\n",
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      "Round: 89\n",
      "[70.    79.546]\n",
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      "Round: 90\n",
      "[70.    79.546]\n",
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      "Round: 91\n",
      "[70.    79.546]\n",
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      "Round: 92\n",
      "[70.    79.546]\n",
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      "Round: 93\n",
      "[70.    79.546]\n",
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      "Round: 94\n",
      "[70.    79.546]\n",
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      "Round: 95\n",
      "[70.    79.546]\n",
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      "Round: 96\n",
      "[70.    79.546]\n",
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      "Round: 97\n",
      "[70.    79.546]\n",
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      "Round: 98\n",
      "[70.    79.546]\n",
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      "Round: 99\n",
      "[70.    79.546]\n",
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      "Round: 100\n",
      "[70.    79.546]\n",
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      "Round: 101\n",
      "[70.    79.546]\n",
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      "Round: 102\n",
      "[70.    79.546]\n",
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      "Round: 103\n",
      "[70.    79.546]\n",
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      "Round: 104\n",
      "[70.    79.546]\n",
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      "Round: 105\n",
      "[70.    79.546]\n",
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      "Round: 106\n",
      "[70.    79.546]\n",
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      "Round: 107\n",
      "[70.    79.546]\n",
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      "Round: 108\n",
      "[70.    79.546]\n",
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      "Round: 109\n",
      "[70.    79.546]\n",
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      "Round: 110\n",
      "[70.    79.546]\n",
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      "Round: 111\n",
      "[70.    79.546]\n",
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      "Round: 112\n",
      "[70.    79.546]\n",
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      "Round: 113\n",
      "[70.    79.546]\n",
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      "Round: 114\n",
      "[70.    79.546]\n",
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      "Round: 115\n",
      "[70.    79.546]\n",
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      "Round: 116\n",
      "[70.    79.546]\n",
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      "Round: 117\n",
      "[70.    79.546]\n",
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      "Round: 118\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[70.    79.546]\n",
      "[70.    81.692]\n",
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     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_8056/3109127715.py:16: RuntimeWarning: overflow encountered in exp\n",
      "  sigma_1 = np.exp(l*mixed_payoff_1)/np.sum(np.exp(l*mixed_payoff_1))\n",
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_8056/3109127715.py:16: RuntimeWarning: invalid value encountered in true_divide\n",
      "  sigma_1 = np.exp(l*mixed_payoff_1)/np.sum(np.exp(l*mixed_payoff_1))\n",
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_8056/3109127715.py:17: RuntimeWarning: overflow encountered in exp\n",
      "  sigma_2 = np.exp(l*mixed_payoff_2)/np.sum(np.exp(l*mixed_payoff_2))\n",
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_8056/3109127715.py:17: RuntimeWarning: invalid value encountered in true_divide\n",
      "  sigma_2 = np.exp(l*mixed_payoff_2)/np.sum(np.exp(l*mixed_payoff_2))\n",
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_8056/699999969.py:34: UserWarning: You have mixed positional and keyword arguments, some input may be discarded.\n",
      "  lgd = ax.legend(handles, labels = labels, loc = 0)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambd = []\n",
    "n = 200\n",
    "for i in range(n):\n",
    "    lambd.append(1.0173182**i - 1)\n",
    "\n",
    "p_1 = np.empty((n,2))\n",
    "p_2 = np.empty((n,2))\n",
    "\n",
    "for i in range(n):\n",
    "    print(\"Round:\", i+1)\n",
    "    Result = policy_iter(lambd[i],[1/2,1/2],'b','l')\n",
    "    p_1[i] = Result[0]\n",
    "    p_2[i] = Result[1]\n",
    "    \n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "ax.set_ylabel('Strategies')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "ax.set_title(\"QRE for game\")\n",
    "ax.set_ylim(0, 1)\n",
    "ax.set_xscale('log')\n",
    "Strategy_names_1 = ['Decide', 'Wait']\n",
    "Strategy_names_2 = ['Decide', 'Wait']\n",
    "\n",
    "# Symmetric Case:\n",
    "\n",
    "for i in range(2):\n",
    "    \n",
    "    ax.plot(lambd,p_1[:,i])\n",
    "    ax.plot(lambd,p_2[:,i],'o',markerfacecolor = \"none\")\n",
    "    labels.append(('A', Strategy_names_1[i]))\n",
    "    labels.append(('B', Strategy_names_2[i]))\n",
    "\n",
    "lgd = ax.legend(handles, labels = labels, loc = 0)         "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9c884642",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Round: 1\n",
      "[70.  70.4]\n",
      "Number of Iterations: 2\n",
      "Round: 2\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 3\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 4\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 5\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 6\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 7\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 8\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 9\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 10\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 11\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 12\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 13\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 14\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 15\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 16\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 17\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 18\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 19\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 20\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 21\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 22\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 23\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 24\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 25\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 26\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 27\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 28\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 29\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 30\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 31\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 32\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 33\n",
      "[70.  70.4]\n",
      "[70.  70.4]\n",
      "Number of Iterations: 3\n",
      "Round: 34\n",
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      "Round: "
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_17672/3109127715.py:16: RuntimeWarning: overflow encountered in exp\n",
      "  sigma_1 = np.exp(l*mixed_payoff_1)/np.sum(np.exp(l*mixed_payoff_1))\n",
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_17672/3109127715.py:16: RuntimeWarning: invalid value encountered in true_divide\n",
      "  sigma_1 = np.exp(l*mixed_payoff_1)/np.sum(np.exp(l*mixed_payoff_1))\n",
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_17672/3109127715.py:17: RuntimeWarning: overflow encountered in exp\n",
      "  sigma_2 = np.exp(l*mixed_payoff_2)/np.sum(np.exp(l*mixed_payoff_2))\n",
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_17672/3109127715.py:17: RuntimeWarning: invalid value encountered in true_divide\n",
      "  sigma_2 = np.exp(l*mixed_payoff_2)/np.sum(np.exp(l*mixed_payoff_2))\n",
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_17672/1953066089.py:34: UserWarning: You have mixed positional and keyword arguments, some input may be discarded.\n",
      "  lgd = ax.legend(handles, labels = labels, loc = 0)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "187\n",
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     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambd = []\n",
    "n = 200\n",
    "for i in range(n):\n",
    "    lambd.append(1.0173182**i - 1)\n",
    "\n",
    "p_1 = np.empty((n,2))\n",
    "p_2 = np.empty((n,2))\n",
    "\n",
    "for i in range(n):\n",
    "    print(\"Round:\", i+1)\n",
    "    Result = policy_iter(lambd[i],[1/2,1/2],'b','h')\n",
    "    p_1[i] = Result[0]\n",
    "    p_2[i] = Result[1]\n",
    "    \n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "ax.set_ylabel('Strategies')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "ax.set_title(\"QRE for game\")\n",
    "ax.set_ylim(0, 1)\n",
    "ax.set_xscale('log')\n",
    "Strategy_names_1 = ['Decide', 'Wait']\n",
    "Strategy_names_2 = ['Decide', 'Wait']\n",
    "\n",
    "# Symmetric Case:\n",
    "\n",
    "for i in range(2):\n",
    "    \n",
    "    ax.plot(lambd,p_1[:,i])\n",
    "    ax.plot(lambd,p_2[:,i],'o',markerfacecolor = \"none\")\n",
    "    labels.append(('A', Strategy_names_1[i]))\n",
    "    labels.append(('B', Strategy_names_2[i]))\n",
    "\n",
    "lgd = ax.legend(handles, labels = labels, loc = 0)         "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "605c8ca3",
   "metadata": {},
   "source": [
    "# Method 2: Agent Normal Form Estimation\n",
    "\n",
    "- [Return](#Content)\n",
    "\n",
    "Probability is defined as a matrix of 5*6 (5 nodes, deciding at 6 turns). It is assumed that each subject with a given lambda will pre-determine the probability of makig a prediction at a certain turn, the probability doesn't change based on what new information is updated as time goes by (Not sure what is a more formal/proper way to describe this)\n",
    "\n",
    "\n",
    "Comment: Got very interesting results!!!\n",
    "\n",
    "The normal form equilibrium is not the bayesian perfect nash equilibrium ... (Maybe because how we use the max to derive the optimal rule...)\n",
    "\n",
    "NOTE: NETWORK B EXPECTED PAYOFF UPDATED ONLY FROM HERE!!!!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d8c1aa95",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Step 1: Define Payoffs for Deciding at each turn; The payoff depends on others' probability of making a prediction \n",
    "\n",
    "# Step 2: Write out the policy iteration \n",
    "\n",
    "# Step 3: for different lambda value, derive the results\n",
    "\n",
    "# Step 4: Based on the estimation result, do two things \n",
    "# A. Draw QRE for each node for each treatment, show the difference, describe\n",
    "# B. Estimate MLE based on realized/observed frequencies in each treatment\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "id": "3039b291",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 1. \n",
    "def payoff(pOther,network, cost):\n",
    "    '''This is for the normal form estimation \n",
    "        pOther = matrix(5,6); each row is for each node; each column is for each turn\n",
    "        '''\n",
    "    diff_pay = 100\n",
    "    q = 0.7\n",
    "    if cost=='h':\n",
    "        c = 8\n",
    "    elif cost == 'l':\n",
    "        c = 1\n",
    "    \n",
    "    if network == 'a':\n",
    "        #In network a, I only consider the pay for A and B, at turn 0 \n",
    "        pay =  np.empty((5,6),dtype=float)\n",
    "        pay[:,0] = ProbCorrect_Bayesian(1,q)*diff_pay\n",
    "        \n",
    "        # indegree = 1, node A / E\n",
    "        pay_1 = ProbCorrect_Bayesian(2,q)*diff_pay - c\n",
    "        pay[0,1] = pay_1 \n",
    "        pay[4,1] = pay_1 \n",
    "        j = 2\n",
    "        while j <= 5:        \n",
    "            pay[0,j] = ProbCorrect_Bayesian(2,q)*diff_pay - j*c\n",
    "            pay[4,j] = ProbCorrect_Bayesian(2,q)*diff_pay - j*c\n",
    "            j += 1\n",
    "        \n",
    "        # indegree = 3, node B\n",
    "        pay_1 = ProbCorrect_Bayesian(4,q)*diff_pay - c\n",
    "        pi_b = pOther[0,0]*ProbCorrect_Bayesian(4,q)*diff_pay + (1- pOther[0,0])*ProbCorrect_Bayesian(5,q)*diff_pay \n",
    "        pay[1,1] = pay_1\n",
    "        j = 2\n",
    "        while j <= 5:        \n",
    "            pay[1,j] = pi_b - j*c\n",
    "            j += 1\n",
    "\n",
    "        # indegree = 2, node C\n",
    "        pay_1 = ProbCorrect_Bayesian(3,q)*diff_pay - c\n",
    "        pay[2,1] = pay_1\n",
    "        pi_c = pOther[0, 0]*pOther[1,0]*ProbCorrect_Bayesian(3,q)*diff_pay + ((1-pOther[0, 0])*pOther[1,0] + pOther[0, 0]*(1-pOther[1,0]))*ProbCorrect_Bayesian(4,q)*diff_pay + (1-pOther[0, 0])*(1-pOther[1,0])*ProbCorrect_Bayesian(3,q)*diff_pay\n",
    "        j = 2\n",
    "        while j <= 5:        \n",
    "            pay[2,j] = pi_c - j*c\n",
    "            j += 1\n",
    "            \n",
    "        # indegree = 1, node D (position 3)\n",
    "        pay_1 = ProbCorrect_Bayesian(2,q)*diff_pay - c\n",
    "        pay[3,1] = pay_1 \n",
    "        pi_d = pOther[0,0]*ProbCorrect_Bayesian(2,q)*diff_pay + (1- pOther[0,0])*ProbCorrect_Bayesian(3,q)*diff_pay \n",
    "        j = 2\n",
    "        while j <= 5:        \n",
    "            pay[3,j] = pi_d - j*c\n",
    "            j += 1\n",
    "        \n",
    "   \n",
    "        \n",
    "    elif network == 'b':\n",
    "         # We know there are 5 nodes, pay matrix is 5X6 ( 6 period)\n",
    "        pay =  np.empty((5,6),dtype=float)\n",
    "        pay[:,0] = ProbCorrect_Bayesian(1,q)*diff_pay\n",
    "\n",
    "        # Note: since here the payoff is about turn 0,1,2, need to do the max in the \n",
    "        # indegree = 2, node A\n",
    "        pay_1 = ProbCorrect_Bayesian(3,q)*diff_pay - c\n",
    "        pi_a = pOther[1,0]*ProbCorrect_Bayesian(3,q)*diff_pay + (1-pOther[1,0])*ProbCorrect_Bayesian(5,q)*diff_pay        \n",
    "        pay[0,1] = pay_1\n",
    "        j = 2\n",
    "        while j <= 5:        \n",
    "            pay[0,j] = pi_a - j*c\n",
    "            j += 1\n",
    "\n",
    "        # indegree = 3, node B\n",
    "        pay_1 = ProbCorrect_Bayesian(4,q)*diff_pay - c\n",
    "        pi_b = pOther[0,0]*ProbCorrect_Bayesian(4,q)*diff_pay + (1- pOther[0,0])*ProbCorrect_Bayesian(5,q)*diff_pay \n",
    "        pay[1,1] = pay_1\n",
    "        j = 2\n",
    "        while j <= 5:        \n",
    "            pay[1,j] = pi_b - j*c\n",
    "            j += 1\n",
    "\n",
    "\n",
    "        # indegree = 1, node C or D or E, (position 2,3)\n",
    "        pay_1 = ProbCorrect_Bayesian(2,q)*diff_pay - c\n",
    "        pay[2:5,1] = pay_1\n",
    "        # Since in bayesian updating, having 3 or 4 signals carry the same informaiton value, can group these points together\n",
    "        pi_e0 =  pOther[0,0]*ProbCorrect_Bayesian(2,q)*diff_pay + (1-pOther[0,0])*ProbCorrect_Bayesian(3,q)*diff_pay \n",
    "        pay[2:5,2] = pi_e0 - 2*c\n",
    "        pi_e =  pOther[0,0]*ProbCorrect_Bayesian(2,q)*diff_pay + (pOther[0,1] + (1- pOther[0,0] -pOther[0,1])*pOther[1,0])*ProbCorrect_Bayesian(3,q)*diff_pay  +(1- pOther[0,0] -pOther[0,1])*(1-pOther[1,0])*ProbCorrect_Bayesian(5,q)*diff_pay \n",
    "        \n",
    "        j = 3\n",
    "        while j <= 5:        \n",
    "            pay[2:5,j] = pi_e - j*c\n",
    "            j += 1\n",
    "#     pay_avg = np.sum(pay,axis=1)\n",
    "#     return pay/pay_avg[:,None]\n",
    "    return pay/70\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "id": "5516a5e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 1.10571429, 1.15442857, 1.14014286, 1.12585714,\n",
       "        1.11157143],\n",
       "       [1.        , 1.10571429, 1.15442857, 1.14014286, 1.12585714,\n",
       "        1.11157143],\n",
       "       [1.        , 0.98571429, 1.07142857, 1.09914286, 1.08485714,\n",
       "        1.07057143],\n",
       "       [1.        , 0.98571429, 1.07142857, 1.09914286, 1.08485714,\n",
       "        1.07057143],\n",
       "       [1.        , 0.98571429, 1.07142857, 1.09914286, 1.08485714,\n",
       "        1.07057143]])"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pOthers = np.ones((5,6))* 1/6\n",
    "network = 'b'\n",
    "waitingcost = 'l'\n",
    "x = payoff(pOthers,network, waitingcost)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "id": "197f5008",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.98571429, 0.97142857, 0.95714286, 0.94285714,\n",
       "        0.92857143],\n",
       "       [1.        , 1.10571429, 1.15442857, 1.14014286, 1.12585714,\n",
       "        1.11157143],\n",
       "       [1.        , 1.10571429, 1.09142857, 1.07714286, 1.06285714,\n",
       "        1.04857143],\n",
       "       [1.        , 0.98571429, 1.07142857, 1.05714286, 1.04285714,\n",
       "        1.02857143],\n",
       "       [1.        , 0.98571429, 0.97142857, 0.95714286, 0.94285714,\n",
       "        0.92857143]])"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pOthers = np.ones((5,6))* 1/6\n",
    "network = 'a'\n",
    "waitingcost = 'l'\n",
    "x = payoff(pOthers,network, waitingcost)\n",
    "x\n",
    "# node_avg =  np.sum(x,axis=1)\n",
    "# node_avg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "id": "54ded374",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Step 2\n",
    "\n",
    "def policy_iter(l,p_ini,network, waitingcost, tol = 1e-10):\n",
    "    \n",
    "    error = 1\n",
    "    pOthers = np.ones((5,6))* p_ini\n",
    "    \n",
    "    nrep = 1\n",
    "    while error > tol:\n",
    "        \n",
    "        mixed_payoff = payoff(pOthers,network, waitingcost)\n",
    "        add_error = np.exp(l*mixed_payoff)\n",
    "\n",
    "        node_avg =  np.sum(add_error,axis=1)\n",
    "        sigma = add_error / node_avg[:,None]\n",
    "\n",
    "        error = np.max(np.sum(np.abs(sigma-pOthers), axis=1))\n",
    "        pOthers = sigma\n",
    "\n",
    "        nrep += 1\n",
    "        \n",
    "    print(\"Number of Iterations:\",nrep)\n",
    "    return pOthers\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "id": "04e4f881",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Step 3\n",
    "# lambd = []\n",
    "n = 200\n",
    "lambd = np.logspace(-1, 2.5, n, endpoint=True)\n",
    "# for i in range(n):\n",
    "#     lambd.append(1.0173182**i - 1)\n",
    "\n",
    "def QRE_Outcome(network, waitingCost):\n",
    "    '''Contains both the prob and graphs'''\n",
    "    \n",
    "    p = np.empty((n,5,6))\n",
    "    for i in range(n):\n",
    "#         print(\"Round:\", i+1)\n",
    "        Result = policy_iter(lambd[i],1/6,network,waitingCost)\n",
    "        p[i] = Result\n",
    "    \n",
    "    \n",
    "\n",
    "    # By Indegree\n",
    "    i = 1 # Node B is always the indegree=3\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.set_xlabel('$\\lambda$')\n",
    "    ax.set_ylabel('Strategies')\n",
    "    handles, labels = ax.get_legend_handles_labels()\n",
    "    ax.set_title(\"QRE for Nodes with Multiple Information Souces\")\n",
    "    ax.set_ylim(0, 1)\n",
    "    ax.set_xscale('log')\n",
    "    for j in range(6):\n",
    "        ax.plot(lambd,p[:,i,j], label='Turn'+str(j))\n",
    "    ax.legend()\n",
    "    fig.savefig(\"..\\\\Output_Figures\\\\05-QRE-Calculation\\\\\"+\"QRE\"+network+\"-\"+waitingCost+\"-mSource\", bbox_inches=\"tight\")  \n",
    "\n",
    "    i = 3 # Node D is always the indegree=1\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.set_xlabel('$\\lambda$')\n",
    "    ax.set_ylabel('Strategies')\n",
    "    handles, labels = ax.get_legend_handles_labels()\n",
    "    ax.set_title(\"QRE for Nodes with Single Information Source\")\n",
    "    ax.set_ylim(0, 1)\n",
    "    ax.set_xscale('log')\n",
    "    for j in range(6):\n",
    "        ax.plot(lambd,p[:,i,j], label='Turn'+str(j))\n",
    "    ax.legend()\n",
    "    fig.savefig(\"..\\\\Output_Figures\\\\05-QRE-Calculation\\\\\"+\"QRE\"+network+\"-\"+waitingCost+\"-sSource\", bbox_inches=\"tight\")  \n",
    "\n",
    "    \n",
    "    return p\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b5c180e",
   "metadata": {},
   "source": [
    "## Obtain QRE and QRE Figures\n",
    "\n",
    "Including empirical data (obtained in the next section)\n",
    "\n",
    "- [Return](#Content)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "id": "66eff350",
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mzRq2bdtGRkYGy5YtY+PGjWzfvp2UlBTmzJnDihUrGDVqFLGxsQQFWX+itLQ0jh7t1DO7lVJd7EDZAX7y0U+oc9fxjzP+wcSkia3PFABaIgiAGTNmnHC554wZM0hLS8NmszFp0iSysrJo6hGi3e0sQinVvKOVR1n08SI8xsOzZz3bbZMA9MISgS/P3DsjKCgIj8cDWNf7OxyO+u8iIyNPmDY0NLT+s91ux+VykZiYSGlpKS6Xi6CgILKzs0lJSema4JVSnVJQXcCijxdR46rhn2f+k8y4zECH1CItEfhJeno669evB+Dtt9/G6XS2a34RYd68efXtDM8++ywXXnihz+NUSvlWWV0Z1/z3GgprCnn8tMcZGT8y0CG1ShOBnyxatIjly5czY8YMVq9e/Y1SQFvcd999PPjgg2RmZlJUVMTVV1/th0iVUr7i9Dj51bJfcaj8EA/Pe7hbVwc1JE3VRXdnTT2PYOfOnYwePTpAEQVeX99+pbqLP6/6M6/sfoU/z/kzF2Z2rxK8iKw3xkxr6jstESillA+8vOtlXtn9CleNvarbJYHWaCJQSqlOWpu3lnvX3Mupaadyw5QbAh1Ou2kiUEqpTiiqKeK3n/+WQdGDuO+U+7Db7IEOqd163eWjSinVVTzGw++//D3ldeUsOW0JUSH+eZSkv2mJQCmlOujpbU/zVc5X3Dzj5h5xmWhzNBEopVQHbMrfxOKNizkz/UwuHnFxoMPpFE0EPlBUVMSkSZOYNGkSycnJpKam1g83vKO4vRYvXkxmZiYiQmFhoQ8jVkp1RrWzmt9/+XuSI5P506w/9fjuX7SNwAeOd0MNcPvttxMVFcVNN93U6nxutxu7vfmGpTlz5nDeeecxd+5cH0WqlPKFhzY8xJGKIzx95tNEh0QHOpxO0xKBn3S2G2qAyZMnk56eHojwlVLNWJ27mpd2vcTloy9nevL0QIfjE72vRPDBLZC31bfLTB4PZ9/rs8W1pRvqk08+2WfrU0r5RqWjkj+u+CND+g3hF1N+EehwfEZLBAHQlm6olVLdz0MbHiKvOo8/z/kz4UHhgQ7HZ3pficCHZ+6d0dluqJVS3cum/E28uvtVFoxewKT+kwIdjk9picBPOtsNtVKq+3B6nNy56k76R/TnusnXBTocn9NE4Ce+6Ib6kUceIS0tjezsbCZMmMBPfvITP0SqlGrNCzteYG/JXn4383dEBrf//3J3p91Q9wJ9ffuV8qejlUf5zlvfYVbKLB759iOBDqfDtBtqpZTqoHvX3IuI8PuZvw90KH6jiUAppZqx4ugKlh1Zxk8n/JTkyORAh+M3mgiUUqoJTo+T+9bex+DowfxozI8CHY5f9b7LR5VSygde2vkSB8sOsvjbiwmxhwQ6HL/SEoFSSjVSVFPE45sfZ07qHE5NOzXQ4fidJgKllGrk7xv/Tq2rlpun39zjexZtC60a8oGioiLmz58PQF5eHna7naSkJMDqVygkpGPFygULFrBu3TqCg4OZMWMGTzzxBMHBwT6LWyn1TftK9vHvff/mslGXkRGT0foMvYBfSwQicpaI7BaRfSJySxPfx4jIuyKyWUS2i8hV/ozHX453Q71p0yauvfZabrzxxvrhlpKA2+1ucbkLFixg165dbN26lZqaGp588klfh66UauShDQ8RGRTJTyf8NNChdBm/JQIRsQOPAmcDY4BLRWRMo8n+H7DDGDMRmAv8VUR6RauML7qhPueccxARRIQZM2aQnZ0dkG1Rqq9Ym7eW5dnLuXr81cSGxQY6nC7jz6qhGcA+Y8wBABF5GbgQ2NFgGgNEi1UJFwUUA53qce2+Nfexq3hXZxbxDaPiR3HzjJt9trz2dkPtdDp5/vnnefjhh30Wg1LqRMYYHlz3IAMiBrBg9IJAh9Ol/Fk1lAocaTCc7R3X0GJgNJADbAVuMMZ4Gi9IRK4RkXUisq6goMBf8XaZ9nZD/fOf/5xTTz2VU045pYsjVarv+OjQR2wr2sb1k68nLCgs0OF0KX+WCJpqam/csdGZwCbg28Aw4L8i8oUxpvyEmYxZCiwFq6+hllbqyzP3zvBVN9R33HEHBQUFPPHEE36OWKm+y+l28vD6hxkRN4Lzhp4X6HC6nD9LBNnAoAbDaVhn/g1dBbxpLPuAg8AoP8bUZXzRDfWTTz7JRx99xEsvvYTNplf6KuUvr+55lezKbH419VfYbc0/R7y38ufRZS0wXEQyvA3APwTeaTTNYWA+gIgMAEYCB/wYU5fxRTfU1157LceOHWPWrFlMmjSJO++80w+RKtW3VTgqWLJ5CScNPInZKbMDHU5A+LUbahE5B3gIsANPG2PuEpFrAYwxS0QkBXgGGIhVlXSvMeaFlpap3VB/U1/ffqU64/FNj/PY5sd45bxXGJPQ+MLG3qOlbqj9ekOZMeZ94P1G45Y0+JwDnOHPGJRSqjlldWU8t+M55g+e36uTQGu04lkp1Wc9v+N5Kp2V/GzizwIdSkBpIlBK9UlldWW8sPMFTh9yOiPjRwY6nIDSRKCU6pOe3f4s1c7qPl8aAE0ESqk+qKS2hBd3vsiZ6WcyPG54oMMJOE0ESqk+59ntz1LjquHaidcGOpRuQbuh9gF/dUN99dVXs27dOowxjBgxgmeeeaa+8zqlVMcU1xbzr13/4qyMsxgWOyzQ4XQLWiLwAX91Q/23v/2NzZs3s2XLFgYPHszixYt9HbpSfc4z256hzl2npYEGNBH4iS+6oe7Xrx9g9VVUU1PTJ56UpJQ/FdYU8vLulzkn4xyGxgwNdDjdRq+rGsq7+27qdvq2G+rQ0aNI/v3vfba89nRDfdVVV/H+++8zZswY/vrXv/osBqX6on9u+yd17ro+9dCZttASQQC0pxvqf/7zn+Tk5DB69GheeeWVAESrVO9QWFPIq7tf5byh55Eekx7ocLqVXlci8OWZe2f4qhvq4+MuueQS7r//fq66qkc+zVOpgHtq61M4PU6unaBtA41picBPOtsNtTGGffv21X9+9913GTWqV/TQrVSXy6/O59Xdr3L+sPMZ1G9Q6zP0Mb2uRNBdLFq0iAsvvJAZM2Ywf/78dndDbYzhyiuvpLy8HGMMEydO5PHHH/dTtEr1bk9tfQqP8XDNhGsCHUq35NduqP1Bu6H+pr6+/Uq1JK8qj3PfPJfzh53P7bNvD3Q4AdNSN9RaNaSU6tWe3PokHuNh0YRFgQ6l29JEoJTqtXIrc3lz75t8d/h3SY1KDXQ43ZYmAqVUr/WPrf/AYFg0XksDLdFEoJTqlXIqc/j3vn/z/eHfZ2DUwECH061pIlBK9UpLtyxFEH4y/ieBDqXb00SglOp1siuyeXvf21w04iKSI5MDHU63p4nAB4qKipg0aRKTJk0iOTmZ1NTU+uGGdxR31PXXX6/dTyvVDku3LMUmNi0NtJHeUOYDx7uhBrj99tuJioripptuanU+t9uN3W5vcZp169ZRWlrqgyiV6huOlB/hnf3vcOmoS+kf0T/Q4fQIWiLwE190Q+12u/nNb37DX/7yl4Bsg1I90ZItSwiyBfHjcT8OdCg9Rq8rEXzx6h4Kj1T6dJmJg6I45QcjfLa8tnZDvXjxYi644AIGDtQrHpRqi0Plh3jvwHtcPvpykiKSAh1Oj9HrEkFP0Fw31EB9N9RDhw7ltddeY9myZQGKUqme54nNTxBiC+GqcdpLb3v0ukTgyzP3zuhsN9QbN25k3759ZGZmAlBdXU1mZmZ9j6RKqRMdLDvIfw7+hyvGXEFieGKgw+lRtI3ATzrbDfW5555LXl4eWVlZZGVlERERoUlAqRYs2byEUHuolgY6QBOBnyxatIjly5czY8YMVq9e3e5uqJVSbXeg9AAfHPyAS0ddSnxYfKDD6XG0G+peoK9vv1I3Lb+JL7K/4MPvf0hcWFygw+mWtBtqpVSvtbt4Nx9lfcSC0Qs0CXSQJgKlVI/22KbHiA6O5sqxVwY6lB5LE4FSqsfaXrSdT498yo/G/oiY0JhAh9NjaSJQSvVYj258lJjQGH40+keBDqVH00SglOqRNuVv4oujX7Bw7EKiQrRTxs7wayIQkbNEZLeI7BORW5qZZq6IbBKR7SKy3J/xKKV6j0c3PUp8WDyXjbos0KH0eH67s1hE7MCjwOlANrBWRN4xxuxoME0s8BhwljHmsIj0yK4Ci4qKmD9/PgB5eXnY7XaSkqx+TtasWUNISEiHlrtw4UKWL19OTIxV9/nMM88wadIkn8SsVE+2Nm8tq3JXcdO0m4gIjgh0OD1emxKBiAwDso0xdSIyF5gAPGeMKW1hthnAPmPMAe8yXgYuBHY0mOYy4E1jzGEAY0x+ezegO/BnN9T3338/F110kS/CVKpXMMaweONiksKTuGTkJYEOp1doa9XQG4BbRDKBp4AM4F+tzJMKHGkwnO0d19AIIE5ElonIehG5oo3xdHu+6IZaKfVNK3NXsiF/Az8Z/xPCgsICHU6v0NaqIY8xxiUi3wUeMsb8XUQ2tjKPNDGu8REuCJgKzAfCgZUissoYs+eEBYlcA1wDMHjw4BZX+tkzS8k/dKCV0Nqn/5ChzFt4jc+W19ZuqAFuvfVW7rzzTubPn8+99957Qgd1SvU1xhge3fgoyZHJXDRCS8q+0tYSgVNELgWuBN7zjgtuZZ5sYFCD4TQgp4lpPjTGVBljCoHPgYmNF2SMWWqMmWaMmXa87r0na64bapvNVt8NNcA999zDrl27WLt2LcXFxdx3330Bilip7uGLo1+wpXALP53wU0LsHWt7U9/U1hLBVcC1wF3GmIMikgG80Mo8a4Hh3mmPAj/EahNo6G1gsYgEASHATOBvbQ2+Kb48c++MznZDDdQ/kCY0NJSrrrqKBx54wN9hK9VteYyHv2/8O2lRaVyYeWGgw+lV2lQi8F7pczOwwTt80BhzbyvzuIDrgI+AncCrxpjtInKtiFzrnWYn8CGwBVgDPGmM2dbRjelOOtsNNUBubi5gJZK33nqLcePG+TRGpXqS9w++z67iXVw3+TqCba1VSKj2aOtVQ+cDD2CdtWeIyCTgTmPMBS3NZ4x5H3i/0bgljYbvB+5vR8w9wqJFi7jwwguZMWMG8+fP71A31AsWLKCgoABjDJMmTWLJkiWtz6RUL+RwO1i8cTGj4kdxdsbZgQ6n12lTN9Qish74NrDMGDPZO26rMWa8n+P7Bu2G+pv6+var3u/FnS9y75p7eeK0J5idOjvQ4fRIvuiG2mWMKWs0Tq9xVEr5XaWjkic2P8HM5JnMSpkV6HB6pbY2Fm8TkcsAu4gMB34BfOW/sJRSyvLM9mcoqSvhl1N/iUhTV6WrzmprieB6YCxQB7wElAO/9FNMSikFQGFNIc/teI4z089kXKJeLOEvbSoRGGOqgVu9r27JGNMnzxb0LmTVmy3ZvASn28n1k68PdCi9WouJQEQeMsb8UkTepYk2gdauGuoqYWFhFBUVkZCQ0KeSgTGGoqIiwsL0NnvV+2SVZfH6nte5aMRFDOk3JNDh9GqtlQie97536zuZ0tLSyM7OpqCgINChdLmwsDDS0tICHYZSPvfX9X8l1B7KtROvDXQovV6LicAYs9773q2fExAcHHxClw1KqZ5tZc5Klh1Zxg1TbiAxPDHQ4fR6bb2hbCvfrBoqA9YBfzbGFPk6MKVU3+TyuPjL2r+QGpXKj8boIyi7QlsvH/0AcPN119M/xOpdtAx4Bjjf55EppfqkN/e+yb7SfTw490FC7drbbldoayKYY4yZ02B4q4isMMbMEZHL/RGYUqrvKXeUs3jjYqYOmMppg08LdDh9RlvvI4gSkZnHB0RkBnD8adEun0ellOqTntj8BKV1pdw8/eY+dQVgoLW1RPAT4GkROX7wrwB+IiKRwD1+iUwp1adklWXxr53/4rvDv8voBO07qyu19YaytcB4EYnB6qiutMHXr/ojMKVU3/LAugcIDQrVm8cCoE1VQyIyQESeAl42xpSKyBgRudrPsSml+ohPD3/K8uzlXDPhGr1cNADa2kbwDNYDZlK8w3vQvoaUUj5Q7azm3jX3khmbqZeLBkhbE0GiMeZVwAP1Tx9z+y0qpVSfsWTLEnKrcrntpNv0yWMB0tZEUCUiCXhvKhORk7DuIVBKqQ7bW7KX57c/z3czv8uUAVMCHU6f1darhn4FvAMME5EVQBJwsd+iUkr1eh7j4c+r/kxkSCQ3Tr0x0OH0aW1NBNuBbwEjse4o3k3bSxNKKfUNb+97mw35G7hz9p3EhcUFOpw+ra0H85XGGJcxZrsxZpsxxgms9GdgSqneq7S2lAfXP8jk/pO5MPPCQIfT57X2PIJkIBUIF5HJWKUBgH5AhJ9jU0r1Un9Z+xcqHBX84aQ/YBOtXAi01qqGzgQWAmnAgw3GVwC/91NMSqle7PPsz3n3wLtcM+EaRsSNCHQ4itafR/As8KyIfN8Y80YXxaSU6qUqHBXcsfIOMmMz+emEnwY6HOXV1i4m3hCRc7EeYB/WYPyd/gpMKdX7PLDuAQprCnl43sOE2EMCHY7yamsXE0uAS4DrsdoJLgb0IaJKqTb76uhXvLn3TRaOXci4xHGBDkc10NZWmtnGmCuAEmPMHcAsYJD/wlJK9SZldWXctuI2MmIy+Pmknwc6HNVIW+8jqPW+V4tIClAE6EOClVKtMsZw58o7Ka4t5u/z/65PHeuG2poI3hWRWOB+YANWVxP/8FdQSqne470D7/HxoY+5YcoNjEkYE+hwVBNaTQQiYgM+8T6D4A0ReQ8IM8ZoX0NKqRYdrTzKXavvYkr/KVw19qpAh6Oa0WobgTHGA/y1wXCdJgGlVGucHie3fH4LAHefcjd2mz3AEanmtLWx+GMR+b7oQ0SVUm30941/Z1PBJm6fdTupUamBDke1oD29j0YCLhGpxbqE1Bhj+vktMqVUj/V59uf8c9s/uXjExZyVcVagw1GtaOsNZdH+DkQp1TvkVeVx65e3MiJuBL+d/ttAh6PaoK03lH3SlnFKqb7N6XZy0/KbqHPX8cC3HiAsKKz1mVTAtZgIRCRMROKBRBGJE5F47yudr59f3NL8Z4nIbhHZJyK3tDDddBFxi8hF7d4CpVS3ce+ae9lcsJk759xJRozeatRTtFY19FOsh9SnAOsbjK8AHm1pRhGxe6c5HcgG1orIO8aYHU1Mdx/wUbsiV0p1K2/seYNX97zKj8f9mLPStV2gJ2mtaugrYDZwkzFmKHAHsA1YDvyrlXlnAPuMMQeMMQ7gZaCpJ1BcD7wB5LcncKVU97GlYAt3rb6L2Smz+cXkXwQ6HNVOrSWCJ4A6Y8zfReRU4B7gWawH1y9tZd5U4EiD4WzvuHoikgp8F1jS0oJE5BoRWSci6woKClpZrVKqK+VW5nLDZzfQP6I/951yn94v0AO1lgjsxphi7+dLgKXGmDeMMbcBma3M29Q9B6bR8EPAzcYYd0sLMsYsNcZMM8ZMS0pKamW1SqmuUumo5P99+v+oddWy+NuLiQ2LDXRIqgNaayOwi0iQMcYFzAeuace82ZzYQ2kakNNommnAy9771BKBc0TEZYx5q7XAlVKB5fK4+M3nv+FA6QEeO+0xMuNaOzdU3VVrB/OXgOUiUgjUAF8AiEgmVvVQS9YCw0UkAzgK/BC4rOEExpj6ywpE5BngPU0CSnV/xhjuXXMvXx79kj/O+iOzU2YHOiTVCa09qvIu7/0CA4GPjTHHq3ZsWI28Lc3rEpHrsK4GsgNPG2O2i8i13u9bbBdQSnVfT2x5gld2v8JVY6/i4hEXBzoc1Umt3llsjFnVxLg9bVm4MeZ94P1G45pMAMaYhW1ZplIqsF7d/SqPbnqUC4ZdwC+n/jLQ4SgfaGunc0opxcdZH/PnVX/mW2nf4vbZt2MTPYT0BvpXVEq1yfIjy7n5i5uZ1H8S93/rfoJtwYEOSfmIJgKlVKu+PPolNy67kVFxo3h0/qOEB4UHOiTlQ5oIlFItWpmzkhs+vYHM2EyWnL6E6BDtjLi30USglGrW59mfc/2n15Mek87S05cSExoT6JCUH2giUEo16eOsj7nhsxsYFjuMp854Su8a7sU0ESilvuHtfW/zm89/w/jE8Tx5xpOaBHq5tj6qUinVBxhjeHLrkzyy8RFOGngSD897mIjgiECHpfxME4FSCgCnx8ldq+7ijb1vcE7GOfzfnP8jxB4S6LBUF9BEoJSiylnFr5f9mhU5K1g0fhHXT74eb2eQqg/QRKBUH3es6hjXfXode0v2cvus2/n+iO8HOiTVxTQRKNWHrc1by03Lb7KeJzB/MSennhzokFQAaCJQqg8yxvD8jud5cP2DDIoexNNnPs2w2GGBDksFiCYCpfqYamc1f/rqT3yY9SHzB8/nz3P+TFRIVKDDUgGkiUCpPmRPyR5u/vxmDpQd4IYpN3D1uKu1UVhpIlCqL/AYDy/ufJGH1j9EVEgUj5/2uD5VTNXTRKBUL5dfnc8fvvwDK3NXMjdtLrfPvp2E8IRAh6W6EU0ESvVSxhg+PmQ9SKbWVcttJ93GxSMu1qog9Q2aCJTqhfKq8rhr9V0sO7KMsQljueeUe8iIyQh0WKqb0kSgVC/i9rh5ZfcrPLzhYTzGw03TbmLB6AUE2fS/umqe/jqU6iW2F23n7tV3s6VgC7NTZnPbSbeRFp0W6LBUD6CJQKkeLr86n0c2PMI7+98hLiyOu0++m/OGnqdtAarNNBEo1UPVump5bsdzPLn1SVweFwvHLWTR+EX6KEnVbpoIlOphnG4n/973b5ZuWcqx6mOcNvg0fjX1VwzqNyigcblKSnBkZeE6lo8rPx9XQYH1XlqCqa7BU12NcTrBZkNsNiQ4GFtsDEGxsdjjEwgZMoSQ9HRChmYQ3L9/QLelr9FEoFQP4fK4eHf/uzyx5QmOVh5lYtJE7jnlHqYnT+/SONzl5dTu3EXtjh3U7d2L4+BBHAcP4i4tPXHC4GCCEhMJiovDFhGBPTEBW0gIxmPA7cY4HLgLi3Ds3YerqAhTV1c/a9DAgURMnkz4tKlEz51LcEpKl25jXyPGmEDH0C7Tpk0z69atC3QYSnUZh9vBewfe46mtT3G44jBjE8Zy3eTrmJMyx+/tAO7KKmq3bKZm6zZqd+ygdudOnIcP139vT0okND2DkAzvK30IwSkpBCUlYY+NRWxtexqu8XhwHTuGIyuLur17qd64kZr1G3Dl5wMQNm4c0WeeQcyFF2ppoYNEZL0xZlqT32kiUKp7Kqsr47U9r/HizhcprClkVPwofj7x58wdNNdvCcCZl0fNhg1Ur99A9cYN1O3aDR4PAMGDBhE2ZszXr7FjCIqP90scYN0Q58jKouK//6Pi44+p3bYNgoLod8YZxF2+gPDJk7VBvB00ESjVgxwqP8TLu17mzb1vUu2qZtbAWSwct5BZA2f59MBnPB7q9u6jZsN6qtdvoGbDBpw5OQBIeDjhEycSMWUy4ZOnED5hPPaYGJ+tuyMcWVmUvPQypW++iaeigojp00n61Y1ETJ4c0Lh6Ck0ESnVzTo+TZUeW8cruV1idu5ogCeLMjDNZOHYho+JH+WQdxu2mdtcuqteupXrtOmrWrcNdVgZAUFIS4VOn1h/4w0aNRIKDfbJeX/NUV1P6+hsULl2Ku7CQqHnz6P+b3xA6VO+cbokmAqW6qQNlB3hv/3u8te8tCmoKGBg5kItGXMR3M79LUkRSp5ZtnE5qd+yoP/BXb9iAp6ICgODBg4mYPo2I6dOJmDaN4NTUHlfN4qmupvi55yl68kmMw0Hiz64l4eqrkZCQQIfWLWkiUKobKaop4sOsD3l3/7tsL9qOTWzMSZnDJSMv4eTUk7Hb7B1arnE4qNm2jeo1a62D/8aNmOpqAEIyMqyD/vTpRMyYTvCAAb7cpIByFRSQd/fdVHzwISGZw0i5517Cx48LdFjdjiYCpQLsWNUxPj3yKZ8c/oR1eetwGzej40dz3tDzOGfoOSSGJ7Z7mZ66Omo2b/66qmfTJkxtLQChwzO/PvBPm0ZQUudKFz1BxWefkXfHnbiKiuj/618Rf+WVPa6U40+aCJQKgEPlh/jk8Cd8cugTthRuASC9XzqnDTmNczLOYXjc8HYtz1VQYF1WuXETNRs2ULNjBzidIELoyJHeA79V3RMUF+ePTer23KWl5Nz6Byo/+YSoefNIuedu7LGxgQ6rW9BEoFQXqHBUsCZvDStzVrIyZyWHK6zr7cckjOG0wacxf/B8hsYObdOyjNtN3d691GzcSPWGjdRs3IgzOxsACQkhbNw4q2F3yhQipk4N+BU93YkxhpLnX+DY/fcTPHAgg5Y8TujQtu333ixgiUBEzgIeBuzAk8aYext9vwC42TtYCfzMGLO5pWVqIlDdRY2rhm2F21iXt46vcr5ia+FW3MZNRFAE05OnMytlFvMGzSMlquW7Yo3HgyMri9rt26ndto2a7dup3bGzvn7fnpRIxOQphE+eTMTkSYSOGYNNG0RbVb1xI9nXXY9xOEh7+CEiZ/ftR3MGJBGIiB3YA5wOZANrgUuNMTsaTDMb2GmMKRGRs4HbjTEzW1quJgIVKIU1hWzM32i9jm1kV/EuXMaFIIxLHMdJA09idspsJiZNJNje9KWXxu3Gcfgwtdt3ULttm3Xw37EDT1UVABIaStioUYSNHUv45EmET57cI6/o6S4c2UfJ/tnPqDtwgIF33E7sRRcFOqSAaSkR+LOvoRnAPmPMAW8QLwMXAvWJwBjzVYPpVwHaebrqFgprCtlZtJMdRTvYWWy951blAhBqD2Vc4jgWjlvI5P6TmZg0kZjQE6tmjDG4Cgqo27OXuj17qNvrfd+/v75BV0JCCB09ipgLLyBs7DjCxo0ldNgwJEi7APOVkLRUhrz0L47+8kZy/3Ab7vIKEn58VaDD6nb8+YtLBY40GM4GWjrbvxr4wI/xKPUNlY5KDpQdYH/p/vr33SW7ya/Or59mSL8hTEqaxILRC5jUfxJj4sfUn/F7HA6chw9TkbUWx6FDVl85Bw/i2Lf/hE7Y7ImJhI0YTtwllxA6YjhhY70H/W5601ZvYo+KYtBjj3L05pvJ/8tfcFeUk/SLX2gpqwF/JoKm9nKT9VAiMg8rEZzczPfXANcADB482FfxqT7C4XaQU5lDdmU2RyqOcLj8cP1B/1j1sfrpQmwhZMRkMD15OmPixzA6YTSj40cTXuvBmZNjvdZvoejweziysnBkZVldMnj74gGwJyQQkp5O9OmnEzpiBKHDhxM6Yrhf++RRrZOQEFIfeIC8qCiKHl+Cp6qKAb/7nSYDL38mgmygYQfpaUBO44lEZALwJHC2MaaoqQUZY5YCS8FqI/B9qKonq3RUkl+dT151HvnV+RyrOsbRyqNkV2aTXZFNXlUepsE5SJg9rP6APzxsMMPc8Qx2RBNXYXDnHcO5OQfn0ZU4c97gaE4OnsrKE9Zni4ggJD2d8AkTiLngAkIy0q1+9IcMwd6vX4e2wRiD2+nBUevGWefGWeeyPnuHXU43HpfB7fLUvzxuax6P24CAdUyT+s8iQlCIjeBQO8GhdoJC7PWfw6KCiegXQlhEMGLrGwdDsdtJvvNObBERFD/7HCI2+t9ysyYD/JsI1gLDRSQDOAr8ELis4QQiMhh4E/iRMWaPH2NRPUydu46S2hKKa4spqS2hpK6kfji/Op9j1cfqD/rVruqvZzSGcAcMNnFkkMRkzyBSnCPpXx1MbBVElNVhLy7HXViIq+C/9Y20tUCudxG26GiCU1IITk0lYvp07+cU6z0lBXtCQv3BwxiDy+HBUeOirMqFo6gMR40LR40bR60LR42Luhrr3VHr9n53/CDv8h703Thq3VY//e0kNsFm/zoWDHD8rQ3LE5sQHhVMZGwo/RLC6JcUTr/EcGKSwolLjiQyNqRXHShFhP633IJxeyh+9lkkOIikX/+6V21jR/gtERhjXCJyHfAR1uWjTxtjtovItd7vlwB/BBKAx7x/CFdzrdqq53G6nVQ4K6hwVFDpqKTcUU6ls5IKR0X96/hwaV1p/YG+vKoYqqoJr4OIOgh3QESdIaIOIh02Ej0RDHWFE+8IJqY2lsjqfoRVOQmurEXKq8DlAgq9r6/ZIiIgKQmSkrCPGot9zgCITcTEJGCi4/BE9oOoWNy2EKrr3NYB/PjBO8eFY78LR+1h6moOnHBAb8sBNyTMTkh4kPUKsxMWEUR0fKh1hh4WREioneAwO8Gh1vfBYXZCQoO84+wEhdiw2W3Yg2zYgwR7kA1bkA1bC2fzx0sZx5ON0+F9r3VTW+mkutxBTYWD6goHVaV1FOVUcXBrIR5Xg9JTVDCJaVEkDoomaVAUAzNjiY4P6+hPolsQEQbc+nuM20XRk09BcDD9b7gh0GEFlN5Q1scYY3B4HDjc1svpceJwO6hz1+HwOHC6reHj09S6aqlx1VBTV0VdbSV1NVU46qqoq6vGUVuFs64aV20Nrrpa3LU1mJpaqKvD1NQiDiehTgh1QojL1H+uH+eECLeNUJedcJedUIed4DobYmx4bCF4bEF4bMG4bcF4jr/s3vfgUExkPwiPwoRHYcIiMaHheILDrJc9BJeE4MaOy9hxuQWn01jVLA53M61V3yQ2ISTcTmj9Qdz7Hm4ntP7z1+NCwoK+nvb4K9TeY6pfPB5DVWkd5QU1FOVUUZhdQeGRSopzqnC7rLaQ6IQwUofHkjIilrRR8T02MRiPh7w//YnS115nwO9/R/wVVwQ6JL8K1OWj3Upx4TFyD+3BbdwYt8HjcePxWGdzHrcb43FjjMHj8WA8bjwuNx5jwOPBeDx4jLHGewzGO854DB7jwbg9gMHjcmOMB7zLwQPGeKzPxvrhGQPGWOs1xlqWx+32fnZ71+MBtzVs3G5r2LtePMdjMuC2lifW6sFtvOsEvO2XxuOtJ/AYMIIYAWwIgs0j2LzjbMaGzYAYG4Ktfrw1LIQihIiNaAQjgpEQjIRhJAkjNjxix9jsGLFhsNV/9ogNI3brZbdhguy4Iu04xYYRGwXYaNt1BU0dub8eZ/PYsDsFu8dgc9cRFOwkKLgGe4iN4GAbYcE2goJtBIVYZ9XWZztBwYI92HoPCrZj874HBdsICrVht9us+nabDZvdjs0eZL3bbNiCgrDZ7N7x1kvsdux2O/bgYGz2oB5X5WCzCdHxYUTHh5E68utuKtxuD8VHq8jZW0rO3lKythaxa1UeAEmDo8mYmMjQSUnEp0T2mG0Wm43k22/HXVrGsbvvwR4XR8z55wc6rIDoMyWCZ274BUV5B/wQkVJNE5uN4NBQgkJCT3z3fg4JCycsKoqwyChCI6MIi4r2DlvvkbFxhPfrh62DvZH6k/EYinOrOLS9iIObCsk7WAYG+iWGMWJGMqNmDSQmKTzQYbaJp66OI4uuoXrDBgY99ihRp54a6JD8QvsaAl5/bDE5q9Y3+Z1p8O/xs1MRb+ObeMc0c5Lz9egT92P9WZF4z8gbzS/el80m1jtWNYRgsImATRABm81aVsN3m03qX3YBsUGQDWxisItgsxlsNggSsNsEu81ajk2MtV6xWhSlwbD12Vhnv432jpwQdYPxUv+x/is5YT9YpRexikPel0HwfD3snQbvODENpsWqwhHjAeOunx88iMcNHpf1cjvB42y07saxNNr/jf+etmAkOBSCwiE4DILCICQKCYvGhFgvT3AknuAoPEER3lc4JjgKt9gxbqtk53G7cLvduJ1OXI46nHV1uOrqrM8O6/Px97qaGuqqKqmtrMDjdjcdp81GZGwcUXHxRMYlEBUXT7+k/sQlpxCbPJDYAQMJDgt81UxVWR1ZWwrZvyGfI7tKwEDqyDhGzx7IsMlJBIV0v2TWkLuykkNXXIHjwEEG//PpXvnUM00EbWCMwaptMbg9BpfHU//ZGv7mZ5fHg8dD/bQuj8HjMTg9BqfLg9PtweH2UHf8c4N3h9ucMHz8vc7twemy5nO4rHlrHG5qnW6qHW5qnNbL4fK0vlENhAXbiA4LJjo0iKiwIKLDgogKDSIqNJho73B0WBCxESHERYQQFxHs/Wy923tCHbfbBe46cDvA5bDej79c3vHOGnBUgbMaHJXW58YvZxXUVUJNifdVDLVlza83NAb6DYTogdAvxfs+EPqlQlwGxKVbyaUZxhicdbXUVlZQW1lpvaoqqC4tpbKkmMqSIqpKiq3PxUXUVlacMH9kXDyxAwYSn5pG0pAMkgankzQkg9CISB/t2PapKK5l96pcdn6VS3lhLaERQYw7NZXx89KIjAkNSExt4SosJGvBAtylZaS/+AKhmZmBDsmnNBH0Qm6PodabFGocjd6dbmodbirrXNar1kVFnYuKWmu4otZpjWs4XOeiuYtfRKBfWPAJySEhKpSk6FD6Rx9/D6v/HBnaC5ue3C4rGdQUQ3WxlSCqi6DyGFTkQnmO9z3XGmcanuGLlRTiMyB+qPXqPwYGjLUSRzvr1OuqqyjNy6X0WC6lebmU5OVQmpdLUfbhE5JEv6QBJGeOIGX4KFJGjCIpfShBXXgns/EYcvaWsmVZNgc2FWC32xg5cwCTTh9MXHJgklRrHNnZZF16KRIUTPrLL/WqB/hoIlCtMsZQWeeitNpJSbWDkmonpdUOiqu+/txwXHGVg4KKOlxNZI/IEDtJ0aEM6BdGamw4qXHhpMSGf/05Jpzwbl5V0CkeN1TmQ/lRKD4IxQdOfFU3uKw1LBYGjIMB3sSQOtVKEh1oFzDGUFlSRMGhgxQcyiI/6wC5e3dRUVgAgD04mORhwxk8bhJDxk8iOXME9i7q16j0WDWbPjnCrpW5uJ0eMqf2Z+YFQ4kdENEl62+P2h07OHT5jwgeNIghLzyPPTo60CH5hCYC5Rcej6Gk2kFBZR355XUUVNSRX3H8vZZj5bXklNaSW1bzjdJGQmQIqXFWckhPjCQjIZKMpEjSEyJJjOpdNzF9Q00J5O+EY9vh2DY4tgPyd1hVVQAhUZA6BQbNhLQZkDYNIjreRUVlcRE5e3eRs2cX2Tu2cezgPjCGkPBw0saMZ+jk6WROP4nIWP8/zKa63MGWz46w+dNs3E4Po+cMZPo5GUTFda8qo8oVKzjy02uJmDqVQf9Y2iu6/dZEoALK5faQ500KR0urySmtJbukhpzSGo6UVHOkuBqn++vfYVRoEOmJEWQkRjEsKZKRA6IZmRzNkITIntFW0REeD5QchKPr4chqOLLGShTHq5j6j4Vh82DoXBgyG0I6XrVSU1nBke1bOLRlI4e2bKQs/xiIMHD4SDKnncTwmbOJS275GQqdVV3uYN0HWWz//ChiEybMTWPaOemEhHefasWyd94h57c30+/cc0m5/y+IzRbokDpFE4Hq1lxuDzmltRworCSrsIqsomoOFFZxsLCS7JIajv9EQ4NsZPaPYmRyNCMHRDMiOZpxKTEkRXevs0mfcVTB0Q1WYji4HA6vshq8bcFWaWHkWTDyHEgY1uFVGGMoOnKIvWtXsm/tKvIP7gcgOXMEY06Zx8jZpxLRz39PPysvrGHNewfZvTqPiOgQ5lyUyfDpA7pNibDoySfJf+CvxF91FQNu/m2gw+kUTQSqx6pxuNmXX8muvHL2HKtgV14Fe45VcKy8rn6alJgwxqfFMCEtlglpMUxIjSUmohd27+yohiOrYP9nsO8TyN9ujU8cCSPPhtHnW20MnTiIlhfms2fll+z44jMKDh3EZreTPmkq4+adzrApM7DZ/dO2cyyrnM9f2k3+oQpShsdy6qUjSEiJ8su62sMYw7G77qbkhRfof8vNJCxcGOiQOkwTgep1Sqsd7MqrYNvRMrZkl7Elu5Ssoq87nxuSEMHEtFimp8cxIyOB4f2jWuyXp0cqyYLdH8Lu9+HQCuueitghMO771mvA2E4lhYLDWez4/FN2fbmMypJiohISmTD/TMZ/+0yi4nzfrbbHY9i5IoeVb+3HWeNm4mmDmHFeRsDvQTBuN0dv/BUVH39M6oN/pd855wQ0no7SRKD6hLJqJ1uPlrHlaClbs8vYcLikvuQQEx7M9PQ4pqfHMyMjnnGpMQTbe3ad7wlqSmDX+7DtDTiwzGpbSBoFky6DiZdCVP8OL9rjdnNgw1o2ffwfDm3ZiM1uJ3PGbKad+x0GDh/pu23wqql0sPLf+9m5IpfYARF8+4rRDBzmv+qptvDU1XH46qup3byFQU8+SeTMGQGNpyM0Eag+yRhDdkkNqw8Ws/ZgMWuzijlQaHU7HR5sZ1p6HKcOT+LUEUmMGBDVbeqlO62qEHa8DVtetaqSbEEw4iyYcgUMmw/2jjfIluQeZfP/PmTbZx9TV1VF6qixTL/g+wydPM3njalHdhbz2fO7qCipZeK8Qcz8zlCCA1g6cJeVkbVgAa5j+Qx54QXCRo4IWCwdoYlAKa/8ilrWZZWw5mAxX+4rZF++dcnmgH6hnOJNCidnJhIf2fMvFwSgYA9sfB42vwRVBRCdYpUSpi6E2EGtzt4cR001Wz/9L+vff4uKwgLiUwcx48KLGH3yXJ+2IzhqXaz89362LT9Kv6RwTls4JqClA2dODlmXWo9VSX/5JYIHDgxYLO2liUCpZuSU1vDF3gI+31PIl/sKKatxIgLjU2M4bfQAzhg7gJEDont+acHthD0fwobnYN//AIHR58HMn8HgkzrcluB2udiz8gvWvvsmBYcOEps8kFkXXcaoOaf6tLO8o7tL+OS5nVQW1zLtnHSmnZOOLUBVe7W793BowQKCByYz5IUXsMcEttqqrTQRKNUGbo9hS3YpX+wtZNnufDYeKcUYGBwfwRljBnDG2GSmDonr+fcylB6Btf+A9c9CbSkMnAgzr7UamIM6dimuMYb961bz1WsvUnDoIHEpacy66FJGzjrZZwnBUePi81f2sHtVHgMy+nH6j8cQkxSYO5OrVq3myKJFhE+cyKCnnsQW2v0vYdZEoFQH5FfU8snOfD7enseKfUU43B4SIkOYP7o/Z45N5pThSYQE9eAGZ0cVbHkFVj8BBbsgMglmXAMzFkF4x+4yNh4P+9au4qvXXqTwyCES0gYz++LLGD5zjs9KVXvXHWPZi7sxHsMpl4xg1KzkgJTYyt9/n6O/+jXRZ55J6oN/Rfx0aa2vaCJQqpMq61ws313AR9vz+GxXPhV1LmLCgzl7XDIXTExh5tCEnltSMAYOfAarHoe9H1tdXExdCLP+n9UpXkcW6fGwZ/UKvnrtXxQfPUJy5gi+dfmPSRs9zichVxTX8r9/7iBnbynDpiQxd8EowiK7/t6RomeeIf/e+4i7/HIG3Pr7bl2FqIlAKR9yuDys2FfIO5tz+Hh7HlUON0nRoZw7fiAXTEph8qDYbn1AaFHeNljxsHUZqthg4g9hzg2QOLxDi/N43OxY/ikrXn2ByuIihk07iVMuu5KE1I43VH+9bMOm/x5m9dsHiIgJ4bSFY054qlpXOXbvfRQ/8wz9b/o1CT/5SZevv600ESjlJzUON5/uyufdzTl8ujsfh8tDWlw435mUyvenppGR2D27W25VSRZ8tdi64shVZ921fPKNVmd4HeCsq2XD+++w5u3XcNbVMWH+mcy66DKfdHSXf6icj5/aTllBDVPOGMKMCzKwd2FDsvF4yLnpN5S//z4D/ngb8Zdd1mXrbg9NBEp1gfJaJx9vP8Y7m3P4cm8BHgPThsRx0dQ0zp0wkOiwHtjtRWUBrF4Ca/4BdWUwdB6cehMMmdOhK42qy8tY+fpLbPnfB9iDgpl+wfeZdt53O/2UNUetiy9f28vOFbn0HxLN6VePJbZ/1zUkG4eD7F/eSOWnn5L8pz8Sd+mlXbbuttJEoFQXO1Zey783HuW1dUfYX1BFWLCNs8Ymc9HUQcweltDzuruoLYd1T8PKR6Eq3+r07pSbYPjpHUoIJblH+eKlZ9m7+isi4+KZ84PLGTt3fqevMNq/IZ/PXtiF22049ZLhjJo1sMuq6bp7MtBEoFSAGGPYnF3G6+uP8M6mHMprXaTEhPG9KWk9s+rIWQMbX7DaEcqOQPJ4OOXXMPqCDj1M5+junSx/4Sly9+wicXA631pwFemTpnYqxIriWj55ZgdH95QybEp/5i4Y2WUNycbhIPuGX1L52Wf0/81NJFx9dZesty00ESjVDdQ63fxv5zFeX5/N53usqqPp6XFcPHUQ50wYSFRPesSn2wlbX4MvHoSivZAw3GpDmPADsLfvoGuMYc+qFXzx0jOUHcsjfeIUTr38xyQNTu9weB6PYePHh1jzzkEiYkI4/cdjSBneNQ3JxuEg55ZbKH//A+Kv/jH9b7qpW1w8oIlAqW4mr+zrqqMDhVVEhNg5e9xALp6WxsyM+G5x4GgTjxt2vgtfPAB5WyFmkHWV0eTLITi8XYtyOZ1s/vg/rHrjZeqqqxk79zTm/GABUfEJHQ7vWFY5/31qO+WFNUw+YzDTz8sgKNj/1/sbt5tjd91Fyb9eIuZ732PgHbcjXfi86KZoIlCqmzLGsOFwCa+ty+a9LblU1rkYHB/BRVOtqqPU2PYdTAPGGKvris8fsDq6i+xv3Ycw7ccQ1q9di6qprGD1m6+w8cP3sAXZmX7+95h2/vcICevYvnDUuljx2l52dHFvpsYYChc/SuGjjxIxcyapD/2NoLiuv7z1OE0ESvUA1Q4XH27L47V12aw8UIQIzBmWyMXT0jhzbDJhXXAm22nGWM9G+OKvsP9TCIuxuq+YeW27n7tcmpfLFy89y55VXxIZG8fsHyxg3NzTO9yp3eEdRXz2wi4qS+qY+O1BzLywa3ozLXv7bXJv+yNB/fuT9tijhI0ITK+lmgiU6mGOFFfz+vpsXl+fzdHSGqLDgjh/YgoXT01jUk+5Ye3oeqsNYdd7EBwJ066CWddBv/b12JmzZyfLnrcalOMGpjDr+5cysoOd2jXuzfTUS0YwZFzHq57aqmbzZrKvux5PVRXJt/+JmAsu8Ps6G9NEoFQP5fEYVh0o4rX12XywLZdap4fh/aO4aGoa352SSv/ozl1/3yXyd8KXf4Otr1t3K4/9rtWnUdq0Nl96aoxh37pVrHz1RQoOZxGfOojZF1/GiJlzOvQchKN7Slj24m5Kj1WTMTGRky8eTr9E/1bDOY8d4+ivfk3N+vX0O+88kv/0R+zR0X5dZ0OaCJTqBcprnfxnSy6vrTvChsOl2G3CyZmJnDdhIGeMTSYmvJvfsFZ80Lo5beOL4KiAlMlWQhj7PQhuW0IzHg9713zFV6/9i6LswySkDWba+d9j1JxvEdTOxli3y8PmT46w9v0sjMcwYV4aU84c4tdLTY3LReHSpRQ++hjByckk33EHUSfP8dv6GtJEoFQvsy+/ktfXZ/Pu5hyOltYQbBdOHZ7EuRMGcvqYAd37Lua6CqvX0zX/sHo9jUiwnp426XJIzGzTIjweN7tXfsnat16j4HAWkXHxTDn7AiacdhZhke176H1lSS0r39rPnjXHCA0PYsqZQxg/N43gUP+1H1Rv3EjuLb/DcegQ0WefxYBbbiF4wAC/rQ80ESjVax2/Ye29zTn8Z2suuWW1hATZOCUzkXmj+vPtUf1J6a5XHhkDBz+HNUth9/tgPJA23XrG8rjvtakrbGMMh7ZsZN17/+bQlo0Eh4Uz5pS5jJt3BgOGZrarLaUwu5JVb+3n0LYiQiODmDBvEBPmpfmthOCpq6PoqacoemIpYrcTf9VVxF95BfZ+7bvKqq00ESjVB3g8ho1HSnlvSw7/23mMI8U1AIxKjq5PCpMHxRIUoCd7tag8F7a+CptegoKdYA+BzNOtp6iNOKtNVxzlZx1g/X/eYs+qFbgcdSQNTmfct89g9CnzCI9qe1183oEy1n94iKwthQSF2hk5YwBjT0klabB/6vMdR46Q/5f7qfjvf7H160f8wiuJv+wy7LGxPl2PJgKl+hhjDPsLKvl0Vz6f7spnXVYJLo8hOiyI6enxzMyIZ0ZGPONSYwjuTonBGMjdDJtfhh1vQ0UOiB3S58Co86xO7xKHt9jIXFddxa4Vy9n66cccO7APmz2IweMnMnzGbDKnn0REv7bdQ1B0tJJN/zvMvnX5uJwe+g+JZsTMZIZN7k9UnO+fSFa7cycFix+l8pNPkNBQ+p11FrE/vITwSZN8cpWYJgKl+rjyWidfeJ/LvPpgEQcKqgCICLEzPjWGCWkxjE+LZUJqDEMSIrrH5anGQM4G2Pke7PoPFO62xkclQ/rJkHEKDJ4NCZnQzJVD+VkH2PnlMvau+YqyY3kgwoCMTNInTmbwuEkkZw5v9Ua1umonu1fnsePLXIqOVgIwcFgMQ8YnMGh0PImDon3aiWDt7j2UvPwS5W+/g6e6muBBg4g+7TSiTz+d8EkTO3SVFAQwEYjIWcDDgB140hhzb6Pvxfv9OUA1sNAYs6GlZWoiUKrz8itqWXOwmDUHi9mcXcbO3HIcLg8A0aFBDO0fRWZSFMP6R5KZFEV6YiQpseGB7Q+paD9kfWG1Kxz8wuoFFawnqiWPt569nDwBEkdA/FCrOsmb0IwxFBw6yP51qzm0dSM5e3ZhPB5EbCSkDSI5cwTJw0aQNCSDuIEphEc3XU9fklfF/g357N9YQOERKymERgaRPDSG/kP60X9INAmpUUTFhiKdTA7uyioqPvyA8o8+pmrVKnA6ibv8cpL/cGuHlheQRCAidmAPcDqQDawFLjXG7GgwzTnA9ViJYCbwsDFmZkvL1USglO853R72HKtga3YZO3LL2V9Qyb78So6V150wXb+wIFJiw0mNDSc+MoT4yBDiIkOIj7De4yKCiQgJIjzETkSInbBgO+HBdoLt4ttShjFQuAey11pVSblbrL6OnFVfTxPaD+IzIHYIRA3wvpIgagB1JoyjRwvJzT5G3uGj5GVlUVtZUT9rWGQUsckDiU1OISo+gYiYWCJjYomIiSU8uh8h4eG4nHYKjtSSu6+K/EOVFOdWgfdwag+2EZMUTmz/CPolhRPRL4SI6GDCo0MIjw4hNCKI4FA7QSF2gkJsre4bd0UFlcs/J2TIYMLHj+/QLgtUIpgF3G6MOdM7/DsAY8w9DaZ5AlhmjHnJO7wbmGuMyW1uuZoIlOo6FbVO9hdUcaS4mpzSGo6W1pBTWkNOaS0l1Q6Kqhz1JYmW2G1CRLCd0GAbNhHstgavBsO2Ez43vaymDpoC2IybZHcuA93ZJLtyGejJZYArl/7uPGI8pUSZymbjMwaKnREcc8RQ7AinzBFGmSOMckcINS47HtNydYxdDDabQbBjsAFBGOx4CMYQhFUpIkDj5Yh3mwyCh+OZpH4LxTSY0hCXNpgf3Xtni7E0p6VE4M9yXipwpMFwNtZZf2vTpAInJAIRuQa4xjtY6U0YMUBZo+U1Htd4OBEobPsmdEpT8flj3tamben75r7Tfdu2aXXfdnzebrhvy4G8FkLqlM7s1xPmv+K+/+vouoY0O4cxxi8v4GKsdoHjwz8C/t5omv8AJzcY/gSY2sblL21tXBPD6/y1vW2Jzx/ztjZtS983953uW923um+7z3719b5t6uXP68aygUENhtOAnA5M05x32zCuqWm6SmfW3Z55W5u2pe+b+073bdum1X3b8Xn72r7t7Hp9uW+/wZ9tBEFYjcXzgaNYjcWXGWO2N5jmXOA6vm4sfsQYM8MvAVnrW2eaqSNTnaP71n903/qP7luL39oIjDEuEbkO+AirpeRpY8x2EbnW+/0S4H2sJLAP6/LRq/wVj9dSPy+/L9N96z+6b/1H9y098IYypZRSvtWN7i1XSikVCJoIlFKqj9NEoJRSfZwmAi8RGSoiT4nI64GOpTcQkUgReVZE/iEiCwIdT2+iv1X/EZHveH+zb4vIGYGOp6v0ikQgIk+LSL6IbGs0/iwR2S0i+0TklpaWYYw5YIy52r+R9mzt3M/fA143xiwCuv5J3T1Me/at/lbbp5379i3vb3YhcEkAwg2IXpEIgGeAsxqO8HZ69yhwNjAGuFRExojIeBF5r9Grf9eH3CM9Qxv3M9bNgce7D3F3YYw91TO0fd+q9nmG9u/bP3i/7xMC2Kes7xhjPheR9EajZwD7jDEHAETkZeBCY3V6d14Xh9grtGc/Y901ngZsoveccPhNO/ftDlSbtWffishO4F7gA9NKl/i9SW/+D9pch3ZNEpEEEVkCTD7eU6pqk+b285vA90XkcQLbZUJP1uS+1d+qTzT3u70eOA246PjNr31BrygRNKOpTmybvXvOGFME9Jk/vA81uZ+NMVX4/07x3q65fau/1c5rbt8+AjzS1cEEWm8uEXSmQzvVdrqf/Uf3rf/ovm2gNyeCtcBwEckQkRDgh8A7AY6pN9L97D+6b/1H920DvSIRiMhLwEpgpIhki8jVxhgXVs+mHwE7gVcb9nyq2k/3s//ovvUf3bet007nlFKqj+sVJQKllFIdp4lAKaX6OE0ESinVx2kiUEqpPk4TgVJK9XGaCJRSqo/TRKCUUn2cJgKllOrjNBEo5QPe51wcEpGfBToWpdpLE4FSPmCM2YrVX80VgY5FqfbSRKCU7+QDYwMdhFLtpYlAKd+5FwgVkSGBDkSp9tBEoJQPiMhZQCTwH7RUoHoYTQRKdZKIhAF/AX4ObAXGBTYipdpHE4FSnfcH4DljTBaaCFQPpIlAqU4QkZHA6cBD3lGaCFSPow+mUUqpPk5LBEop1cdpIlBKqT5OE4FSSvVxmgiUUqqP00SglFJ9nCYCpZTq4zQRKKVUH6eJQCml+rj/D3JApF0iHhxyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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O7hfH347vvHtOz507l2XLljF48GBmzZrFokWLWL58Of369WPixIl89913jBw5koSEBBz+A0hZWVls2bJH9/FWSnWxppUryT/3PBBh4D9fInJMt7x3vdYIQiEvL2+H0z3z8vLIysrCZrORm5vLxo0baek+EXpgWKmeo3n9evLPOx8JD2fQq//qtkkAemGNoDP33PeEw+HA5/MB1vn+Ltcv9+COjo7eYdrwgLZCu92Ox+MhJSWFqqoqPB4PDoeDgoIC+vXb4X7fSqluylVQYNUEbDYGvvB8tzgzqC1aIwiSQYMGsWDBAgDee+893G73Ls0vIhx++OHbjzO89NJLnHjiiZ0ep1Kqc7mLS8g/51x8TU0MfO45wnvAxZ6aCIJk+vTpzJ49m7y8PObMmfOrWkBH3HvvvTzwwAMMGzaM8vJyzj///CBEqpTqLL7GRgouvhhPRQUDn3maiBFd21XE7graPYuDpaX7EaxYsYJRo0aFKKLQ6+ufX6nuwPh8bLnyKmq/+IKsJx4n9vDDQx3SDkRkgTFmQkvjtEaglFKdoPThR6j9/HPSbri+2yWB9mgiUEqpPVT9wYeUP/UUCaedRtLZZ4c6nF2miUAppfZA89q1bL3lFiIn7EvGX2/ukad5ayJQSqnd5GtooODKK7FFRdF/5gNID70vSK+7jkAppbqCMYatt96Ka916Bj7/HGHpaaEOabdpjUAppXZD9dtvU/P+B6RcegnRBx4Y6nD2iCaCTlBeXk5ubi65ublkZGTQv3//7cOBVxTvqscee4xhw4YhIpSVlXVixEqpPeHatImiu+4m6oADSLnoolCHs8e0aagTbOuGGuDWW28lJiaGa6+9tt35vF4vdru91fETJ07kuOOOY9KkSZ0UqVJqTxmPh8Lrb0AcDvrdczfSxn+4p9AaQZDsaTfUAOPGjWNQN++jRKm+pvyZZ2hcsoSMW24hLCMj1OF0it5XI/jkRiha2rnLzNgLjrmn0xbXkW6oDz744E5bn1KqczQuXUbp408Qd+yxxB93bKjD6TRaIwiBjnRDrZTqXozLxdabbsKRnEzGLX8NdTidqvfVCDpxz31P7Gk31Eqp7qX8uedoXrOGrCeewB4fH+pwOpXWCIJkT7uhVkp1H83r11P2xD+Im3oMsUf0rH6EOkITQZB0RjfUjzzyCFlZWRQUFLD33ntzwQUXBCFSpVRbjM/H1r/egkRFkX7TTaEOJyi0G+peoK9/fqWCqfL11ym69TYy77qLhJNPCnU4u027oVZKqd3gLi6mZMb9RB14APEn/TbU4QSNJgKllGqBMYai227HeL1k3nZbj+xVtKM0ESilVAvqvvqKuq++IvWyS3EOHBjqcIJKE4FSSu3E19RE8V13E54zjKSzzgp1OEHX+64jUEqpPVT+zLO4t2xh4Esv9dh7DOwKrREopVQA1+bNlD/zDHFTpxK9f16ow+kSWiPoBOXl5UyePBmAoqIi7HY7qampgNWvkNPp3K3lTps2jfnz5xMWFkZeXh5PPfUUYX1g70SpUCq++x5wOEi74fpQh9JlglojEJEpIrJKRNaKyI0tjI8XkQ9EZImILBeRc4MZT7Bs64Z68eLFXHTRRVx11VXbh9tKAl6vt83lTps2jZUrV7J06VIaGxt59tlnOzt0pVSAutmzrQPEF/8fYenpoQ6nywQtEYiIHXgcOAYYDZwhIqN3muwS4GdjzD7AJGCmiOze7nM30xndUE+dOhURQUTIy8ujoKAgJJ9Fqb7A53JRdNddOAcP7hMHiAMFs2koD1hrjFkPICKvAycCPwdMY4BYsU7QjQEqgD3qce3eufeysmLlniziV0YmjeSGvBs6bXm72g212+3m5Zdf5uGHH+60GJRSO6p4/gXcm/IZ8NyzyG425/ZUwWwa6g9sDhgu8L8X6DFgFFAILAWuMMb4dl6QiFwoIvNFZH5paWmw4u0yu9oN9cUXX8yhhx7KIYcc0sWRKtU3uItLKHv6aWKPPJKYiRNDHU6XC2aNoKXL8Hbu2OhoYDFwBDAU+EJEvjXG1OwwkzFPA0+D1ddQWyvtzD33PdFZ3VDfdtttlJaW8tRTTwU5YqX6rtKHHwa3m7Tr2r/FbG8UzBpBATAgYDgLa88/0LnAO8ayFtgAjAxiTF2mM7qhfvbZZ/nss8947bXXsNn0TF+lgqHp55+p/s9/SPzjH3v9FcStCebWZR6QIyKD/QeATwfe32mafGAygIikAyOA9UGMqct0RjfUF110EcXFxRx44IHk5uZy++23ByFSpfouYwzF99yLPSGBlIv+FOpwQiao3VCLyFTgIcAOPG+MuVNELgIwxjwpIv2AF4FMrKake4wxr7S1TO2G+tf6+udXanfV/ve/FFx6Gem3/JWkM88MdThB1VY31EG9oMwY8zHw8U7vPRnwuhA4KpgxKKVUS4zLRfGMGTiHDiXxtNNCHU5I6ZXFSqk+qeLVV63TRZ9+CnH07U2hHoFUSvU5nspKyp74B9EHH0zMoYeGOpyQ00SglOpzyh5/Al9dHWnXXxfqULoFTQRKqT6lef16Kl97jYTTTiVi+PBQh9MtaCJQSvUpJffehy0yktTLLgt1KN1G3z5C0kmC1Q31+eefz/z58zHGMHz4cF588cXtndcppXZd3XffUTd7NmnXXoMjOTnU4XQbWiPoBMHqhvrBBx9kyZIl/PTTTwwcOJDHHnuss0NXqs8wXi8l995HWFYWiX/8Y6jD6VY0EQRJZ3RDHRcXB1hXPzY2NmJ10qqU2h1Vb79N8+rVpF17DbaA/r1UL2waKrrrLppXdG431OGjRpJx002dtrxd6Yb63HPP5eOPP2b06NHMnDmz02JQqi/x1tVT+sijRI4bR+zRR4c6nG5HawQhsCvdUL/wwgsUFhYyatQo/v3vf4cgWqV6vvJnn8FbVkb6jTdozboFva5G0Jl77nuis7qh3vbe73//e2bMmMG55/bIu3kqFTLurVupeOFF4qZOJXKffUIdTrekNYIg2dNuqI0xrF27dvvrDz74gJEje0UP3Up1qdKHHgJjSL366lCH0m31uhpBdzF9+nROPPFE8vLymDx58i53Q22M4eyzz6ampgZjDPvssw//+Mc/ghStUr1T47LlVL/3PsnTL8CZtfMNEtU2Qe2GOhi0G+pf6+ufX6mWGGPIP+tsmteuZejnn2GPjQ11SCHVVjfU2jSklOqV6r78koZ580i57NI+nwTao4lAKdXrGJeLkhn34xwypM/fa6Aj9BiBUqrXqXz937g2bSLryX/0+XsNdITWCJRSvYq3upqyxx8n6sADiDnssFCH0yNoIlBK9SplTz6Ft6aG9Bv04rGO0kSglOo1XPn5VL7yCvEnnUSEXnfTYZoIOkF5eTm5ubnk5uaSkZFB//79tw8HXlG8uy677DLtflqpDiiZ+QA4HKRecUWoQ+lR9ChKJ9jWDTXArbfeSkxMDNdee22783m9Xux2e5vTzJ8/n6qqqk6IUqnerWHhQmo/+4yUSy8lLD0t1OH0KFojCJLO6Iba6/Vy3XXXcd9994XkMyjVUxhjKL73XhxpaSSfp/1x7apeVyP49o3VlG2u69RlpgyI4ZDTOu/eph3thvqxxx7jhBNOIDMzs9PWrVRvVPPxxzQt+YnMO+/EFhUV6nB6nF6XCHqC1rqhBrZ3Qz1kyBDefPNNZs2aFaIoleoZfI2NlNw/k/BRo4j/7YmhDqdH6nWJoDP33PfEnnZDvWjRItauXcuwYcMAaGhoYNiwYdt7JFVKWcqffQ7P1q30n3Ef0s4xN9UyPUYQJHvaDfWxxx5LUVERGzduZOPGjURFRWkSUGon7i1bKH/2WeKmHkPUhBb7U1MdoIkgSKZPn87s2bPJy8tjzpw5u9wNtVKqfcX33w8ipHXgLD3VOu2Guhfo659f9U31c+eSf9bZpFx6KamXXhLqcLo97YZaKdWrGK+X4rvuxtEvk+Tzzwt1OD1erztYrJTq/arefIvmlSvp/+AD2CIjQx1Oj6c1AqVUj+Ktrqb0oYeImjCB2ClTQh1Or6CJQCnVo5Q+/rjVu+hfbtLeRTuJJgKlVI/RvHYtlf96lYRTTyVCT5DoNEFNBCIyRURWichaEbmxlWkmichiEVkuIrODGY9SqucyxlB8113YoqNJveLyUIfTqwTtYLGI2IHHgSOBAmCeiLxvjPk5YJoE4AlgijEmX0R6ZJeB5eXlTJ48GYCioiLsdjupqamA1a+Q0+ncreWec845zJ49m/j4eABefPFFcnNzOyVmpXqa2k8/pf77H0i/+WYcSUmhDqdX6VAiEJGhQIExpllEJgF7A/80xlS1MVsesNYYs96/jNeBE4GfA6Y5E3jHGJMPYIwp2dUP0B0EsxvqGTNmcMopp3RGmEr1WN66OorvupuI0aNJPOP0UIfT63S0aehtwCsiw4DngMHAq+3M0x/YHDBc4H8v0HAgUURmicgCETmrg/F0e53RDbVSylL26GN4ysrI+Nst2p9QEHS0achnjPGIyEnAQ8aYR0VkUTvztHQ4f+ctnAPYF5gMRAI/iMiPxpjVOyxI5ELgQoCBAwe2udKvX3yakk3r2wlt16RlD+Hwcy7stOV1tBtqgL/85S/cfvvtTJ48mXvuuWeHDuqU6guaVq2i4pVXSDjtNCL32SfU4fRKHa0RuEXkDOBs4EP/e2HtzFMADAgYzgIKW5jmU2NMvTGmDPgG+NU3bYx52hgzwRgzYVvbe0/WWjfUNpttezfUAHfffTcrV65k3rx5VFRUcO+994YoYqVCw/h8FN12O/a4ONKuujLU4fRaHa0RnAtcBNxpjNkgIoOBV9qZZx6Q4592C3A61jGBQO8Bj4mIA3AC+wMPdjT4lnTmnvue2NNuqIHtN6QJDw/n3HPP5f777w922Ep1K9XvvkfjwoVk3nkn9oSEUIfTa3WoRuA/0+cGYKF/eIMx5p525vEAlwKfASuAN4wxy0XkIhG5yD/NCuBT4CdgLvCsMWbZ7n6Y7mRPu6EG2Lp1K2AlknfffZexY8d2aoxKdWfeqipKZswgctw44k/6bajD6dU6etbQ8cD9WHvtg0UkF7jdGHNCW/MZYz4GPt7pvSd3Gp4BzNiFmHuE6dOnc+KJJ5KXl8fkyZN3qxvqadOmUVpaijGG3NxcnnzyyfZnUqqXKJ4xA29NjXWA2KbXvgZTh7qhFpEFwBHALGPMOP97S40xewU5vl/Rbqh/ra9/ftX71P/4I/nnnEvy9AtIu+aaUIfTK3RGN9QeY0z1Tu/pOY5KqU7na2pi6y1/I2zgQFIu0fsMdIWOHixeJiJnAnYRyQEuB74PXlhKqb6q7PEncOfnM/DFF7BFRIQ6nD6hozWCy4AxQDPwGlADXBmkmJRSfVTTihWUP/888b87megDDgh1OH1Gh2oExpgG4C/+R7dkjOmTXdLqVciqtzAeD1v/egv2hATSr7su1OH0KW0mAhF5yBhzpYh8QAvHBNo7a6irREREUF5eTnJycp9KBsYYysvLidDqs+oFKl5+haZly+j/wEy9ZqCLtVcjeNn/3K2vZMrKyqKgoIDS0tJQh9LlIiIiyMrKCnUYSu0R18aNlD78MDGTJhF7zDGhDqfPaTMRGGMW+J+79X0CwsLCduiyQSnVcxivl8I/34Q4nWTcdlufqtV3Fx29oGwpv24aqgbmA383xpR3dmBKqb6h4sWXaFy0iH733UtYeo+8JUmP19HTRz8BvPzS9fTpWL2LVgMvAsd3emRKqV6vee1aq0lo8mTijtfNSKh0NBFMNMZMDBheKiLfGWMmisgfghGYUqp3Mx4PhX++CVtUFJm33apNQiHU0esIYkRk/20DIpIHxPgHPZ0elVKq1yt/9jmali4l42+34EhJCXU4fVpHawQXAM+LyLaNfy1wgYhEA3cHJTKlVK/VtGoVpY8/TuyUKcTpWUIh19ELyuYBe4lIPFZHdVUBo98IRmBKqd7J19RE4bXXYY+PJ+Nvt4Q6HEUHm4ZEJF1EngNeN8ZUichoETk/yLEppXqhkhn307xmDf3uvgtHYmKow1F0/BjBi1g3mOnnH16N9jWklNpFtbNmUfmvf5F09lnEHHJIqMNRfh1NBCnGmDcAH2y/+5g3aFEppXodT2kpW/98E+EjRpB69dWhDkcF6GgiqBeRZPwXlYnIAVjXECilVLuMz0fhn2/C19BA/5n3Ywu4T7cKvY6eNXQ18D4wVES+A1KBU4MWlVKqV6l8+WXq//c/Mv52C+HDhoU6HLWTjiaC5cBhwAisK4pX0fHahFKqD2tctpyS+2cSc8QRJJx+eqjDUS3o6Mb8B2OMxxiz3BizzBjjBn4IZmBKqZ7PW13NliuuwJ6SQuadf9erh7up9u5HkAH0ByJFZBxWbQAgDogKcmxKqR7M+HwU3vhn3CUlDHrlZT1VtBtrr2noaOAcIAt4IOD9WuCmIMWklOoFKp5/nrqvvyb9ppuI3GefUIej2tDe/QheAl4Skd8ZY97uopiUUj1cw7x5lDz4ELFTppD4R+2XsrvraBcTb4vIsVg3sI8IeP/2YAWmlOqZPGVlbLn6GpxZWWT+/Q49LtADdPTGNE9iHRM4HHgWOAWYG8S4lFI9kHG72XL1NXhrahjw7DPYY2Lan0mFXEfPGjrIGHMWUGmMuQ04EBgQvLCUUj1R8T330jB3Lpm330bEiBGhDkd1UEcTQZP/uUFE+gFuQG8SrJTarvLNN61+hM49l/gTTwx1OGoXdPSCsg9EJAGYASzE6mrimWAFpZTqWRoWLqLo9juInjiRtGu0H6Gept1EICI24Ev/PQjeFpEPgQhjjPY1pJTCXVREweWXE9Yvk/4PzEQcHd2/VN1Fu01DxhgfMDNguFmTgFIKrJvMFFx6GaahgQGPP449Pj7UIand0NFjBJ+LyO9EzwNTSvkZn4/C62+gafly+t0/QzuT68F2pffRaMAjIk1YXU0YY0xc0CJTSnVrJTNnUvv556TdcAOxRxwR6nDUHujoBWWxwQ5EKdVzVL7+OhXPPU/imWeQdM7ZoQ5H7aGO3rP4y468p5Tq/eq++Yai2+8g5rDDSL/pJr1yuBdoMxGISISIJAEpIpIoIkn+xyB+uX9xW/NPEZFVIrJWRG5sY7r9RMQrIqfs8idQSnWZppUr2XLlVYSPHKFnCPUi7X2Lf8K6SX0/YEHA+7XA423NKCJ2/zRHAgXAPBF53xjzcwvT3Qt8tkuRK6W6lKuggM3TL8QWF8eAfzyJLTo61CGpTtJe09D3wEHAtcaYIcBtwDJgNvBqO/PmAWuNMeuNMS7gdaClyw0vA94GSnYlcKVU1/GUlZF//vn4XC4GPP0UYelpoQ5JdaL2EsFTQLMx5lERORS4G3gJ68b1T7czb39gc8Bwgf+97USkP3AS8GRbCxKRC0VkvojMLy0tbWe1SqnO5K2tJf/CC/GUlDLgyX8QMXx4qENSnay9RGA3xlT4X/8eeNoY87Yx5q9AeycNt3QEyew0/BBwgzHG29aCjDFPG2MmGGMmpKamtrNapVRn8TU3U3DxJTSvXkPWIw8TNW5cqENSQdDeMQK7iDiMMR5gMnDhLsxbwI49lGYBhTtNMwF43X/WQQowVUQ8xph32wtcKRVcxuNhy9XX0DB/Pv1mzCDmkENCHZIKkvY25q8Bs0WkDGgEvgUQkWFYzUNtmQfkiMhgYAtwOnBm4ATGmO09mIrIi8CHmgSUCj3j9VJ4003Uffkl6TffTPxxx4Y6JBVE7d2q8k7/9QKZwOfGmG1NOzasg7xtzesRkUuxzgayA88bY5aLyEX+8W0eF1BKhYbx+dh681+pef8DUq+6iqQ/TAt1SCrI5Jdte88wYcIEM3/+/FCHoVSvZHw+iv52K1VvvknKpZeSeukloQ5JdRIRWWCMmdDSuI52OqeU6uWMMRTdcQdVb75J8kV/IuWSi0MdkuoimgiUUhhjKL7rbqpee53kC84n9YortOuIPkSvD1eqjzM+H0W33U7Vv/9N0tlnk3rNNZoE+hhNBEr1YcbjYetf/kL1e++TPH06qVdfpUmgD9JEoFQfZVwutlx3PbWffUbqlVeQctFFoQ5JhYgmAqX6IF9TEwVXXEH97G9Iu/EGks85J9QhqRDSRKBUH+OtqaHgkktpmD+fjNtuI/H3p4U6JBVimgiU6kPcRUVsnj6d5o2b6Ddjhl4xrABNBEr1GU2rV7P5wj/hq6tj4DNPE33AAaEOSXUTeh2BUn1Aw7x5bPrDH8HrJfuVlzUJqB1oIlCql6t+7z3yzzsfR2oqg15/jYiRI0MdkupmtGlIqV7KeL2UPvgg5c8+R1ReHlmPPIw9ISHUYaluSBOBUr2Qt66OwmuupW72bBLOOJ2Mm25CwsJCHZbqpjQRKNXLuPLz2Xzxxbg2bCT9lr+SdOaZ7c+k+jRNBEr1IrVffUXhjX8GEQY++wzRBx4Y6pBUD6CJQKlewLjdlDz4EBXPP0/E6NH0f+hBnAMHhjos1UNoIlCqh3MXFbHl6mtoXLiQhDNOJ/3GG7GFh4c6LNWDaCJQqger/eprtv7lL5jmZvrNvJ/4Y7vHlcI+n8Hn8WFz2LDZtDfT7k4TgVI9kLeunuJ77qb6rbcJHzmS/g88QPiQwUFfrzGG2vImygrqqC5tpKaskdryJhpqXDTWuWiq9+B1eQm8A67NIYQ57UTGOolOcBKTEEFCehTJWTEk948mNilCu74OMU0ESvUwDfPnU3jjn3EXFpJ84YWkXHoJNqczKOuqr26mcHUVxRtrKNtcS1lBHc0Nnu3jnZEO4lIiiIoLJ6lfNBExYYQ57djsgs0u+LwGj8uLu8lLQ62L+qpmtqyuZNWcou3LiIp3kjUikayRiQwck0x0vDZrdTVNBEr1EL7GRkoffYyKF14gLCuL7FdeJmr8+E5dR1Odm80rK9iyuootqyqpKm4AwB5mI7l/DMP2TSN1YCzJWTEkpEUREb171ya4Gj2UF9ZTXlBL4ZoqNq+oYPXcYhDoPzyBnAnpDB2fttvLV7tGTGAdrgeYMGGCmT9/fqjDUKpL1c2eTdHtd+DesoWE004j/YbrsUVH7/FyjTFUbK1n09JyNi4to2hdNcZAWISdfjkJ9M9JpP+IBFKyYrDZg9cjjTGGisJ61i0sYc38EqqKG3CE2Rh+QAZ7T8oiuX9M0NbdV4jIAmPMhJbGaY1AqW7MXVxC8d13U/vppziHDiX75X8Std9+e7zc8sI61swtZs38YmrKmgBIHRjLvlMHkT02mbSBsUHd8O9MREjuH0Ny/xj2O24wZZvrWDa7gFU/FvHzt4UMHJPEAScOJXVgbJfF1JdojUCpbsjnclH5r1cpe/xxjMtFysX/R/J55yF7cCygpryRtfNLWD23mPItdYhNyBqZyNBxqWSPTSEmsfu1zTfWuVj+bSGL/5tPc72HoeNT2f+EISRm7HltqK9pq0agiUCpbsQYQ+1nn1MycybuzZuJPuQQMm7+C87s7N1aXmOti7ULSlgzr5it66oByBgSz/A8qw0+Ki44B5k7W3OjhyX/zWfxfzfj9fgYd9RAJhwzCIfTHurQegxNBEr1AI2LF1N87300LlpE+PDhpF13HTGHHLzLy3E1ediwpIzVc4vZvKIC4zMk9YtmeF46ORPSiUuJDEL0XaOhxsX376xl1Y9FxKVEcNiZIxg4OjnUYfUImgiU6sYalyyh9IknqJ/9DfbUFFIvv5yEk09G7B3f2/W6fWxaXs6aecVs/KkMj9tHbFIEOfulMzwvvdcdbC1YVcnsV1dRVdzA3odnceDJQ3GEae2gLXqwWKluqGHhIsoef5z6777DnpBA6lVXkfSHaR0+G8jnMxSuqWLN3CLWLSqlucFDREwYow7KJCcvg4whcb32Qq2sEYn8/ub9+OE/6/jpqwIKVlVy1Pljel3C6ypaI1CqCxmvl7qvv6bipX/SMG8e9qQkks8/j8TTT+9QAjDGULKxljXzrTN+GqpdhIXbGZKbSk5eOlkjE7F34dk+3cGm5eV8+dIK3I0eDj9rJMP3ywh1SN2SNg0pFWLeujqq336bipdfwV1QgKNfJkl/PIvE35+GLSqqzXmNMZRtrmPtgmLWLiihpqwJm0PIHpNMzn7pDNo7hbA+ftC0ocbFp08vZevaasYdOZADThqqfRztRJuGlAoBYwxNS5ZQ9fY71Hz0Eb6GBiL33Ze0664jdvIRiKPtv1/5ljrrjJ/5xVSXNGKzCVmjEpkwdTBDclMIj9KrbreJinNy4pXj+O7NNSz6Ip/yLXUcPX0szkjdxHWElpJSncxTWkr1+x9Q9c47uNatQyIjiZsyhcRp04gcO6bV+YzPULyxhg0/lbFhcSmVRQ2IQP8RiYw7ciBDx6UREaMb/9bYHTYOPWMEKQNimf3qKv7zwEKOu3Qf7buoAzQRKNUJPOXl1H7xBTWffErDvHng8xE5bhyZf7+D2CnHYI9puf3f4/JSsLKSDUtK2bC0nMYaF2IT+uUksNekrB51rn93MfrgfkQnhvPp08t4+74FnHB5LgnpbTe/9XV6jECp3eTKz6du9jfUfvklDXPngs+Hc8gQ4qZMIe64YwkfMuRX82zr26dgRSX5P1dQuLoSj9tHWISd7DHJDN4nhYFjkrWztU5QsqmGDx9bgvHBCVfk9vnuKUJ2sFhEpgAPA3bgWWPMPTuNnwbc4B+sA/7PGLOkrWVqIlCh4mtspHHRIuq++Za62bNxbdgA4N/4H03s0VMIH57zq1M266ua2bKmks0/V7D55wrqq10AJKRHMWBUEoP2TqZ/TiL2sL51tk9XqCpp4L2HFuFu8nL85bmkD4oLdUghE5JEICJ2YDVwJFAAzAPOMMb8HDDNQcAKY0yliBwD3GqM2b+t5WoiUF3F19hI4+LF1M+dS8PceTT+9BO43UhYGFF5ecQcdhgxkw7b4d7AxhiqihvYuraawrVVbF1btb1Tt/BoBwNGJjFgdBIDRiURmxTRKXEan4+mhnqa6mqtR63/ub4Or9uN1+vF5/Xg83hABEeYk7DwcBzOcBzh4UTGxhGdkEh0QiJRcfGIrXclpJqyRt57aBFNdW6OvzyXjCHxoQ4pJEKVCA7E2rAf7R/+M4Ax5u5Wpk8Elhlj+re1XE0EKhiMMbjz82lcuoympUtp/OknGpctA7cb7HYixowhar8JRO23H9H77bf9nP/66mZKN9VSsqmGkvxaSjbW0FjrBiAyNozMoQlkDounX04CKQNid+uURq/HTW15OTWlxVSXFlNTWkJNSTHVpSXUlJVQV16OMb72FyQC7fzfHc5wEjIySczoR/KAbNKHDCNjyDBiknp2Nw61FU2899AiGqpdnHBlLhmD+14yCNXpo/2BzQHDBUBbe/vnA58EMR6lADBuN66NG2les4amVautDf/y5fiqrU7ZJDyciFGjSD77LKLy8ogcPx4ioqgqaaCosJ6KL63eO0s21VJf1WzNI5CYGU32mGQyh1kb/4T0qA5d2ev1uKktK/tlI1/q38j7n+srKnbY0IvYiElOJj41nQGj9yI2OZWouDgiYmL9jxgiYuKIiI7GHubE5rBjdziw2ewYY/C63XhcLtyuJjzNzTTU1NBQVUldVQXVxUVUFhVSVpDP2nk/bl9vbEoqA8fsw8Cxe5O99ziiExKD8M0ET2xSBCddPZ53Zi7kw0eX8Nurx5OSpVchbxPMGsGpwNHGmAv8w38E8owxl7Uw7eHAE8DBxpjyFsZfCFwIMHDgwH03bdoUlJhV7+Ktq8Odn48rP9/a8K9eQ/OaNTRv3Gjt6QM4HIQPzyFyzFgi9hqLffgYmuP7UV3hpmJrPRWF9VRsrae6uAGfz/qviFjt+6nZsaQNjCM1O5aUrBicES3vV7ldzdSWlVJTVurf0O+4sa+rrNhhT13ERmxKCnEpacSlphGXmk78tue0NGKSUrC3cw1CZ3A3NVGyaQPF69ewZcVy8n9eSlNtDYjQL2ckw/IOZPj+E4lPSw96LJ2lpqyRd+5fiM9nOPma8X3qbKJu3TQkInsD/wGOMcasbm+52jSktvE1N+MpLsZdVISnqAjX5s3Whn9TPq7Nm/GW77hPEZaVhWPYCHyDRuHJGExzXAb1EktNhYuaskaqSxtpqnP/MoNAXEokSZnRJPWLJrmf9ZyQHrW9gzNjDI21NdaGvrTE2tiXlfyy4S8robGmeoc4tm/oU9OIT03/1cY+Jim5Szb0u8r4fJTmb2TdgjmsnfsjJRvXATBg9F6MmfQbhu8/kbCIzjnuEUyVRfX8Z+ZC7GE2Tr523047VtPdhSoROLAOFk8GtmAdLD7TGLM8YJqBwFfAWcaY7zuyXE0EvZ+vsRFPeQXeygq8FRV4yivwlGzb4BfjLi7GU1SEt7ISAAN47eG4w6LxZQ7ClzEIT3IW7rhUmpwJNBFJY7OduhoXzfWeHdYlAjFJEcSnRhKXErn9OSbRgTPCRXN9NfVVldRXVVjPlZXUV1dSX1lBfVUV9VWV+Lw7LtMRHk5ccipxqWnEpqTu+Doltcv26IOtuqSIFd/OYvnsL6kq3kp4VDRjjziKcUcf1+1rCaX5tbz74CIiY8M4+dp9+8S1GqE8fXQq8BDW6aPPG2PuFJGLAIwxT4rIs8DvgG1tPZ7WAt1GE0HPYLxefHV1eGtr8dXU4K2tw1dbg7em1nreNlxdg6eyAm95Be6KSpprGnF7wGOPxOOIxOuI8L+OwBubgicuBU90Im5nLC57FC7jpNltw+ttIQbjIyLGEBUrRET7CI/04XB6sNubQZoRmvB5G2mqr9t+tk1jXQ1NtbW4m5t+vUARImJjiYiLIzw+FmdsDM54azgyKYHIpEQikxIJi7aODYgIYbYwwu3hOO1OnHan9drm7FW9ghpj2LJiOYs//4jVc74DAzn7H8QBvzud1IGDQh1eq7auq+b9hxeRkB7FSdeMb7Vpr7fQTufUdsYYjNuNcbl2fDQ349s+7Ma4mvE1NOJrbMDX2IS3vhF3QyO+xmbcDc14G114mlx4ml14m9y4m7143D48Lh+eZg8ej8Frc+K1O/H5n702Jz67E68tDI/diS8sEk9YOG67E4/NhhcB4wY8GOMBPGCsh8EDxo3YPYjDi9jdYHNjpBljXBhfE8bnwudxYTwurGzSQnYILAsBjxPcTnA5fTSHGZrDvDQ5vTQ6PNQ73TSEe2gI99IYbr1vOunMylhnLAnhCcQ744kP/+WRHpVOv5h+ZEZn0i+mHymRKdik55zOWVNWyuLPPmTJFx/jamwkZ/+DOPCUM7ttQti0vJyPHv+JAaMSmXrx3r2651ZNBEBNUTElq9ZgvAbj8+HzefB5fRivwWc84DN4PT6Mz4fxeTE+g/H6MMaHz+d/32swZts0Pmsan8Hn84Exv7xnDGyf1ho2xud/NjtO418W/se2ZRpjMF5rr9Z6NhiDfxxgwPj4ZZnbxhMwHb/Mh7GGsWa1HjYbRgSDWM8i+BAQdno/YC5jAC8GHxgv4AV8YHwYvFZQ+N/3vzbGPw3egGl87O4+scHgsRu8NoPbYXA7fLgdPlwOHx6HweXw4Q0TTJgN47RhnHYIdyBOB0Q4sEWGY4sKxxEZjtO/tx5mC8Npd+KwOQizhRFmD7OebWG/vNfC+3ZpvddPn/Hh9rlxeV24vC6avc24fC4aPY3Uumqpbq6m2lVNdZP1XNVURa27dodlRNgjGJowlJzEHHIScshJzGF08mjiw7v36Y+NdbUs/Pg9Fn78Pq6mRsYcOpmJv/8DsckpoQ7tV37+XyFfv7KS0RMzmfSHkb2qthZIEwHw7BVXUl20NggR9T7+c2OshLD92UoOCBib4PM/YxOMTTA2MHYwdgG7YByAXcAhiF0Qhx2x27DZ7Yjdjs3hsJ7tduzOMGzOMOxhYTicTuxhThxOJ2HhETjDIwgPjyQiPApnRCQRkVFEOKN2aG5x2py/vPZv1HvSXnSgenc9hXWFbK3fSmFdIZtqNrG2ai2rK1dT0VQBgCDkJOawb/q+jE8fz4T0CaREdr8NLEBTXR1z3n2DRZ+8j9jsTDjut+T99lTCwrvXAdo5769n/scb2f+EwUyYOjjU4QSFJgLgg6dmsHnOYv9eqAH5Zf/Yv+8LAsi219s2h/7xsm0/2gcCNv8esk3848Rg7U9vmxbE/x7C9vmtaQPHGSsmmw9rO2uwic+/fB8iXgQfNjHYxOtfvvWeGIPDZjDGhkfs+LDjM3a8YsOLAy92/3MYXgnDZ3NgxImxOfHZwjF2J8YWjscejQmLxuuIxoTFIs4Y7BFxSEQMYREx2CPjcUZEExXuIMrpINppJ9JpJ8rpIMppJ8ppJzrcQbjD1mv3prqD8sZyVleuZknpEhYUL2BJ6RIaPY0AjEoaxaQBk5g0YBKjkkZ1u++huqSIb1/7J6u+/4b4tHQmn38xg3P3DXVY2xlj+PLFFayaU8Tkc0Yx8oDMUIfU6TQRdDVjwOdvAjFe67XPYz28bvC5MV43Po8bj9tq1/Z63Hg9v7z2edx4vdumc2E8bnxet//ZhfG6rWV5mhBPM3ibke2vmxBPEzZvM+J1Yfdar+0+Fw5fMw5jPTuNCxsduCIV8BmhnggaCKfeRFBLFNUmmhqiqTbRVBNNrcTgcsThCY/H64yHyAQkKhGJTiUyOoa4iDDiIsOIjwwjKcpJUrST5BgniVFOnI6euQcfSm6fm5XlK5lTNIfZm2ezpHQJBkN2XDZTB0/lmMHHMDi+e+3dbl7+E188+wSVhQWMOPAQJp09nZjEpFCHBYDX4+ODR5ewdU0Vx12+DwNGdo+4OosmAtU6jwtcdeCq3/G52XrtaarB3VCLp6kGb1MdvqZaTHMdNNdia67C0VyNw1WN01OD3bR+cLbehFNm4iknjjITT5mJo4x4yk08ZSaeemcyTVGZ+GIyiY+JIiXGSVpsBJnxEaTHW88ZcRHER4Z1u73d7qKiqYJZm2fx8fqPmVs0F4NhfNp4Th1xKkdmH0m4vXv0y+9xu5n33lvMefcN7I4wDvvjeex1xNHd4nttbvTwzowF1FU0cfJ1+/aqeyBrIlDBZ4yVRJqqoLESGqt+eV1fBvVleGuL8daWYOpKkIYywpoqrOaxAD6ESklkq0ki35tEkUmi0CSz1SRTYFIocvQjMi6FjPgIMuMjyUqMZGBSFNnJ0WQnR5EWG94tNiihVtJQwkfrP+Kt1W+RX5tPQngCvx/xe6aNmkZiRPfoHqJy6xa+eOZxNi//iSHj9+OoP13eLbquqK1o4u175yM24XfXTyAmsXsk0D2liUB1Tz6vlSjqSqC2EGoKoXoL1BRA9RZM9RZMTQE2d8MOs9XbYim0ZbLBl85KVwobfelsNBmsNf1whcUxIDGK7OQoBiVHk5MeQ056LDlpMcRG9L0+/n3Gx5ytc3ht5Wt8vflrIh2R/C7nd5w95mwyokN/k3fj87Ho0w/49tWXcEREcNT0S8nZ/6BQh0VZQS3vzFhIXGokJ1/bO64x0ESgei5joKkaarZAVT5UrIfyddZzxXpM9WYkoEO2mrBU8h2DWOntz/zGDJZ7slhj+tNEOP3iI8hJj2V4egzD02MZlRnHiIxYwnrxueOB1let57llz/Hx+o8BOH7o8Vyce3G3SAjlBZv55PGZFK9fy+hDj2DyeRfhjAxtP0CB1xgce/He2Hr470QTgeq9PC5/glgHpSuh+Gco+RlKV4HX6hnUIFRHZrHOkcNCzyC+rh3AYk82DUTgdNgYnRnH3lnx7J2VwN5Z8QxNjcG+G91F9xRb67by0s8v8eaqNxERzhx1JhfsdQFxztDetMXr8fDjO68z5503SMjI5PirbiQ1O7QHu5d/u4VZ/1rF6EP6MenMET262VETgep7fF6o2GAlhZKfoWgpFC62mp0AIzZqY4awIXwEP7hzeL8ym59daYAQG+5gfHYieYOTyBucxN5Z8YQ7Wr9wrKfaWreVxxY/xgfrPiDWGcuFe1/IGSPPwGkPbb87m39eykePzKC5ro4jzruIsYcfGdIN8A//WcfCzzZx4ElDGX90dsji2FOaCJTapq4EChfBloVQuBC2LIAGq5dST2QqRQnjWGwbxYfVg/msLAWDDafDRu6ABA4Yksxhw1PYJysBRw9vJgi0qmIVDy54kO8KvyM7Lpub8m7ioP6hbaevr6rk48dmkr90MaMPOZzfXHBJyHo2NT7DF88vZ838Eo66YAw5E7p3h3qt0USgVGuMgbI1sOk7yP8BNv0A1fkA+KJSKE45gLm2cbxdM5z/bbXjMxAX4eCQnFQOG5HKYcNTSY/rXlfJ7q7vtnzH3XPvZlPNJo7MPpLr97s+pMcPfD4vP779b354+zWS+w/g+KtuJDlrYPszBoHH7eX9hxdTsrGWE67Mpd+whJDEsSc0ESi1K6oLYON3sO4r61FfAoA3bQwbEg7gc1cu/yxIp6jO6n56VGYcU8ZkMHWvDHLSY0MZ+R5zeV28sOwFnln6DDaxcUnuJUwbNQ2HLXRnzWxaupiPH70fV1MjR02/lFGHHB6SOJrq3Lw9YwGNdS5OuX5Cj7upjSYCpXaXzwfFS2Htl1ZSyP/RujI8OpWqAUfyvfNAXi4ayJzN9RgDQ1OjmbpXJseMzWRUZmyPPbhYUFvAvXPvZVbBLEYnj+aOiXcwPHF4yOKpq6zgo4fvo2DFMvY56lgmnXUBjrCuPx24urSBt+5dgDPSwSnX70tkbM+5j4EmAqU6S1MNrP0CVnwIaz63rsIOj6Np0BH8GHkYzxUP47uNtfgMDEqO4rfj+vO78VkMSOpZe4/bfL7xc+6ccyc1rhou3OtCLtjrAsLsobkew+f18u1rLzH/g3fIHDaC4666kbiU1C6Po2h9Ne8+uIjUATGceOU4HM6ecSKBJgKlgsHdBBtmw4oPYNXH1kHniASaRpzAd5FH8MLmdL5bX4kxkDc4iVPGZzF170xiwnvWxUmVTZXcO+9ePlr/ETmJOdwx8Q7GJI8JWTxr5nzPp/94EJsjjGMvv45Be4/r8hjWLSzh02eWMTQ3laOmj8XWA0431kSgVLB5PbB+Fvz0b1j5IbgbIH4gtcNP4n0O5bkVDtaX1RMRZmPKmAzO3D+b/QYl9qimo1mbZ3HHD3dQ3lTOOWPO4f9y/y9k/RdVFG7hgwfuoqwgn4mn/YH9f3sqYuvaM7kW/zef795a22PuY6CJQKmu1FwHKz+yksL6r62b9mRPZOOgU3mxYi/eWVpObZOHEemx/OHAbE4a17/H1BJqXDXMnD+Td9a8w5D4Idwx8Q72Tt07JLG4m5r4/OlHWfndbIaM349jLrmGiJiu7SRu230M9pk8gImnDOvWyUATgVKhUlsMS16FBS9B5QaITMQz9jS+iJzCY8vCWF5YQ7TTzsnjs/jDAdmMyOgZZx19v+V7/vbD3yhpKOHsMWdzSe4lIakdGGNY8vnHfP3SM8QmJ3P81TeRPnhol67/f2+s4aevC9jvuMHkHde9uv0OpIlAqVDz+WDjN7DgRetAs8+NGXggG4f+gSeKRvHe0hJcHh8HDU1m+qFDmDQ8tVvvXQLUumqZOX8mb695m8Hxg7lj4h3sk7pPSGIpXL2SDx66h8aaaiaf/3/sdfhRXbZu4zN89cpKVn6/lYmnDCP3N6G51qE9mgiU6k7qy2Dxv2Dec1C1CeKyaMg9h9e9R/D0vCqKaprISYvhgkMGc2JufyLCuvdZKTvUDkafzcW5FxPh6PqL7BpqqvnokRnkL13M2MOPYvJ5F+Fwds3pnT6f4fNnl7NuYQmHnTmCsYf275L17gpNBEp1Rz4vrP4M5vwDNnwDjgi8Y0/j64STmLkkjBVba0iJCefsA7P5wwHZJEZ333PW61x1zFwwk7dWv8WguEH8/eC/h6R24PN5+f6NV5nzn3+TNngoJ1z9Z+LTuubqaK/Hx6dPLWXj0nIOPjWHfSYP6JL1dpQmAqW6u+KfYc6T8NMb4GnEDDqEldnTuG/DIL5eXUFEmI1T9x3ABYcMJjs5OtTRtur7wu+59ftbKW4o5qzRZ3FJ7iUhqR2sWzCXTx6fiSAcc9k1DBm3X5es1+vx8flzy1m/qJQDfjuEfacM6pL1doQmAqV6ioYKWPhPmPuM1VNq4mBKxpzLI+V5vPFTFR6fjyljM7jw0KHkDkgIdbQtqnPV8cCCB3hz9ZsMihvEHRPvIDctt8vjqCou4v0H7qJ043oO+N3pHHjKGdhswW9m83l9/PfFFayZV8z4KdkccOKQbnG8RxOBUj2N1wMr3ocfn4CCeRAeT8PYM3nJdzRPLHJR2+Rh/8FJ/OmwIUwantYtL2j6ofAH/vb93yiqL7JqB+MuIdIR2aUxuF3NfPX8kyz7+guyRo9lyv9dRXxa8HsP9fkMs19dxc//K2R4XjpH/HEU9rDQ9liriUCpnmzzPCsh/PweYPCMOI6Po0/inqVxFNY0k5MWw/RDh3Bibr9ud9+Eenc9D8x/gDdWv0H/mP5cv9/1HD7g8C7fQ14++0u+euFJjIFJZ13AXkccFfQYjDEs+GQTc95fT//hCUz5015ERIfudqmaCJTqDao2w7xnrFNQm6rx9duX+Zmnc9vaYSwvbiQ9LpxzJw7mzP0HEtfN7s88r2ged825i7VVazmk/yHcmHcjA+O69jTLmtISPv3HQ2xe/hODx03gqAsvIyYpOejrXTWniK9eXkFsYgRT/rQXKVlde9HbNpoIlOpNmutgyWvw4z+gYh0mrj8bhpzJ3SX788V6FzHhDs7cfyDnThxEZnzXNsW0xe1z8+qKV3li8RO4fW7OHXsu5409j+iwrjv4bXw+Fn32Id/+60UcTieHTDuHvQ4/KujdU2xdW8WnzyzD1eDhsDNHMPLAzKCuryWaCJTqjXw+qwfUHx+3Tj8Ni6I85xT+0fgbXlgVhgAn5PZj+iFDGJUZ2vsRByppKOH++ffzyYZPSIpI4sK9L+TU4ad26S0yKwoL+PypR9mycjmZw0fym/MvJm3QkKCus6HGxefPLWPLqipGHpTJwafmEB7ZdV2LaCJQqrcrWgo/PglL3wCvi8bsw3nfdiR/X5tNrVuYkJ3IHw7I5pi9MrrNcYSfSn/i4YUPM7doLv2i+3HJuEs4dvCx2LvgzB6w2vB//uYrZr/8HE11dex1xFEceOqZxCQmBW2dPq+PuR9uYOGnm4hOCGfStJFkjw1+8xRoIlCq76grgfnPW30b1Rbii0plWcpU7ivN43+ViSRFOzl1Qha/nzCAIamhaasOZIzhh60/8NCCh1hRsYJBcYM4Z8w5HD/0+C6rITTW1fLDm6+y5IuPsTkcTDjuZPY99kQiooNXPsUbavjynyuo3FrP8P3TOfC3Q4lJDO71FpoIlOprvB5Y96V1TcKqT8B4qUneh0+YyAOFYyg2ieQOSODk8f05fu9+Ib9q2Wd8/HfTf3l26bOsqFhBamQqZ4w8g5NyTiIlMqVLYqgsKuR/r7/M6h++xRkZRe7Rx7Lv1BOJik8Iyvq8bh/zPt7Aoi/ysYmQe+RAxh01EGdEcJqLNBEo1ZfVFsGS12HZW1C0FINQmLAvbzfn8a/K0VTYkzlseBpHjUln8sg0kmNCc48B+KWG8MKyF/hx6484bA4mD5zMyTknk5eR1yX3Ti7esI65777J6jnf4XCEMfLgw9j7N1PIGDo8KKec1pQ18uO761gzv4SI6DDGTurP3pOyOv02mJoIlFKW0lWw7G1Y+hZUrAOgKCqHT5r34YOGsSxlKLnZKRw5Op3DhqeRkxYTsovV1lev563Vb/He2veocdWQFJHE0YOO5qjso8hNyw16UqgoLGD+h/9hxf9m4WluJm3QUEYfejg5+08Myi0yizfUMP+TjWz8qQx7mI0ReemMODCTzCHxSCd8B5oIlFI7MgZKV1qd3q3+DLN5DmK8NNujWSbDmdU4lPlmBBvDR7HPkH7sPySJ/Qcnk5MeQ5i9a6+QbfY2823Bt3y84WO+KfiGZm8zsc5YDup3EAf1O4jxaePJjssO2gVizQ31rPh2Fku/+pySjVbyzBw+kqHj88jeK5e0IUM7teuKyqJ6Fv93M6vnFuFx+YhNjiBnv3QG75NCenbcbieFkCUCEZkCPAzYgWeNMffsNF7846cCDcA5xpiFbS1TE4FSQdBYCeu+gk3fQ/6PmOLlCAYfNvIlk2WeAazwDWSdbSAmeTjJ/YYyckAKOWmxDEyOIiMuAnsX1BzqXHX8sPUHvi34lm+3fEtZYxkASRFJ7J26N8MTh5OTmENOQg7ZcdmdXmuo3LqF1T9+x+o531GywUoKEdExZA4fScbQ4WQMyyFlwCBik5L3+NoEV5OHDYtLWTW3mIIVFRgDex2exaG/H75bywtJIhARO7AaOBIoAOYBZxhjfg6YZipwGVYi2B942Bizf1vL1USgVBdorILNc61+joqX49m6DEfNpu2jfQglJoHNJpUtJoUKEvFEJmOLScUek0pYbDLRMfHExicSExtPRHQc0VHRREeEER3uICbcsceJwxjDhuoNLCxZyKKSRSwtW0p+TT5e4wUgzBZGv5h+ZERlkB6dTmZ0JmlRaSSEJxAfHm89nPFEhUUR4YjAaXPuUq2iobqKTcuWkL90MVvXrKJ8y2arpgU4wpwkZGSSkNGPhIxMouMTiIpPICounsj4BCKiYwiLiCDMGY4jPLzd9TbVu8lfXk58WhTpg3bvmpBQJYIDgVuNMUf7h/8MYIy5O2Cap4BZxpjX/MOrgEnGmK2tLVcTgVIh0lwLJSugfB2mahONJetxlW/EUVOAs7kcp6+pzdm9RmgkHA92PNjxYseDA6/Y8OLAJ9awT+yAIMIOG0jDttfWs5FfhraNawa2hvnI9z9K7T7K7YYyu49Ku9k+T0vEQJgBJ4LTgMOADUEM2PzrsQG2be8HDAPYPEJ0bRiR9WFENjqIaPA/mhzYfG1v6L02Hz67wWc3GMCIAbE+oxF/3GKIGpTGdX/5V5vLavXztZEIgnm0pT+wOWC4AGuvv71p+gM7JAIRuRC40D9Y508Y8UD1Tsvb+b2dh1OAso5/hD3SUnzBmLe9adsa39o4LduOTatlu/vz9rWy3ZNy3WH+629+dXfXld3qHMaYoDyAU7GOC2wb/iPw6E7TfAQcHDD8JbBvB5f/dHvvtTA8P1iftyPxBWPe9qZta3xr47RstWy1bLtPuXZ22bb0CObh/wIg8F5tWUDhbkzTmg868F5L03SVPVn3rszb3rRtjW9tnJZtx6bVst39efta2e7pejuzbH8lmMcIHFgHiycDW7AOFp9pjFkeMM2xwKX8crD4EWNMXlACstY337TSRqb2jJZt8GjZBo+WrSVoxwiMMR4RuRT4DOv00eeNMctF5CL/+CeBj7GSwFqs00fPDVY8fk8Hefl9mZZt8GjZBo+WLT3wgjKllFKdK7Q30VRKKRVymgiUUqqP00SglFJ9nCYCPxEZIiLPichboY6lNxCRaBF5SUSeEZFpoY6nN9HfavCIyG/9v9n3ROSoUMfTVXpFIhCR50WkRESW7fT+FBFZJSJrReTGtpZhjFlvjDk/uJH2bLtYzicDbxljpgMndHmwPcyulK3+VnfNLpbtu/7f7DnA70MQbkj0ikQAvAhMCXzD3+nd48AxwGjgDBEZLSJ7iciHOz3Suj7kHulFOljOWBcHbus+xNuFMfZUL9LxslW75kV2vWxv9o/vE4J/u58uYIz5RkQG7fR2HrDWGLMeQEReB040Vqd3x3VxiL3CrpQz1lXjWcBies8OR9DsYtn+jOqwXSlbEVkB3AN8YtrpEr836c1/0NY6tGuRiCSLyJPAuG09paoOaa2c3wF+JyL/ILRdJvRkLZat/lY7RWu/28uA3wCnbLv4tS/oFTWCVrTU72urV88ZY8qBPvPFd6IWy9kYU0/wrxTv7VorW/2t7rnWyvYR4JGuDibUenONYE86tFMdp+UcPFq2waNlG6A3J4J5QI6IDBYRJ3A68H6IY+qNtJyDR8s2eLRsA/SKRCAirwE/ACNEpEBEzjfGeLB6Nv0MWAG8Edjzqdp1Ws7Bo2UbPFq27dNO55RSqo/rFTUCpZRSu08TgVJK9XGaCJRSqo/TRKCUUn2cJgKllOrjNBEopVQfp4lAKaX6OE0ESinVx2kiUKoT+O9zsUlE/i/UsSi1qzQRKNUJjDFLsfqrOSvUsSi1qzQRKNV5SoAxoQ5CqV2liUCpznMPEC4i2aEORKldoYlAqU4gIlOAaOAjtFagehhNBErtIRGJAO4DLgaWAmNDG5FSu0YTgVJ77mbgn8aYjWgiUD2QJgKl9oCIjACOBB7yv6WJQPU4emMapZTq47RGoJRSfZwmAqWU6uM0ESilVB+niUAppfo4TQRKKdXHaSJQSqk+ThOBUkr1cZoIlFKqj/t/br9YOhmHjkUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Obtain the QRE and output QRE figures\n",
    "\n",
    "QRE_a_l = QRE_Outcome('a', 'l')\n",
    "QRE_a_h = QRE_Outcome('a', 'h')\n",
    "QRE_b_l = QRE_Outcome('b', 'l')\n",
    "QRE_b_h = QRE_Outcome('b', 'h')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "id": "a3ff29f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.96528167, 0.96513883, 0.96499014, 0.96483534, 0.9646742 ,\n",
       "       0.96450646, 0.96433184, 0.96415007, 0.96396085, 0.9637639 ,\n",
       "       0.96355888, 0.96334548, 0.96312335, 0.96289216, 0.96265151,\n",
       "       0.96240105, 0.96214037, 0.96186906, 0.96158669, 0.96129283,\n",
       "       0.960987  , 0.96066874, 0.96033754, 0.95999288, 0.95963424,\n",
       "       0.95926105, 0.95887274, 0.9584687 , 0.95804833, 0.95761096,\n",
       "       0.95715593, 0.95668254, 0.95619008, 0.9556778 , 0.95514492,\n",
       "       0.95459064, 0.95401413, 0.95341452, 0.95279093, 0.95214243,\n",
       "       0.95146807, 0.95076685, 0.95003775, 0.94927971, 0.94849164,\n",
       "       0.9476724 , 0.94682082, 0.94593571, 0.9450158 , 0.94405982,\n",
       "       0.94306643, 0.94203427, 0.94096194, 0.93984797, 0.93869088,\n",
       "       0.93748912, 0.93624113, 0.93494527, 0.93359989, 0.93220327,\n",
       "       0.93075367, 0.92924929, 0.92768831, 0.92606885, 0.924389  ,\n",
       "       0.92264681, 0.92084032, 0.91896749, 0.91702629, 0.91501465,\n",
       "       0.91293048, 0.91077165, 0.90853604, 0.90622151, 0.90382592,\n",
       "       0.90134713, 0.898783  , 0.89613141, 0.89339028, 0.89055754,\n",
       "       0.88763118, 0.88460924, 0.88148983, 0.87827113, 0.87495143,\n",
       "       0.87152912, 0.86800269, 0.86437082, 0.86063231, 0.85678616,\n",
       "       0.85283155, 0.8487679 , 0.84459484, 0.8403123 , 0.83592046,\n",
       "       0.83141984, 0.82681126, 0.82209592, 0.81727539, 0.81235164,\n",
       "       0.80732705, 0.80220446, 0.79698716, 0.79167891, 0.78628397,\n",
       "       0.78080709, 0.77525352, 0.76962902, 0.76393986, 0.75819278,\n",
       "       0.75239503, 0.74655431, 0.74067876, 0.73477694, 0.72885776,\n",
       "       0.7229305 , 0.71700471, 0.71109019, 0.70519694, 0.6993351 ,\n",
       "       0.69351492, 0.68774668, 0.68204068, 0.67640716, 0.67085629,\n",
       "       0.66539814, 0.66004264, 0.65479958, 0.64967859, 0.64468915,\n",
       "       0.63984059, 0.63514209, 0.63060273, 0.62623145, 0.62203711,\n",
       "       0.61802847, 0.61421422, 0.61060296, 0.60720318, 0.60402326,\n",
       "       0.60107142, 0.59835567, 0.59588375, 0.59366307, 0.59170059,\n",
       "       0.59000281, 0.58857559, 0.58742414, 0.58655289, 0.58596543,\n",
       "       0.58566447, 0.58565178, 0.58592819, 0.58649355, 0.58734681,\n",
       "       0.58848604, 0.58990851, 0.59161076, 0.59358875, 0.59583794,\n",
       "       0.59835341, 0.60113005, 0.60416262, 0.6074459 , 0.61097479,\n",
       "       0.61474444, 0.61875027, 0.6229881 , 0.62745412, 0.63214496,\n",
       "       0.63705767, 0.6421897 , 0.64753887, 0.65310327, 0.65888125,\n",
       "       0.66487128, 0.67107186, 0.67748142, 0.6840982 , 0.69092012,\n",
       "       0.69794463, 0.70516861, 0.7125882 , 0.72019869, 0.72799438,\n",
       "       0.73596843, 0.74411278, 0.75241797, 0.76087309, 0.76946565,\n",
       "       0.77818153, 0.7870049 , 0.79591821, 0.80490213, 0.81393564,\n",
       "       0.82299605, 0.83205909, 0.84109907, 0.85008903, 0.85900096])"
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "avg_turn[t, :,[0,1]].mean(axis=0)\n",
    "# .mean()\n",
    "\n",
    "# .mean(axis=(0))\n",
    "# .mean(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "id": "5b6a5fc6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculate the average waiting turns for each treatment, ndoes with 1 or multiple information \n",
    "turns = np.array([0,1,2,3,4,5])\n",
    "QREs = [QRE_a_l, QRE_a_h, QRE_b_l, QRE_b_h]\n",
    "TreatmentName = ['NC_l','NC_h', 'C_l', 'C_h']\n",
    "Network = ['nc', 'nc', 'c','c']\n",
    "Cost = ['l','h','l','h']\n",
    "\n",
    "avg_turn = np.empty((4,n,5))\n",
    "for t in range(4):\n",
    "    for i in range(n):\n",
    "        QRE = QREs[t]\n",
    "        x = QRE[i]*turns\n",
    "        avg_turn[t][i] = x.sum(axis=1)\n",
    "\n",
    "\n",
    "fig, axes = plt.subplots(nrows=1, ncols=3,  sharex=True,   constrained_layout=True, figsize=(10,4))\n",
    "fig.set_constrained_layout_pads( w_pad=1 / 100)\n",
    "\n",
    "linestyle = {'c':'-', 'nc':':'}\n",
    "markerstyle = {'l': '>', 'h': 'o' }\n",
    "y_max = 5\n",
    "y_step = 1\n",
    "\n",
    "# Defining custom 'xlim' and 'ylim' values.\n",
    "# custom_xlim = (1, 11)\n",
    "custom_ylim = (0, y_max)\n",
    "# custom_xtick = np.arange(1,11,step=1)\n",
    "custom_ytick = np.arange(0,y_max,step=y_step)\n",
    "# custom_xticklabel = [1,5,10]\n",
    "\n",
    "plt.setp(axes, yticks= custom_ytick, ylim=custom_ylim)\n",
    "\n",
    "for t in range(4):\n",
    "    axes[0].plot(lambd,avg_turn[t].mean(axis=1), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]])\n",
    "    axes[0].set_title('All nodes', fontsize=15) \n",
    "    \n",
    "    if t<=1:\n",
    "        axes[1].plot(lambd,avg_turn[t, :, [0,3,4]].mean(axis=0), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]])\n",
    "    else : \n",
    "        axes[1].plot(lambd,avg_turn[t, :, [2,3,4]].mean(axis=0), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]])\n",
    "    axes[1].set_title('Nodes with $InDegree=1$', fontsize=15) \n",
    "    \n",
    "    \n",
    "    if t<=1:\n",
    "        axes[2].plot(lambd,avg_turn[t, :, [1,2]].mean(axis=0), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]])\n",
    "    else : \n",
    "        axes[2].plot(lambd,avg_turn[t, :, [0,1]].mean(axis=0), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]])\n",
    "\n",
    "    axes[2].set_title('Nodes with $InDegree>1$', fontsize=15) \n",
    "    \n",
    "    axes[1].set_xlabel('$\\lambda$', fontsize=15)\n",
    "    axes[0].set_ylabel('Average Waiting Turns', fontsize=15)\n",
    "    axes[0].set_xscale('log')\n",
    "handles, labels = axes[0].get_legend_handles_labels()\n",
    "fig.legend(handles, labels, bbox_to_anchor=(.5,-0.05), loc=\"center\" , ncol=4, frameon=False, prop={'size':15})\n",
    "fig.savefig(\"..\\\\Output_Figures\\\\05-QRE-Calculation\\\\\"+\"QRE_Normal_AvgTurns\"  , bbox_inches=\"tight\")  \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "bdde9242",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>app_name</th>\n",
       "      <th>network</th>\n",
       "      <th>waiting_cost</th>\n",
       "      <th>0.0</th>\n",
       "      <th>1.0</th>\n",
       "      <th>2.0</th>\n",
       "      <th>3.0</th>\n",
       "      <th>4.0</th>\n",
       "      <th>5.0</th>\n",
       "      <th>Early</th>\n",
       "      <th>Late</th>\n",
       "      <th>Optimal</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>dcn</td>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>17.50</td>\n",
       "      <td>65.42</td>\n",
       "      <td>17.08</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>17.50</td>\n",
       "      <td>17.08</td>\n",
       "      <td>65.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>dcn</td>\n",
       "      <td>c</td>\n",
       "      <td>l</td>\n",
       "      <td>16.50</td>\n",
       "      <td>44.17</td>\n",
       "      <td>35.17</td>\n",
       "      <td>4.17</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>49.83</td>\n",
       "      <td>6.50</td>\n",
       "      <td>43.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>dcn</td>\n",
       "      <td>nc</td>\n",
       "      <td>h</td>\n",
       "      <td>15.42</td>\n",
       "      <td>66.67</td>\n",
       "      <td>17.08</td>\n",
       "      <td>0.83</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>15.42</td>\n",
       "      <td>17.92</td>\n",
       "      <td>66.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>dcn</td>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>11.35</td>\n",
       "      <td>56.35</td>\n",
       "      <td>25.00</td>\n",
       "      <td>5.19</td>\n",
       "      <td>0.96</td>\n",
       "      <td>1.15</td>\n",
       "      <td>46.92</td>\n",
       "      <td>13.46</td>\n",
       "      <td>39.62</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  app_name network waiting_cost    0.0    1.0    2.0   3.0   4.0   5.0  Early  \\\n",
       "0      dcn       c            h  17.50  65.42  17.08   NaN   NaN   NaN  17.50   \n",
       "1      dcn       c            l  16.50  44.17  35.17  4.17   NaN   NaN  49.83   \n",
       "2      dcn      nc            h  15.42  66.67  17.08  0.83   NaN   NaN  15.42   \n",
       "3      dcn      nc            l  11.35  56.35  25.00  5.19  0.96  1.15  46.92   \n",
       "\n",
       "    Late  Optimal  \n",
       "0  17.08    65.42  \n",
       "1   6.50    43.67  \n",
       "2  17.92    66.67  \n",
       "3  13.46    39.62  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "waiting_distr =  pd.read_csv('..\\\\ImportedData\\\\03-Experiment-Analysis-Summary-Statistics-WaitingDist_m.csv')\n",
    "waiting_distr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7c2bdc8b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "239bcf02",
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_nearest(array, value):\n",
    "    array = np.asarray(array)\n",
    "    idx = (np.abs(array - value)).argmin()\n",
    "    nearest_value = array[idx]\n",
    "    return idx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "8cf25bb6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Adding the empirical prob distribution \n",
    "# Use the multiple information source as an example\n",
    "waiting_distr =  pd.read_csv('..\\\\ImportedData\\\\03-Experiment-Analysis-Summary-Statistics-WaitingDist_m.csv')\n",
    "\n",
    "column_names = ['0.0', '1.0', '2.0','3.0','4.0','5.0']\n",
    "estimated_lamda = [8.959 , 6.748, 8.959 , 9.329]\n",
    "\n",
    "treatment_cond = (waiting_distr['network']=='c') & (waiting_distr['waiting_cost']=='h')\n",
    "QRE_data = QRE_b_h \n",
    "lamda_e = estimated_lamda[3]\n",
    "name= \"-b-h-\"\n",
    "\n",
    "i = 1 # Node B is always the indegree=3\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "ax.set_ylabel('Strategies')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "# ax.set_title(\"QRE for Nodes with Single Information Source\")\n",
    "ax.set_ylim(0, 1)\n",
    "ax.set_xscale('log')\n",
    "for j in range(6):\n",
    "    ax.plot(lambd,QRE_data[:,i,j], label='Turn'+str(j))\n",
    "    distr = float(waiting_distr[treatment_cond][column_names[j]])/100\n",
    "#     idx = find_nearest(QRE_a_l[:,i,j], distr) # this is to find the closes dot on the QRE line\n",
    "#     ax.scatter(lambd[idx], distr, marker='o', s=100)\n",
    "    ax.scatter(lamda_e, distr, marker='o', s=100)\n",
    "\n",
    "ax.legend()\n",
    "fig.savefig(\"..\\\\Output_Figures\\\\05-QRE-Calculation\\\\\"+\"QRE\"+name+\"mSource\", bbox_inches=\"tight\")  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "7fb5adb2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Adding the empirical prob distribution \n",
    "# Use the multiple information source as an example\n",
    "waiting_distr =  pd.read_csv('..\\\\ImportedData\\\\03-Experiment-Analysis-Summary-Statistics-WaitingDist_s.csv')\n",
    "\n",
    "column_names = ['0.0', '1.0', '2.0','3.0','4.0','5.0']\n",
    "estimated_lamda = [11.895 , 8.959 , 4.322 , 6.223]\n",
    "\n",
    "treatment_cond = (waiting_distr['network']=='nc') & (waiting_distr['waiting_cost']=='h')\n",
    "QRE_data = QRE_a_h \n",
    "lamda_e = estimated_lamda[1]\n",
    "name= \"-a-h-\"\n",
    "\n",
    "i = 3   # Node D is always the indegree=1 (comparable)\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "ax.set_ylabel('Strategies')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "# ax.set_title(\"QRE for Nodes with Single Information Source\")\n",
    "ax.set_ylim(0, 1)\n",
    "ax.set_xscale('log')\n",
    "for j in range(6):\n",
    "    ax.plot(lambd,QRE_data[:,i,j], label='Turn'+str(j))\n",
    "    distr = float(waiting_distr[treatment_cond][column_names[j]])/100\n",
    "#     idx = find_nearest(QRE_a_l[:,i,j], distr) # this is to find the closes dot on the QRE line\n",
    "#     ax.scatter(lambd[idx], distr, marker='o', s=100)\n",
    "    ax.scatter(lamda_e, distr, marker='o', s=100)\n",
    "\n",
    "ax.legend()\n",
    "fig.savefig(\"..\\\\Output_Figures\\\\05-QRE-Calculation\\\\\"+\"QRE\"+name+\"sSource\", bbox_inches=\"tight\")  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "41866929",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IbgYeU0odvvm3ADcrpRKA34QlMiFE1NFa87t3dpKb4uCaucMiHU7UCLVB2VpgklIqBVBa68Z2q18IR2BCiOjzzpYqNpY38vvLJuOwWyMdTtQIdfD6bKXUo8BzWutGpdR4pdRNYY5NCBFF/AGDe97dyejsRC6dnh/pcKJKqO8IHsccYCY3OL8L6WtICNGLXlhXQVltG987dyxWS2dDnotwCTURDNFav4A5ihhaaz9mdVIhhDhprR4/f/7vLmYMS+PscVmRDifqhJoI2pRSGQQblSmlTsFsQyCEECftwQ9KqGnx8OPzx6GUPA30tVBrDX0Hc+D5YqXUx0AmcHnYohJCRI3yeiePfLSHS6blMa0wLdLhRKVQE8FW4AxgDGaL4p2E/jQhhBBd+r+3tmNViv9dNDbSoUStUG/mq7TWfq31Vq31Fq21D1gVzsCEEIPf6rI63t5SxW0LislJka4kIqW78QhygDwgTik1DfNpACAZkM7BhRAnLGBo7n59G3mpcdxy+ohIhxPVuisaOhe4HsgH/tRueQvwwzDFJISIAs+vLWf7wWYeuGqaNB6LsO7GI3gCeEIpdanW+qU+ikkIMcg1u3388b2dzB6ezvmThkY6nKgXahcTLymlzsccwN7RbvkvwhWYEGLw+vP7u6h3ennigvFSXbQfCLWLiYeArwLfxHxPcDkgPUIJIXpsy4Emnli5l6vnFDIxLyXS4QhCrzU0T2t9LdCgtb4bmAsUhC8sIcRgFDA0P3plC+kJMXzvXKku2l+EmgjcwW+nUioX8AFF4QlJCDFYPfvJfjaWN/Lj88fLWAP9SKgNyl5XSqUC9wCfYnY18Y9wBSWEGHxqWjz8/p0dzCvO4MKpud3vIPpMt4lAKWUBlgTHIHhJKfUG4NBaS19DQoiQ/eKNbbh9Br+8aKK8IO5nui0a0lobwB/bzXskCQgheuK9rVW8vrGSb541kuLMxO53EH0q1HcE7ymlLlWSxoUQPdTk8vHjV7Ywbmgyty6Qwej7o570PpoA+JVSbswqpFprnRy2yIQQg8Kv39xGXZuXx66fhd0qfVX2R6E2KEsKdyBCiMHnw101vLCugtsWFEubgX4s1AZlS0JZJoQQhzU6vfzvi5sozkzgzoWjIh2OOI7jJgKllEMplQ4MUUqlKaXSg5/hHB2/+Hj7L1JK7VRKlSilfnCc7WYppQJKqct6/BcIIfodrTU/fmULta0e7r1COpXr77orGvo65iD1ucD6dstbgL8eb0ellDW4zTlABbBWKfWa1npbJ9v9Dni3R5ELIfqtVzdU8samg3zv3DFSJDQAdFc0tBKYB3xXaz0CuBvYAiwHnulm39lAida6TGvtBZ4DLuxku28CLwHVPQlcCNE/HWh08ZNXtzBzWBq3niG1hAaC7hLB3wGP1vp+pdTpwG+AJzAHrn+4m33zgPJ28xXBZUcopfKAi4GHjncgpdRipdQ6pdS6mpqabk4rhIgUf8Dg289twDA0f/rKVKwWqXE+EHSXCKxa6/rg9FeBh7XWL2mtfwKM7Gbfzv4F6A7zfwG+r7UOHO9AWuuHtdYztdYzMzMzuzmtECJS/vzfXXyyt55fXzyJwgwZxHCg6O4dgVUpZdNa+4GFwOIe7FvBsT2U5gOVHbaZCTwXbKc2BPiiUsqvtX6lu8CFEP3L8l01/PWDUq6cXcBF0/K630H0G93dzJ8FliulagEXsAJAKTUSs3joeNYCo5RSRcAB4ArgqvYbaK2P9GCqlHoceEOSgBADT1WTm28/v4GxOUn87IIJkQ5H9FB3Q1X+OtheYCjwntb6cNGOBfMl7/H29Sul7sCsDWQFHtNab1VK3Rpcf9z3AkKIgcHjD3D7M5/i9gV44KrpUlV0AOq2ZbHWenUny3aFcnCt9VvAWx2WdZoAtNbXh3JMIUT/8vPXtrF+XwMPXDWNkVnSodxAJB1/CCFO2L9W7+PZT/Zz24JivjRZxhgYqCQRCCFOyCd76vn5a1tZMCaT//nCmEiHI06CJAIhRI/tqW3j60+toyA9nnuvmCbtBQY4SQRCiB6pb/Nywz8/AeCx62fJ2MODQKjjEQghBG5fgJufWEtlk5tnb5lD0ZCESIckeoE8EQghQuIPGNz13AY+K2/kL1+dyoxh6ZEOSfQSSQRCiG4ZhuYHL2/mna1V/Pj88Xxx0tBIhyR6kSQCIcRxaa35xRvbeHF9Bd8+ezQ3zS/qficxoEgiEEJ0SWvNPe/u5PGVe7nltCLuXNhdX5NiIJKXxUKITmmt+e07O/j78jKunF3ID784jmAHkWKQkUQghPicw8VB//x4L187pZBffHmiJIFBTBKBEOIYAUPz01e38PSa/dx4ahE/+ZI8CQx2kgiEEEe4fQG+/fwG3t5SxTcWFPO/546RJBAFJBEIIQBocvq45al1fLKnnp98abzUDooikgiEEOyvc3LTE2vZV+fk/iunccEU6Uk0mkgiECLKrSyt5banP0VrePzGWcwrHhLpkEQfk0QgRJTSWvPU6n3c/fo2RgxJ4JHrZjIsQ/oOikaSCISIQq0ePz98eTOvbaxk4dgs/nLFVJIc0ototJJEIESU2VHVzG3/+pS9dW189wujuW3BSCwynkBUk0QgRJQwDM0Tq/by27d3kBJn55lbTuGUERmRDkv0A5IIhIgCBxpdfPeFjawqq2Ph2Cx+e+lkMpNiIx2W6CckEQgxiBmG5ulP9vP7t3dgaM3vLp3EV2YWSCMxcQxJBEIMUjurWvh/L2/i0/2NzCvO4LeXTKYwIz7SYYl+SBKBEINMo9PLvUt289SqfSQ5bPzx8ilcMj1PngJElyQRCDFIeP0GT63ex31LdtPi9vHVWQV879yxpCfERDq0Y2kNfjd428DbCiiwxoAtFmKTwSq3pb4mV1yIAc4wNO9tq+J37+xkT20bp40awo/OH8fYnOQIBhWA+j1Qsx1qdkDNTmiqgOZKaDkIAW/n+ykLJOZA8lDIGAW50yBvOuRMBrujb/+GKCKJQIgByjA072yt4r4lu9lR1UJxZgL/vH4WC8Zk9m0xkNZQXwYH1kPFWqhYB4e2QsBzdJuUAkgdBgWzIWkoxKVBTCLExAPK3NbvBWedmSyaK6DsA9j0nLm/PR6Kz4Kx58PoRRCf3nd/XxSQRCDEABMwNG9tPsj9S3ez61ArIzIT+PNXp3DB5Fxs1j4YfVZrqCuFPctgz4ew9yPzBg5gTzB/wc9ZDJnjIGssDBkNsUkndp6Wg3DgUyhdCjvfhh1vgDUWJl0Gs28xnxjESVNa60jH0CMzZ87U69ati3QYQvS5JqeP59ft58lV+6hocDEqK5FvLhzF+ZOGYg13y+CmCvOmX7bc/G6pNJcn50PR6VA4B/JmQtY4sFjDE4PWUPkpfPY0bHwOfG1QOBfO+gkMPzU85xxElFLrtdYzO10niUCI/m3XoRaeWLmXlz89gMsXYE5ROjecOpwvjM8JX9cQbbXmDf/wp77UXB6fYd74i84wv9NHQCRqI7mbYMMz8PG95lPDqHPh7J9B9oS+j2WAkEQgxADT5PTx2qZKXlxfwcbyRmJsFi6amsv184oYnxuGl8DuZti3EvYEf/Ef2mIuj0mC4fODN//TIWs8WPqg+ClUXid88ndY8WezBtL8u+D0/5UXy52QRCDEAOD2Bfhody2vbDjAe9sO4fUbjM1J4rIZ+VwyPb93q4F6WmH/ati7wizjr/wMdABsDiiYY970RyyAoVMHRnVOZz2892PY8LT5TuLLD5jFVeIISQRC9FNuX4Dlu2p4e/NB/ru9mlaPn9R4OxdNzeOyGflMyE3unRpA3rbgjf8j8+Zf+RkYfrDYzLL94fNhxBmQP3tg/5ou+S+8fhc0HzDfHZx6V/96gomg4yWCAZDqhRhcyuudLNtZzfJdNawsrcPpDZAab+f8SUM5b1IO84qHEGM7yZtXWy2UfwIVn5hFPgfWH73x506HeXdC0Wnmr/+YQTQYzciz4Rsr4fU7YcndUL4GLn7IrK4quhTWRKCUWgTcC1iBR7TWv+2w/mrg+8HZVuAbWuuN4YxJiL7W6vGzdm89y3fW8OGuGspq2wDIT4vjkul5nDshh1NGZGA/0aqfRgCqtwVv/GvNm199mbnOYoOhU2DuHcEb/ykQm9hLf1k/5UiGy/4JhfPg3R/C30+Hq/5tVmUVnQpb0ZBSygrsAs4BKoC1wJVa623ttpkHbNdaNyilzgN+rrU+bsGeFA2J/q66xc26vQ18sqeedfvq2VbZjKEh1mbhlBEZLBiTyRmjMykaktDzYp+AH+p2w8GNx368reb6hEyzeKcg+Bk6NdhoK0pVrINnrzQbrH31aTMZRqlIFQ3NBkq01mXBIJ4DLgSOJAKt9cp2268G8sMYjxC9rtntY+uBZrZWNrH5QBMbyxvZW+cEwGG3MK0gjTvOHMmsonRmDU/HYe9BHXt3k9k1Q/V2qNoMBzdA1Rbwu8z1tjjImQRTroT8WeaNP214ZKpz9lf5M+Hm/8LTl8NTF8OFf4UpX410VP1OOBNBHlDebr4CON6v/ZuAt8MYjxAnzB8w2F/vZHd1KyXVreyoamHLgSb2BIt5AIamOJiUl8JVcwqZNTydCbkpoZX1uxqhdrfZL0/1jmDfPDvMF56HxSTB0Mkw8wazqGfoFLMvnoFQoyfS0obBTe/C89fAfxabCXbO4khH1a+E819RZz9LOi2HUkqdiZkI5nexfjGwGKCwsLC34hPiGFprmlw+yutd7Ktvo6S61bzxH2plT20b3oBxZNu81Dgm5iVz6fQ8JualMDEvhSGJXYz4pbVZvbG+rPOPq/7otrY4yBxt1uLJHGu21M0cA6nDpfbLyYhLg6+9BC/eCG9/z3yqOvVbkY6q3whnIqgACtrN5wOVHTdSSk0GHgHO01rXdXYgrfXDwMNgviPo/VBFNNBaU9/mparZTXWzh4pGF+X1TvbXOSlvcLK/3kmL239ke6WgIC2eUVmJLBibyaisJEZlJVKclUhibLv/dXwuaCqHQ+Xmr/imCnO+KTjdfAB8znaRKLMTtvQiGH8hZBRDerH5MjN1WPi6aIh2tli4/HF4eTG8/1Pzv9sZ35eiNMKbCNYCo5RSRcAB4ArgqvYbKKUKgZeBa7TWu8IYixjEXN4AdW0eGtp81Du91Ld5qG72HLnhVzW7qWpyU9PiOeZXPUCMzUJBWhyF6fHMGJZGYXo8BenxFCYpiuJdONx10HoI2rZCaw0cqobW4Ket2lzmafp8UIk5kJIH2eNh1BcgJd/sjiF9hFlUYZPxgiPCaodLHzEbzi37jVmr6vTvRjqqiAtbItBa+5VSdwDvYlYffUxrvVUpdWtw/UPAT4EM4MFg7Ql/V2+1xeDm9gVocftpcfuC38Fpz9HpJpeP+jYv9W1eGpxe6lu91Du9uH3G544Xg48hMV6GJ2pGJgQ4IztA1jA/OTEeMq1O0ixtpKg24gPNKFcjuBvhQAOUNJhl9odfyHbkSIGELEjMMl/UHp5OyT/6ScoFWz8bDEYcZbGaL421AUt/afaMOufrkY4qoqRlseiS1hpfQOMLGHj9Bt5234eXubwBXL4Abl8AZ3Da5T123h1c5vQGcHu9BHwe/B43fo8z+HFhMTw48OJQXhx4icXXbtqcT7b5SbEHSLH5SbL6SLZ4SFRuEnDhMJzEGi7sgTasvjaU4ev+D7QnQFyqWX4cl2be5A9Px6WaVTETs4PfWeZ38Je81hq/9hMwAgR0AL/hx2/4j0wHjAB+fXRZwAjgM3xHpv2G/8j+7b8P7xvQwe3bH//wdu3O4zf8GNrAoizYLDasyorFYsGmbFgtVnN5cDrOFke8LZ54e/wx06mxqaQ50oi1RtlTSsAP/77O7Nr6wgdh2tWRjiispGUx0OZso66+BkMbaK0xDI1GYxgBtDYwDAN9ZJmB1gEMrdHaXG5oA41GG4a5TGsCWoPWaCNg7qcPrw+ABoPgMbXG0AH04e21brfOAG0eH22eO2CYcRnBWAzDwNCH4zKOxKyNANoIgDa/DSMAhg6e32/+4jkSz+HtNOjAMccwlxvtvs1pQxsoZaDQ2JQfKwYW/FiVgYUAVvxYlIFVBbBgLrNjEKsMLO2WWZSBBQOFgVIaAzAAbQUjXmHEm7UIDAXm2cz1hgKNMrcFDKVos9ppstgIWO0ErDH4bXYCVjuGNRm/JZ2A1UbAYsVvsRFQVgIWCwGLBb+yYCjzO2CxEFCKwOdu5k4M3UqgbS/+Fn/nN+3DN3YdiNi/ZZvFht1ix6qsWC1WrMpKQAcwDOOYv6enMSbaE0l3pJPuSCfNkUZOQg75ifnkJeWRn5hPQVIB8fZB1CbBaoPLHoNnvgqv3WG2sJ5wUaSjioioSQTP/b/v03TocO0MFazS1P4lkTrmWx1n3bFrO677/BbHHrfjPrqT46kOMap2c+rIfkofu4f1yMOduU6128bc02quw4LSMSitAY0l+FR4eF4Fj2FOa7Qy0AQAP2Cg8ZtJRJnL/ATM9SqAxo9BAK3MZVoFgvN+tNJoFbzBBz9GJ/NagWGBgIKAVRGwcOzHCn4LYA2grRrD6gOrB2xWtNWCtlnBZgOrFWxWlM2GtlrM+Rg7ym7DGmvHGhODw+445oZ6ePrwr2irsmKz2I782j687vB8+3U2i+1z662W4DbB4x2zX7tz2C32Ts/X8TwWFXrNIR38gXH46cEdcOP0OXH6ncd8N3oaqXfX0+BuoM5dR727nvKWctZWraXV13rMMfMS8xidNvrIZ8KQCeQm5PbtiGi9yRYLVzxttjF46WYzGYw6J9JR9bmoSQTZI0fhrNtoVuU7cgPuWJ+1YzGZDi46vK1ut00n2xI8/JFtO26nO5xVt1ut260P/gbWOrjEOLL+uDrLXSfNAljNsWSxgbKgcASXWQEbStlA2T83jbKhjkzbzQSEFSsWlFZYj3zAaiishh+r4cNi+LAEvFj83uC8F4vhx2J4sQZ8WAMerAEPtoDbnPa7j04HXFgMX+h/vs2GJSYG5XCgYmPN6dhYlMNxdDo2FhUbg8URhyUhAUt8PJYEhzmdkIAlIR5LQgLWI/NHP8oWuf/FlFJmMsJKjDWGeHs86Y7Qh3jUWtPsbaaipYLy1nL2N+9nd8NudjXsYnnFcvMpFshJyGF61nRmZM9gZvZMilKKBlZiiEmAq16AJy6AF66F69+AvBmRjqpPyTuCAUYbZtGQETCLcYxAsKjIMNotCxyzzDAMdHCZYRgY/gABvw+/z0/A68Xv8xHwBeePTPsI+I/OB/x+c5k3uNx/eDsvfq8Xv89DwGeW/5vrvBiBEMrp21HKhrLGoiyxKBUDKgaIQWs7EAMqFqUcoOJQyoGyHJ1GOVDBX8tKgd1uPhTYbRqbVWO3amJsBjFWPzHKTwxebNpDjPZgD7ixBZzY/S7snhaUz4X2eNEeD4bHfXTa5cJwOjHa2iAQWrGLJSEBa0oK1tRUrKkpWA5Pp6RgTUnFmpqKbUgGtiFDsGVmYk1LQ1n7f/VRt99NaWMpm2o3sf7QetYfWk+tqxYwnxrOLDiTswrPYlrWNGyWAfJ7s7UaHjnb7Kn15vfNGl6DiHRDLSJCGwZ+rxef14Pf68Hn8eD3eMx5txufx4PH5cTrcuJ1Oo9Ou1x4XU48Tidet+vIendbq/kOowu2mDhsMfFYY+Kx2ROx2hOxWBNQlgQ08RiBOPy+WLweB9qwdfmr1RZjIT45hrikGPM7OYb44LS53E5cnCLO5sPiPZocOn4Cra0Yzc0EGhsJNDYRaGoyp5vMaTr7W6xWbOnpWDPNxGDPysKel3fMx5aZiepnjcu01pS3lLOmag3Ly5ezqnIVXsNLSmwKC/IX8OXiLzMzZ2aPirYionY3PHoOxKXDTe9DQkakI+o1kgjEoKC1xuty4m5twdXSgrulGVdbq/nd0oK7rQV3Swuu1hacTY04Gxtoa2rsNHnYYmKJT0kjPiUDR2I6sfFp2GJTsNqTwZKM4Y/H3QbOZi+uFi+uVl+nJXNxSXaS0h0kpjlITI8lMc0RnI8lKd1BfEpMpwlHGwZGayuBxkb8tXX4a2rw19YEv2vx19QQqKnFd+gQgboO7Sztduy5Q4nJy8NeWEjsiBHEFI0gtngEtpycfpEknD4nKytXsnT/Uj4o/4BWXyu5CblcOPJCLht9GVnxWZEOsWv718CTXzarB1/72qDptE8SgYha2jBwtbbQ1thAW2ODmRyCn9b6OprramipraG1of7oC56guKRkkjOzSc0ZSmr2UOJTs3AkDsHuyMDniaGt0UNrg4fWejctwW+f59giI1uMhZTMeFKz4kjJiiclK+7IdHxy50miI8PlwnfwIL4DB9p9KvEeqMC7dx9G09EGbSoujpii4ThGjcIxfjyO8eOJHTcOa2Lkup52+V0s3b+UV0teZfXB1ViVlXOGncPV469mSuaUiMV1XNteM98XjD0fvvLkoGjtLYlAiG4E/H5a6+toqa05khyaa6tpqj5EY1UlzTU1ZlXfoNj4BFJzcsnIyyejYBhDCoaRkV9IbEIarQ1eWhvctNS5aap20VjjpKnaRXOtCyNw9P+3GIeV9NxEMvISjnxn5CXiSLCHHLfWmkB9Pd6yMjxle/CWleIpLcOzaxf+6uoj29mHFeIYP564iZOInzEdx4QJKHvo5+kt+5v38+yOZ3ml5BVafa3MypnF4smLmZMzp/+9YF79ELzzfZh1C3zxngHfFYUkAiFOUsDvCyaFgzQcrKTxUCUNByupO1BOa13tke1i4uLIyCs8khyyRxSTVVRMjCMOI2DQUu+hqdpJY7WLxqo26irbqDvQisd5tI+j+JQYMvISySxIInt4MlnDk0hIje3xjdJfU4N7+3bc27bh3roN99at+CrN7r6Uw0HclCnEz5xJ/MwZxE2ZgiW+74pA2nxtvLTrJR7f+jg1rhomZ07mrul3MStnVp/FEJJ3fwSrHoCz74b5d0U6mpMiiUCIMHK3tVJXvp/a8n3Ulu+jrmI/tfv34mppNjdQioy8ArJHjCR7xChyikeSOXwE9pijrZTbGr3UV7ZSd6CNuspW6g60Un+gDcMw//+MT44ha3gy2cOTyB6RQk5RCvbYnhdX+GtqcK7/FOf69TjXr8OzY6f50tpuJ37GDBJPO42E0+YTO2pUn/xC9wQ8vFryKn/f9HeqndUsyF/AXTPuoji1OOznDolhwEs3wdaX4dJHYdJlkY7ohEkiECICWhvqOVRWwqGy3RwqK6GqdDfOpkYAlMVCZmEReePGkz92AnljJ5CQeuy4un5fgNqKVqr3NlO9t4Xqfc00VJm9mFosisxhSeSOTCV3VCo5xSk9KlI6LNDSgmvDBtpWr6btwxV4du8GwJaTQ+KCM0j+wheInz077O0h3H43/9r+Lx7Z/Aguv4tLRl3C7VNvZ0jckLCeNyQ+N/zrEnMo0GtehqLTIx3RCZFEIEQ/oLWmtb7uSFI4uHs7lbt24vd6AEgbmkteMCnkj51ASnbO536Ve5w+qsqaqSxp5ODuRg7ta8bwa1CQWZBEwfh0CsenkzMiBWsog+J04KuqonXFCto+/JDWjz5Gu1xYU1NJXHgWyeeeS8LcuWF9t1DvrufhTQ/z/I7ncdgc3Dn9Tr4y+itYI/2y1tUAjy2C5oNw49uQPSGy8ZwASQRC9FMBv5/qPaVU7NhKxfYtVO7YhrvN7NYhOTOLYZOnMXzyNAomTiEuMelz+/u9AQ7tbaZydyMVOxqoKm3CMDT2WCt5Y9IoHJ/OsIkZJA+J63FshstF60cf0fLe+7R+8AFGayvWjAxSvnQ+KRddROzYsWErPtrbtJdfrfkVaw6uYdKQSfx07k8Zmx7hwecby802BspitjFIyYtsPD0kiUCIAUIbBnUV+6nYvpV9mzewf8tGvC4nSlnIKR7FsMlTKZo2k6Ejx3TaXsDr8lOxs4HybfXs31ZHc60bgIz8REZMzWTE1Ewy8hJ6fAM3vF7aVqyg6ZVXaVm2DHw+YkePJuWSi0m9+GKsKSm98ecfQ2vNW3ve4vdrf0+jp5Grx13NHVPviGzHd1Wb4bHzILXQfDJw9P7fHS6SCIQYoIxAgIMlu9i36VP2bvqMqt270NogPiWVEdNnUzxzDsMmTcEe6/jcvlprmqpd7N1cS9mGGg6WNoGG5CEORkzNpHh6FtlFyT2vjdTQQMs779D4n1dwb9qEcjhIPv+LpF15FXETe7/IpMnTxL2f3su/d/2bgqQCfj3/10zLmtbr5wlZ6Qfw9GUwbB5c/dKAGXtCEoEQg4S7tZU9G9dTum4Nez5bh9flxGaPoXDyVEbNmsvIWXNxdNF4zNnsZc/GGso21FKxox4joEke4mD07BxGz84mLSeh5/Fs307Ds8/R9PrraJcLx+TJpF97LcmLzu31F8xrq9byk49/QmVrJddPvJ7bp94euTEUNj4H//k6TLocLn54QIwnLYlAiEEo4PdRsX0rpevWULp+Dc011VisNoZPmcboU+YzctYpxMZ3fnP3uPzs2VjDrjVVVOxoQGvILExi9OxsRs3KJiGlZzfYQEsLTa+8SsMzz+Ddswd7bi7p119H6qWXYknoeYLpSpuvjT+s+wMv7nqRkakj+fX8XzM+Y3yvHb9HVvwJltwNs26GL/6h3zc4k0QgxCCnteZQ6W52rv6InatW0FJbg9VmY/jUGYyZdzojZ87ptPgIoK3Jw+61h9j1ySFq9regFAybNITx83MZNiEdi7UHYyAYBq3LllH36GO41q/HkpJC2pVXkH7dddjS0ro/QIhWVKzgZyt/RoO7gcVTFnPzpJuxW/q4pbTW8P5PYeV9cOpdcPbP+3UykEQgRBTRWnNw9052rV7BztUf01pXS0xcHKNPmc+E0xeSN3Z8lx3TNVS1sWNVFdtXHcTV7CUhJYZxp+Yybt7QHtc8cm3YQN1j/6Tl/fexxMWRdvXVpN94Q68lhCZPE7/55De8WfYmEzMm8pvTfsPwlOG9cuyQaQ1v/g+sexTO+gmc/t2+PX8PSCIQIkppw6Bi+xa2Ll/KrjUf43O7SM7MZvzpZzH+9DNJy8ntdL9AwGDfpjq2flTJ/m1m76cF49KZtCCfYRMzsFhC/+XrKSmh9sG/0fz226i4ONKvvor0G27Alh76IDnH897e9/jF6l/g8Xv47szv8pUxX+nbfosMA175Bmx6Dhb9Dk65te/O3QOSCIQQ+Nxudq9dxbYPl7Jv8wbQmtzR45h41jmMnXs6dkfnRUct9W62rzzIto8qaWv0kDzEwaQF+YybN5TY+NCLYzwlJdT+7SGa33rLTAhXXUn6TTf1yhNCtbOan3z8E1ZWrmR+3nx+eeov+7ZVcsAPL14P21+HC+6FGdf33blDJIlACHGMlrpatn+0jK3L/kt9ZQUxcXGMm7+ASQsXkV3UeT8/gYDBng21bPqgnIMlTdhiLIw5ZSiTF+STnhv6C2FPaamZEN58E0t8POnXXUf6DddjTfp8g7me0Frz7I5n+dP6PxFni+Pnc3/OwmELT+qYPeL3wPNfg93vwXn3wJzFfXfuEEgiEEJ0SmvNgZ3b2LzkXXat+gi/z0v2iFFMPvtcxs47nZi4zhtv1ZS3sPmDCnZ9coiA3yB/bBqTz8xn2KQhIRcbeUpKqLn/AVrefRdLSgoZN95I+jVfO+leUMsay/jBih+wvX47F428iB/M/gEJ9t6ruXRcfg+8eCPseKPf9VgqiUAI0S13ayvbVnzA5iXvUFu+D7sjjrGnns7khYvIHjGy03J3V6uXbR9VsmX5AVobzGKjyWcWMG7eUGLiQmtH4Nq6ldr77qd1+XKsGRkMWXwLqVdcgSX2xNsI+AI+/rbxbzy65VGGJgzl/+b/H9Ozp5/w8Xok4DPbGGx5CU77H/Mlcj+oTSSJQAgRssO1jjYteYedq1bg93jIGl5sPiWcuoDYTn6xGwGDsg21bFpazsHSJuwOK+PmDWXymfmkZIb2C9/52WfU3HcfzlWrsWVnM+Qbt5J6ySWomBNvuftZ9Wf8cMUPqWyr5MaJN3LblNuwW/ugmqkRgNe/BZ89BZO/Cl9+IOItkCURCCFOiMfZxvYVy9i09F1q9pZhi41l7LwzmLzwXHJGju70KeHQ3mY2LS2nZF01htYUTR7C5LMKyBudGlJtnrbVa6i5915cn32GPT+fIbffTsqXL0BZT6wH0jZfG7/75Hf8p+Q/jEsfx93z7mZcxrgTOlaPaA0f/gE++BUMPw2++hTE9V5bip6SRCCEOClaaw6VlbBpyTvs+Gg5Po+bzMLhTDp7EePmL8CR8PluLdoaPWz58ABbPjyAu9VHRl4iUxbmM2pWNjb78W/qWmvaVqyg5i/34t62jZgRI8j85h0knXtul20gurNk/xJ+ueqXNHoauWb8NXxjyjf6pgO7jc/Dq7dDagF85SnImRj+c3ZCEoEQotd4XU52fPwhm5a8w6GyEmwxsYyZexqTzz6XoaM+3zW13xtg19pDbFpaTt2BNuKS7Ew4LY+JZ+R125WF1pqW99+n9v778ewuIXbMGDK/dSeJZ555Qm0FmjxN/Hn9n3lp90vkJebx41N+zPy8+T0+To/tWwX/vh7cTfClP8PUK8N/zg4kEQghwuLwU8L2j5bjc7sYUjCMSQvPZfxpZ32u8zuzhlIDG5dWsHdzLRaLYuTMLKacVUDWsOTjnkcHAjS/9TY1D9yPb99+HJMnk/mtO0mYN++EEsL6Q+u5e9Xd7Gnaw7nDz+XbM75NXmKYxxdoOWQOe7l3BUz9Giz6vz7txloSgRAirLxuFztXrmDTkneoKtmFzR7D6FNOZfwZCymYMAlLhxHGGqudbF5WwfaPD+LzBBhanMLkswoYMXXIcfs20j4fTa++Ss2DD+KvPEjcjBlk3HgDiQsW9Pgdgjfg5dEtj/LY5scwtME146/h5kk3kxjTee+tvSLgh2W/gY/+BElD4YL7YNTZ4TtfO5IIhBB9pnpvGZuWvMv2FR/gdTlJTEtnzLzTGTd/AVlFxcf8gve4/OxYeZBNH5TTXOsmPiWGsafkMHbu0ON2i214vTT++9/UP/oYvspK7MMKSb/2WlIvvrjH7RCq2qq4/7P7ea30NVJjU7luwnVcNfaq8L4/qFgPr94GNTvMWkULfxb2Ec8kEQgh+pzP66Fs/Vq2f7SMPZ+twwj4Sc/NZ+z8Mxgz9zTSc/OPbGsYmn2ba9n28UH2balDG5qcESmMmzeUEdMycSR0XuVT+/20/Pe/1P3zn7g3bsKSkkLqRReRcuklOEaP7lG8W2u38tcNf2XFgRWkxqZy7fhruXz05aQ6Uk/mMnTN74Hlvzd7L1VWmHcHnPotiD25FtZdkUQghIgoV2sLu1d/zPaPl1GxbQsAabn5jJw5h+KZp5A76ujQm21NHnauqWLHyoM0VDmxWBT549IYOSOLoimdJwWtNa7PNlD/5JO0LFkCPh+OSZNIveRiks8/H2vy8d9BtLepZhMPbnyQjw98jMPq4PwR53PVuKsYndazxBKyhr2w5BdmA7S4dJh9C8xeDAm921eSJAIhRL/RUldLybrVlK5bQ/nWTRiBAHHJKQybNJXCiVMYNmkqyZlZaK2p3tdC6fpqSj6tpqXOjcWiyB2dSuH4DAonpJOe+/nxl/0NDTS//jqNL72MZ+dOlN1O/CmnkLTwLBLPPAt7dlZIce5u2M3T25/mjbI38AQ8jEsfxwXFF3Be0Xnh6dCuYp3Z7mDX22BzwOSvwJSroGBOr4yAJolACNEvudta2bNhPXs+Xcv+LRtpa2wAIDV7KHnjJjB05BhyRo4mI7+Q+koXJeuq2buljoaDbQDEp8RQMC6docUpZBelkJ6bcKSvI6017m3baH7jTVqWLsG3bz8AjkmTSDxtPnHTphM3bSrWLob2PKzB3cBbe97itdLX2Fa3DYViUuYkFuQv4LT80xiVOgqr5cQau3WqZhesuh82vwg+J6QWwsTLYOz5kDv9hJNCxBKBUmoRcC9gBR7RWv+2w3oVXP9FwAlcr7X+9HjHlEQgxOCktab+QDn7Nm9g/5aNVO7cjqulGQCbPYbMohEMKRhGRl4BccnZuFoTqanQHNjRhLvNZ24XayWrMIms4cmk5cSTlpNAWk48sfE2vKWltCxZSuvSpbi2bIFAACwWYseMIX7aVGJHjyF2ZDExxcVddo1d2ljKe/ve48PyD9lSZxZxJdmTmJI1hamZUxmbPpYx6WPIjs8++TERPK1m53WbnoeyZaANmP11+OLvT+hwEUkESikrsAs4B6gA1gJXaq23tdvmi8A3MRPBHOBerfWc4x1XEoEQ0UFrTXPNIQ6W7KKqZBdVpbupO1COO5gcAKx2O4npQ4hPSsdiT8IIJOJqteJsUWgjFmVxgIolLimJpPQkEtPiSUyLJyHRgr3pELq8DKN0B8bOLVha67H5Xdj8bmzpacQMG4YtOxt7dja27Gxs2VlYU1KxJiZgSUqiweZlXes21jdt5rPqDZQ2lR6JK8meRG5i7tFPQi6Z8ZmkxKSQEptCcmwyyTHJxNnisFvs3ScNZz2ULIGMEZA344SuZ6QSwVzg51rrc4Pz/w9Aa/2bdtv8HVimtX42OL8TWKC1PtjVcSURCBHdnM1N1B8op/5ABQ1VlbTU1QY/NbTW16ENI4Sj2MyaOthQyoZZaBG8GQdvygoFGkCjgrfJY27X7Zd1uI/rdlO6izWdU51OHpaclcWN997TzTG6OPJxEkFo/cSemDygvN18Beav/u62yQOOSQRKqcXA4VEeWoMJIwVo6nC8jss6zg8BakP/E05KZ/GFY9/utj3e+q7WybUNbVu5tie+b7Rd25O5rsfsf9N9fzjRcw3rcg+tdVg+wOWY7wUOz18D3N9hmzeB+e3mlwAzQjz+w90t62R+Xbj+3lDiC8e+3W17vPVdrZNrK9dWrm3/ua69fW07+5x8naSuVQAF7ebzgcoT2KYrr4ewrLNt+srJnLsn+3a37fHWd7VOrm1o28q1PfF9o+3anux5e/Pafk443xHYMF8WLwQOYL4svkprvbXdNucDd3D0ZfF9WuvZYQnIPN863UUZmTg5cm3DR65t+Mi1NYXtHYHW2q+UugN4F/NNzGNa661KqVuD6x8C3sJMAiWY1UdvCFc8QQ+H+fjRTK5t+Mi1DR+5tgzABmVCCCF6VzjfEQghhBgAJBEIIUSUk0QghBBRThJBkFJqhFLqUaXUi5GOZTBQSiUopZ5QSv1DKXV1pOMZTOTfavgopS4K/pt9VSn1hUjH01cGRSJQSj2mlKpWSm3psHyRUmqnUqpEKfWD4x1Da12mtb4pvJEObD28zpcAL2qtbwG+3OfBDjA9ubbyb7VnenhtXwn+m70e+GoEwo2IQZEIgMeBRe0XBDu9+ytwHjAeuFIpNV4pNUkp9UaHT2gdlIvHCfE6YzYOPNx9SKAPYxyoHif0ayt65nF6fm1/HFwfFcLZ11Cf0Vp/qJQa3mHxbKBEa10GoJR6DrhQm53efamPQxwUenKdMVuN5wMbGDw/OMKmh9d2GyJkPbm2SqntwG+Bt3U3XeIPJoP5f9CuOrTrlFIqQyn1EDDtcE+pIiRdXeeXgUuVUn8jsl0mDGSdXlv5t9oruvp3+03gbOCyw41fo8GgeCLoQmcdfHfZek5rXQdEzX/4XtTpddZatxH+luKDXVfXVv6tnryuru19wH19HUykDeYngpPp0E6ETq5z+Mi1DR+5tu0M5kSwFhillCpSSsUAVwCvRTimwUiuc/jItQ0fubbtDIpEoJR6FlgFjFFKVSilbtJa+zF7Nn0X2A680L7nU9Fzcp3DR65t+Mi17Z50OieEEFFuUDwRCCGEOHGSCIQQIspJIhBCiCgniUAIIaKcJAIhhIhykgiEECLKSSIQQogoJ4lACCGinCQCIXpBcJyLfUqpb0Q6FiF6ShKBEL1Aa70Zs7+aayMdixA9JYlAiN5TDUyIdBBC9JQkAiF6z2+BWKXUsEgHIkRPSCIQohcopRYBCcCbyFOBGGAkEQhxkpRSDuD3wG3AZmBiZCMSomckEQhx8n4MPKm13oskAjEASSIQ4iQopcYA5wB/CS6SRCAGHBmYRgghopw8EQghRJSTRCCEEFFOEoEQQkQ5SQRCCBHlJBEIIUSUk0QghBBRThKBEEJEOUkEQggR5f4/Kwmzxshis1UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# a-l Node A/E's graph:\n",
    "treatment_cond = (waiting_distr['network']=='nc') & (waiting_distr['waiting_cost']=='l')\n",
    "QRE_data = QRE_a_l \n",
    "lamda_e = estimated_lamda[0]\n",
    "name= \"-a-l-\"\n",
    "\n",
    "i = 0   # Node D is always the indegree=1 (comparable)\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "ax.set_ylabel('Strategies')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "# ax.set_title(\"QRE for Nodes with Single Information Source\")\n",
    "ax.set_ylim(0, 1)\n",
    "ax.set_xscale('log')\n",
    "for j in range(6):\n",
    "    ax.plot(lambd,QRE_data[:,i,j], label='Turn'+str(j))\n",
    "    distr = float(waiting_distr[treatment_cond][column_names[j]])/100\n",
    "#     idx = find_nearest(QRE_a_l[:,i,j], distr) # this is to find the closes dot on the QRE line\n",
    "#     ax.scatter(lambd[idx], distr, marker='o', s=100)\n",
    "#     ax.scatter(lamda_e, distr, marker='o', s=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cee774da",
   "metadata": {},
   "source": [
    "# Estimate lambda\n",
    "\n",
    "-[Return](#Content)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "389c86a4",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>network</th>\n",
       "      <th>waiting_cost</th>\n",
       "      <th>participant.code</th>\n",
       "      <th>.player.type</th>\n",
       "      <th>.player.period</th>\n",
       "      <th>date</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>1tkgpojc</td>\n",
       "      <td>a</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>1tkgpojc</td>\n",
       "      <td>a</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>1tkgpojc</td>\n",
       "      <td>b</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>1tkgpojc</td>\n",
       "      <td>b</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>1tkgpojc</td>\n",
       "      <td>b</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1434</th>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>z1pxbhxi</td>\n",
       "      <td>c</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1435</th>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>z1pxbhxi</td>\n",
       "      <td>d</td>\n",
       "      <td>2.0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1436</th>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>z1pxbhxi</td>\n",
       "      <td>d</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1437</th>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>z1pxbhxi</td>\n",
       "      <td>e</td>\n",
       "      <td>1.0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1438</th>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>z1pxbhxi</td>\n",
       "      <td>e</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1439 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     network waiting_cost participant.code .player.type  .player.period  date\n",
       "0          c            h         1tkgpojc            a             2.0     4\n",
       "1          c            h         1tkgpojc            a             3.0     2\n",
       "2          c            h         1tkgpojc            b             1.0     1\n",
       "3          c            h         1tkgpojc            b             2.0     4\n",
       "4          c            h         1tkgpojc            b             3.0     1\n",
       "...      ...          ...              ...          ...             ...   ...\n",
       "1434      nc            l         z1pxbhxi            c             3.0     1\n",
       "1435      nc            l         z1pxbhxi            d             2.0     5\n",
       "1436      nc            l         z1pxbhxi            d             3.0     3\n",
       "1437      nc            l         z1pxbhxi            e             1.0     5\n",
       "1438      nc            l         z1pxbhxi            e             2.0     3\n",
       "\n",
       "[1439 rows x 6 columns]"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Step 4 b. Use the calculated QRE to estimate logL\n",
    "# datafolder = \"C:\\\\Users\\\\xinxi\\\\Purdue\\\\EffectiveSocialLearningProject\\\\DataAnalysis\\\\RawData\\\\Session_Formal\"\n",
    "datafolder = \"..\\\\RawData\\\\Session_Formal\"\n",
    "datafolder2 = \"..\\\\ImportedData\\\\\"\n",
    "outputfolder = \"..\\\\Output_Figures\\\\\" \n",
    "\n",
    "# Import data\n",
    "\n",
    "data  = pd.read_csv(datafolder2+\"02-Experiment-Clean-Data.csv\")\n",
    "\n",
    "for col in data.columns:\n",
    "    if type(data[col].unique()[1]) == str:\n",
    "        data[col] = data[col].str.lower()\n",
    "\n",
    "# Change the rounds into matches  \n",
    "data.loc[data['app_name']=='pdcn', 'match'] = data['.subsession.round_number']\n",
    "condition = data['app_name']=='dcn'\n",
    "data.loc[condition, 'match'] = ((data.loc[condition, '.subsession.round_number'] -1)/ 3).astype(int) +1 \n",
    "condition = (data['app_name']=='dcn') & (data['date']=='03/19/2021')\n",
    "data.loc[condition, 'match'] = ((data.loc[condition, '.subsession.round_number'] -1)/ 4).astype(int) +1 \n",
    "# data['match'] = data['.subsession.round_number']\n",
    "data[['match', 'app_name', '.subsession.round_number']]\n",
    "\n",
    "# DataExperiment= data[data['app_name']=='dcn'] \n",
    "DataExperiment= data[(data['app_name']=='dcn') & (data['.subsession.round_number']>=1)]\n",
    "\n",
    "\n",
    "# Count any variable will be the same\n",
    "\n",
    "BySessions = DataExperiment.groupby(['network', 'waiting_cost','session.code',\n",
    "                                     '.player.type','.player.period']).count().reset_index()\n",
    "BySessions = BySessions[['network', 'waiting_cost','session.code',\n",
    "                                     '.player.type','.player.period','date']]\n",
    "\n",
    "ByIndividuals = DataExperiment.groupby(['network', 'waiting_cost','participant.code',\n",
    "                                     '.player.type','.player.period']).count().reset_index()\n",
    "ByIndividuals = ByIndividuals[['network', 'waiting_cost','participant.code',\n",
    "                                     '.player.type','.player.period','date']]\n",
    "\n",
    "# BySessions['session.code'].unique()\n",
    "ByIndividuals\n",
    "# BySessions.pivot(index=['network', 'waiting_cost','session.code','.player.type'], columns='.player.period')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "c430a884",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[15.16716888,  8.2620045 ],\n",
       "       [ 3.38961797,  5.97560538]])"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# By treatments\n",
    "\n",
    "QREs =np.array([[QRE_a_l, QRE_a_h], [QRE_b_l, QRE_b_h]])\n",
    "\n",
    "nn = 200\n",
    "EstimatedL =  np.empty((2,2))\n",
    "EstimatedLogl =  np.empty((2,2))\n",
    "for n,network in enumerate(['nc', 'c']):\n",
    "    for l,waitingcost in enumerate(['l','h']):\n",
    "        logL =  np.zeros(nn)\n",
    "        for i in range(nn):\n",
    "            QRE_lamda=QREs[n,l][i]\n",
    "            for pos, node in enumerate(['a','b','c','d','e']):\n",
    "                for turn in range(6):\n",
    "                    freq = BySessions.loc[(BySessions['network']==network) & \n",
    "                       (BySessions['waiting_cost']==waitingcost) &\n",
    "                      (BySessions['.player.type']==node) & \n",
    "                     (BySessions['.player.period']==turn) , 'date' ].sum()\n",
    "                    logL[i] += freq*np.log(QRE_lamda[pos,turn])\n",
    "        logL = logL[~np.isnan(logL)]\n",
    "        max_l = np.argmax(logL)\n",
    "        EstimatedLogl[n,l] = logL[max_l]\n",
    "        EstimatedL[n,l] = lambd[max_l]\n",
    "EstimatedL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "d18c919e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[15.16716888,  8.2620045 ],\n",
       "       [ 3.38961797,  5.97560538]])"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Normalize the payoffs by dividing 70 gives me reasonable lambda \n",
    "EstimatedL\n",
    "\n",
    "# For all 30 rounds\n",
    "\n",
    "# array([[15.16716888,  8.2620045 ],\n",
    "#        [ 3.38961797,  5.97560538]])\n",
    "# For latter 15 rounds\n",
    "\n",
    "# array([[67.86694366,  8.95903651],\n",
    "#        [ 3.38961797,  5.97560538]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "f933dfc7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2261.51087696,  -750.97797749],\n",
       "       [-2662.99031181,  -907.86025399]])"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "EstimatedLogl  # because logL also depends on how many observations I have\n",
    "\n",
    "# For all 30 rounds\n",
    "# array([[-2261.51087696,  -750.97797749],\n",
    "#        [-2662.99031181,  -907.86025399]])\n",
    "# For latter 15 rounds\n",
    "# array([[-1250.66311514,  -383.79953918],\n",
    "#        [-1419.69653271,  -483.66594404]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "c41309d3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[8.95903651 6.74754405]\n",
      " [8.95903651 9.32930403]]\n",
      "[[ -913.07553497  -327.3827763 ]\n",
      " [-1026.52455389  -324.81681414]]\n"
     ]
    }
   ],
   "source": [
    "# By treatments and information sources: multiple sources \n",
    "\n",
    "QREs =np.array([[QRE_a_l, QRE_a_h], [QRE_b_l, QRE_b_h]])\n",
    "\n",
    "nn = 200\n",
    "EstimatedL =  np.empty((2,2))\n",
    "EstimatedLogl =  np.empty((2,2))\n",
    "for n,network in enumerate(['nc', 'c']):\n",
    "    for l,waitingcost in enumerate(['l','h']):\n",
    "        logL =  np.zeros(nn)\n",
    "        for i in range(nn):\n",
    "            QRE_lamda=QREs[n,l][i]\n",
    "            if n=='nc':\n",
    "                list_infor = ['b','c']\n",
    "            else :\n",
    "                list_infor = ['b','a']\n",
    "            for pos, node in enumerate(list_infor):\n",
    "                for turn in range(6):\n",
    "                    freq = BySessions.loc[(BySessions['network']==network) & \n",
    "                       (BySessions['waiting_cost']==waitingcost) &\n",
    "                      (BySessions['.player.type']==node) & \n",
    "                     (BySessions['.player.period']==turn) , 'date' ].sum()\n",
    "                    logL[i] += freq*np.log(QRE_lamda[pos,turn])\n",
    "        logL = logL[~np.isnan(logL)]\n",
    "        max_l = np.argmax(logL)\n",
    "        EstimatedLogl[n,l] = logL[max_l]\n",
    "        EstimatedL[n,l] = lambd[max_l]\n",
    "print(EstimatedL)\n",
    "print(EstimatedLogl)\n",
    "\n",
    "# 30 rounds\n",
    "# [[8.95903651 6.74754405]\n",
    "#  [8.95903651 9.32930403]]\n",
    "# [[ -913.07553497  -327.3827763 ]\n",
    "#  [-1026.52455389  -324.81681414]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "dd79641f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[11.89534067  8.95903651]\n",
      " [ 4.3219366   6.22257084]]\n",
      "[[-1352.09390136  -442.24833978]\n",
      " [-1589.60767198  -542.3661108 ]]\n"
     ]
    }
   ],
   "source": [
    "# By treatments and information sources: single sources \n",
    "\n",
    "QREs =np.array([[QRE_a_l, QRE_a_h], [QRE_b_l, QRE_b_h]])\n",
    "\n",
    "nn = 200\n",
    "EstimatedL =  np.empty((2,2))\n",
    "EstimatedLogl =  np.empty((2,2))\n",
    "for n,network in enumerate(['nc', 'c']):\n",
    "    for l,waitingcost in enumerate(['l','h']):\n",
    "        logL =  np.zeros(nn)\n",
    "        for i in range(nn):\n",
    "            QRE_lamda=QREs[n,l][i]\n",
    "            if n=='nc':\n",
    "                list_infor = ['a','d','e']\n",
    "            else :\n",
    "                list_infor = ['c','d','e']\n",
    "            for pos, node in enumerate(list_infor):\n",
    "                for turn in range(6):\n",
    "                    freq = BySessions.loc[(BySessions['network']==network) & \n",
    "                       (BySessions['waiting_cost']==waitingcost) &\n",
    "                      (BySessions['.player.type']==node) & \n",
    "                     (BySessions['.player.period']==turn) , 'date' ].sum()\n",
    "                    logL[i] += freq*np.log(QRE_lamda[pos,turn])\n",
    "        logL = logL[~np.isnan(logL)]\n",
    "        max_l = np.argmax(logL)\n",
    "        EstimatedLogl[n,l] = logL[max_l]\n",
    "        EstimatedL[n,l] = lambd[max_l]\n",
    "print(EstimatedL)\n",
    "print(EstimatedLogl)\n",
    "\n",
    "# 30 rounds:\n",
    "\n",
    "# [[11.89534067  8.95903651]\n",
    "#  [ 4.3219366   6.22257084]]\n",
    "# [[-1352.09390136  -442.24833978]\n",
    "#  [-1589.60767198  -542.3661108 ]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "id": "bfbf08b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>network</th>\n",
       "      <th>waiting_cost</th>\n",
       "      <th>session.code</th>\n",
       "      <th>.player.type</th>\n",
       "      <th>.player.period</th>\n",
       "      <th>date</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>hyi8cnuz</td>\n",
       "      <td>a</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>hyi8cnuz</td>\n",
       "      <td>a</td>\n",
       "      <td>1.0</td>\n",
       "      <td>33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>hyi8cnuz</td>\n",
       "      <td>a</td>\n",
       "      <td>2.0</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>hyi8cnuz</td>\n",
       "      <td>b</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>hyi8cnuz</td>\n",
       "      <td>b</td>\n",
       "      <td>1.0</td>\n",
       "      <td>31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>hyi8cnuz</td>\n",
       "      <td>b</td>\n",
       "      <td>2.0</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>hyi8cnuz</td>\n",
       "      <td>c</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>hyi8cnuz</td>\n",
       "      <td>c</td>\n",
       "      <td>1.0</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>hyi8cnuz</td>\n",
       "      <td>c</td>\n",
       "      <td>2.0</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>hyi8cnuz</td>\n",
       "      <td>c</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>hyi8cnuz</td>\n",
       "      <td>d</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>hyi8cnuz</td>\n",
       "      <td>d</td>\n",
       "      <td>1.0</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>hyi8cnuz</td>\n",
       "      <td>d</td>\n",
       "      <td>2.0</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>hyi8cnuz</td>\n",
       "      <td>d</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>hyi8cnuz</td>\n",
       "      <td>e</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>hyi8cnuz</td>\n",
       "      <td>e</td>\n",
       "      <td>1.0</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>hyi8cnuz</td>\n",
       "      <td>e</td>\n",
       "      <td>2.0</td>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   network waiting_cost session.code .player.type  .player.period  date\n",
       "0        c            h     hyi8cnuz            a             0.0     7\n",
       "1        c            h     hyi8cnuz            a             1.0    33\n",
       "2        c            h     hyi8cnuz            a             2.0    20\n",
       "3        c            h     hyi8cnuz            b             0.0     6\n",
       "4        c            h     hyi8cnuz            b             1.0    31\n",
       "5        c            h     hyi8cnuz            b             2.0    23\n",
       "6        c            h     hyi8cnuz            c             0.0    11\n",
       "7        c            h     hyi8cnuz            c             1.0    22\n",
       "8        c            h     hyi8cnuz            c             2.0    26\n",
       "9        c            h     hyi8cnuz            c             3.0     1\n",
       "10       c            h     hyi8cnuz            d             0.0    11\n",
       "11       c            h     hyi8cnuz            d             1.0    20\n",
       "12       c            h     hyi8cnuz            d             2.0    27\n",
       "13       c            h     hyi8cnuz            d             3.0     2\n",
       "14       c            h     hyi8cnuz            e             0.0     8\n",
       "15       c            h     hyi8cnuz            e             1.0    23\n",
       "16       c            h     hyi8cnuz            e             2.0    29"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# BySessions['session.code'].unique()\n",
    "\n",
    "ss = \"hyi8cnuz\"\n",
    "BySessions[BySessions['session.code']==ss]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "id": "aa7ddccb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# By Sessions\n",
    "\n",
    "QREs =np.array([[QRE_a_l, QRE_a_h], [QRE_b_l, QRE_b_h]])\n",
    "\n",
    "nn = 200\n",
    "Sessions = BySessions['session.code'].unique()\n",
    "outcome = pd.DataFrame(columns = [\"SessionCode\", \"Network\", \"WaitingCost\",\"EstimatedL\",\"EstimatedLogl\"])\n",
    "\n",
    "EstimatedLogl =  np.empty((len(Sessions),5))\n",
    "for s_n, ss in enumerate(Sessions):\n",
    "    EstimatedLogl[s_n, 0]= s_n\n",
    "    data = BySessions[BySessions['session.code']==ss]\n",
    "    if BySessions[BySessions['session.code']==ss].network.unique()[0]=='c': \n",
    "        n = 1\n",
    "        \n",
    "    else :\n",
    "        n = 0 \n",
    "    \n",
    "    if BySessions[BySessions['session.code']==ss].waiting_cost.unique()[0]=='l':\n",
    "        l = 0\n",
    "    else :\n",
    "        l = 1\n",
    "    EstimatedLogl[s_n, 1]= n\n",
    "    EstimatedLogl[s_n, 2]= l\n",
    "    logL =  np.zeros(nn)\n",
    "    for i in range(nn):\n",
    "        QRE_lamda=QREs[n,l][i]\n",
    "        for pos, node in enumerate(['a','b','c','d','e']):\n",
    "            for turn in range(6):\n",
    "                freq = data.loc[(data['.player.type']==node) & \n",
    "                 (data['.player.period']==turn) , 'date' ].sum()\n",
    "                logL[i] += freq*np.log(QRE_lamda[pos,turn])\n",
    "    logL = logL[~np.isnan(logL)]\n",
    "    max_l = np.argmax(logL)            \n",
    "    EstimatedLogl[s_n, 3]= lambd[max_l]\n",
    "    EstimatedLogl[s_n, 4]= logL[max_l]            \n",
    "                \n",
    "                    \n",
    "#     for l,waitingcost in enumerate(['l','h']):\n",
    "#         logL =  np.zeros(nn)\n",
    "#         for i in range(nn):\n",
    "#             QRE_lamda=QREs[n,l][i]\n",
    "#             for pos, node in enumerate(['a','b','c','d','e']):\n",
    "#                 for turn in range(6):\n",
    "#                     freq = BySessions.loc[(BySessions['network']==network) & \n",
    "#                        (BySessions['waiting_cost']==waitingcost) &\n",
    "#                       (BySessions['.player.type']==node) & \n",
    "#                      (BySessions['.player.period']==turn) , 'date' ].sum()\n",
    "#                     logL[i] += freq*np.log(QRE_lamda[pos,turn])\n",
    "#         logL = logL[~np.isnan(logL)]\n",
    "#         max_l = np.argmax(logL)\n",
    "#         EstimatedLogl[n,l] = logL[max_l]\n",
    "#         EstimatedL[n,l] = lambd[max_l]\n",
    "# EstimatedL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "id": "6379b610",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   0.   ,    1.   ,    1.   ,    7.026, -430.157],\n",
       "       [   1.   ,    1.   ,    1.   ,    4.88 , -473.363],\n",
       "       [   2.   ,    1.   ,    0.   ,    0.1  , -537.888],\n",
       "       [   3.   ,    1.   ,    0.   ,   13.987, -475.817],\n",
       "       [   4.   ,    1.   ,    0.   ,    1.508, -536.496],\n",
       "       [   5.   ,    1.   ,    0.   ,    8.262, -512.119],\n",
       "       [   6.   ,    1.   ,    0.   ,    1.773, -536.055],\n",
       "       [   7.   ,    0.   ,    1.   ,    8.262, -368.741],\n",
       "       [   8.   ,    0.   ,    1.   ,    7.934, -382.004],\n",
       "       [   9.   ,    0.   ,    0.   ,    0.789, -537.438],\n",
       "       [  10.   ,    0.   ,    0.   ,    5.292, -534.66 ],\n",
       "       [  11.   ,    0.   ,    0.   ,   45.267, -645.031],\n",
       "       [  12.   ,    0.   ,    0.   ,   62.587, -482.719]])"
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.set_printoptions(suppress=True)\n",
    "EstimatedLogl.round(3)\n",
    "\n",
    "# 30 rounds:\n",
    "# array([[   0.   ,    1.   ,    1.   ,    7.026, -430.157],\n",
    "#        [   1.   ,    1.   ,    1.   ,    4.88 , -473.363],\n",
    "#        [   2.   ,    1.   ,    0.   ,    0.1  , -537.888],\n",
    "#        [   3.   ,    1.   ,    0.   ,   13.987, -475.817],\n",
    "#        [   4.   ,    1.   ,    0.   ,    1.508, -536.496],\n",
    "#        [   5.   ,    1.   ,    0.   ,    8.262, -512.119],\n",
    "#        [   6.   ,    1.   ,    0.   ,    1.773, -536.055],\n",
    "#        [   7.   ,    0.   ,    1.   ,    8.262, -368.741],\n",
    "#        [   8.   ,    0.   ,    1.   ,    7.934, -382.004],\n",
    "#        [   9.   ,    0.   ,    0.   ,    0.789, -537.438],\n",
    "#        [  10.   ,    0.   ,    0.   ,    5.292, -534.66 ],\n",
    "#        [  11.   ,    0.   ,    0.   ,   45.267, -645.031],\n",
    "#        [  12.   ,    0.   ,    0.   ,   62.587, -482.719]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "7be85ad8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>network</th>\n",
       "      <th>waiting_cost</th>\n",
       "      <th>participant.code</th>\n",
       "      <th>.player.type</th>\n",
       "      <th>.player.period</th>\n",
       "      <th>date</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>1tkgpojc</td>\n",
       "      <td>a</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>1tkgpojc</td>\n",
       "      <td>a</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>1tkgpojc</td>\n",
       "      <td>b</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>1tkgpojc</td>\n",
       "      <td>b</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>1tkgpojc</td>\n",
       "      <td>b</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1434</th>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>z1pxbhxi</td>\n",
       "      <td>c</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1435</th>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>z1pxbhxi</td>\n",
       "      <td>d</td>\n",
       "      <td>2.0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1436</th>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>z1pxbhxi</td>\n",
       "      <td>d</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1437</th>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>z1pxbhxi</td>\n",
       "      <td>e</td>\n",
       "      <td>1.0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1438</th>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>z1pxbhxi</td>\n",
       "      <td>e</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1439 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     network waiting_cost participant.code .player.type  .player.period  date\n",
       "0          c            h         1tkgpojc            a             2.0     4\n",
       "1          c            h         1tkgpojc            a             3.0     2\n",
       "2          c            h         1tkgpojc            b             1.0     1\n",
       "3          c            h         1tkgpojc            b             2.0     4\n",
       "4          c            h         1tkgpojc            b             3.0     1\n",
       "...      ...          ...              ...          ...             ...   ...\n",
       "1434      nc            l         z1pxbhxi            c             3.0     1\n",
       "1435      nc            l         z1pxbhxi            d             2.0     5\n",
       "1436      nc            l         z1pxbhxi            d             3.0     3\n",
       "1437      nc            l         z1pxbhxi            e             1.0     5\n",
       "1438      nc            l         z1pxbhxi            e             2.0     3\n",
       "\n",
       "[1439 rows x 6 columns]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ByIndividuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "8e4154a6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "LogL\n",
      "[[  0.      1.      1.      3.827 -49.578]\n",
      " [  1.      1.      1.     12.387 -31.844]\n",
      " [  2.      1.      1.      8.262 -40.659]\n",
      " [  3.      1.      1.      8.959 -38.227]\n",
      " [  4.      1.      1.      6.748 -43.634]\n",
      " [  5.      1.      1.      5.082 -46.855]\n",
      " [  6.      1.      1.      4.88  -47.586]\n",
      " [  7.      1.      1.      5.511 -46.057]\n",
      " [  8.      1.      1.      5.292 -46.467]\n",
      " [  9.      1.      1.      5.082 -47.245]\n",
      " [ 10.      1.      1.      4.501 -48.254]\n",
      " [ 11.      1.      1.      3.827 -49.473]\n",
      " [ 12.      1.      1.      5.738 -45.534]\n",
      " [ 13.      1.      1.      4.88  -47.484]\n",
      " [ 14.      1.      1.      8.603 -39.462]\n",
      " [ 15.      1.      1.      3.255 -50.619]\n",
      " [ 16.      1.      1.      6.748 -43.885]\n",
      " [ 17.      1.      1.      5.292 -46.517]\n",
      " [ 18.      1.      1.      4.88  -47.593]\n",
      " [ 19.      1.      1.     12.387 -32.332]\n",
      " [ 20.      1.      0.     47.138 -33.592]\n",
      " [ 21.      1.      0.     38.497 -36.583]\n",
      " [ 22.      1.      0.      8.262 -51.193]\n",
      " [ 23.      1.      0.     10.116 -49.9  ]\n",
      " [ 24.      1.      0.      7.619 -51.413]\n",
      " [ 25.      1.      0.     15.794 -46.437]\n",
      " [ 26.      1.      0.      5.082 -52.604]\n",
      " [ 27.      1.      0.      3.002 -53.316]\n",
      " [ 28.      1.      0.     34.093 -38.254]\n",
      " [ 29.      1.      0.      0.1   -53.778]\n",
      " [ 30.      1.      0.     24.658 -42.183]\n",
      " [ 31.      1.      0.      0.1   -53.782]\n",
      " [ 32.      1.      0.     10.97  -49.05 ]\n",
      " [ 33.      1.      0.     10.116 -49.541]\n",
      " [ 34.      1.      0.     26.738 -40.987]\n",
      " [ 35.      1.      0.     27.843 -40.357]\n",
      " [ 36.      1.      0.      0.1   -53.937]\n",
      " [ 37.      1.      0.      3.53  -53.151]\n",
      " [ 38.      1.      0.     22.74  -42.675]\n",
      " [ 39.      1.      0.     12.387 -48.661]\n",
      " [ 40.      1.      0.      7.619 -51.385]\n",
      " [ 41.      1.      0.     15.794 -46.556]\n",
      " [ 42.      1.      0.      5.292 -52.566]\n",
      " [ 43.      1.      0.     17.126 -45.923]\n",
      " [ 44.      1.      0.      4.88  -52.747]\n",
      " [ 45.      1.      0.      8.959 -50.22 ]\n",
      " [ 46.      1.      0.      9.329 -50.225]\n",
      " [ 47.      1.      0.     30.193 -39.613]\n",
      " [ 48.      1.      0.      3.676 -53.158]\n",
      " [ 49.      1.      0.     12.387 -48.211]\n",
      " [ 50.      1.      0.      0.1   -53.834]\n",
      " [ 51.      1.      0.      0.1   -53.915]\n",
      " [ 52.      1.      0.      1.282 -53.672]\n",
      " [ 53.      1.      0.      0.1   -53.858]\n",
      " [ 54.      1.      0.      0.1   -53.937]\n",
      " [ 55.      1.      0.      0.1   -53.822]\n",
      " [ 56.      1.      0.     15.167 -46.913]\n",
      " [ 57.      1.      0.      0.1   -53.878]\n",
      " [ 58.      1.      0.      8.959 -50.475]\n",
      " [ 59.      1.      0.      4.501 -52.864]\n",
      " [ 60.      1.      0.     13.987 -47.267]\n",
      " [ 61.      1.      0.     11.895 -48.528]\n",
      " [ 62.      1.      0.     12.387 -48.57 ]\n",
      " [ 63.      1.      0.      0.1   -53.805]\n",
      " [ 64.      1.      0.      0.1   -53.89 ]\n",
      " [ 65.      1.      0.     10.97  -49.21 ]\n",
      " [ 66.      1.      0.      7.619 -51.407]\n",
      " [ 67.      1.      0.      0.1   -53.787]\n",
      " [ 68.      1.      0.      3.53  -53.151]\n",
      " [ 69.      1.      0.      0.1   -53.944]\n",
      " [ 70.      0.      1.      4.501 -46.43 ]\n",
      " [ 71.      0.      1.      8.603 -35.552]\n",
      " [ 72.      0.      1.      6.748 -40.93 ]\n",
      " [ 73.      0.      1.      7.619 -38.362]\n",
      " [ 74.      0.      1.      6.223 -42.452]\n",
      " [ 75.      0.      1.      8.959 -34.84 ]\n",
      " [ 76.      0.      1.     14.565 -23.949]\n",
      " [ 77.      0.      1.      9.329 -33.738]\n",
      " [ 78.      0.      1.      9.329 -33.325]\n",
      " [ 79.      0.      1.     12.899 -25.334]\n",
      " [ 80.      0.      1.      7.619 -38.797]\n",
      " [ 81.      0.      1.     11.423 -29.732]\n",
      " [ 82.      0.      1.     12.899 -26.397]\n",
      " [ 83.      0.      1.      9.715 -32.397]\n",
      " [ 84.      0.      1.      5.976 -41.631]\n",
      " [ 85.      0.      1.      8.262 -36.514]\n",
      " [ 86.      0.      1.      5.511 -43.589]\n",
      " [ 87.      0.      1.      7.317 -39.64 ]\n",
      " [ 88.      0.      1.      4.88  -45.025]\n",
      " [ 89.      0.      1.      7.619 -38.079]\n",
      " [ 90.      0.      0.     67.867 -64.598]\n",
      " [ 91.      0.      0.     17.126 -66.768]\n",
      " [ 92.      0.      0.     12.387 -51.864]\n",
      " [ 93.      0.      0.     86.534 -36.802]\n",
      " [ 94.      0.      0.     30.193 -46.49 ]\n",
      " [ 95.      0.      0.     38.497 -43.436]\n",
      " [ 96.      0.      0.     45.267 -51.697]\n",
      " [ 97.      0.      0.     51.114 -36.872]\n",
      " [ 98.      0.      0.     36.969 -62.922]\n",
      " [ 99.      0.      0.     62.587 -41.057]\n",
      " [100.      0.      0.      2.261 -53.69 ]\n",
      " [101.      0.      0.     26.738 -49.106]\n",
      " [102.      0.      0.     45.267 -44.073]\n",
      " [103.      0.      0.      0.1   -53.79 ]\n",
      " [104.      0.      0.     27.843 -63.808]\n",
      " [105.      0.      0.     83.099 -64.82 ]\n",
      " [106.      0.      0.    105.956 -35.073]\n",
      " [107.      0.      0.     32.74  -62.446]\n",
      " [108.      0.      0.     97.712 -42.509]\n",
      " [109.      0.      0.     32.74  -47.114]\n",
      " [110.      0.      0.    135.099 -29.886]\n",
      " [111.      0.      0.     15.794 -52.157]\n",
      " [112.      0.      0.     60.103 -47.718]\n",
      " [113.      0.      0.      0.1   -53.799]\n",
      " [114.      0.      0.     40.088 -58.073]\n",
      " [115.      0.      0.     45.267 -44.878]\n",
      " [116.      0.      0.     15.794 -51.745]\n",
      " [117.      0.      0.     73.593 -49.118]\n",
      " [118.      0.      0.     16.447 -50.824]\n",
      " [119.      0.      0.     20.138 -51.461]\n",
      " [120.      0.      0.     45.267 -43.38 ]\n",
      " [121.      0.      0.      0.1   -53.806]\n",
      " [122.      0.      0.     32.74  -50.561]\n",
      " [123.      0.      0.     49.086 -44.517]\n",
      " [124.      0.      0.      8.262 -53.22 ]\n",
      " [125.      0.      0.     17.834 -68.978]\n",
      " [126.      0.      0.     86.534 -43.773]\n",
      " [127.      0.      0.     28.994 -48.239]\n",
      " [128.      0.      0.     76.634 -39.191]\n",
      " [129.      0.      0.     35.502 -57.524]]\n"
     ]
    }
   ],
   "source": [
    "# By Individuals\n",
    "\n",
    "\n",
    "QREs =np.array([[QRE_a_l, QRE_a_h], [QRE_b_l, QRE_b_h]])\n",
    "\n",
    "nn = 200\n",
    "Sessions = ByIndividuals['participant.code'].unique()\n",
    "outcome = pd.DataFrame(columns = [\"ParticipantCode\", \"Network\", \"WaitingCost\",\"EstimatedL\",\"EstimatedLogl\"])\n",
    "\n",
    "EstimatedLogl =  np.empty((len(Sessions),5))\n",
    "for s_n, ss in enumerate(Sessions):\n",
    "    print(s_n)\n",
    "    EstimatedLogl[s_n, 0]= s_n\n",
    "    data = ByIndividuals[ByIndividuals['participant.code']==ss]\n",
    "    if ByIndividuals[ByIndividuals['participant.code']==ss].network.unique()[0]=='c': \n",
    "        n = 1\n",
    "        \n",
    "    else :\n",
    "        n = 0 \n",
    "    \n",
    "    if ByIndividuals[ByIndividuals['participant.code']==ss].waiting_cost.unique()[0]=='l':\n",
    "        l = 0\n",
    "    else :\n",
    "        l = 1\n",
    "    EstimatedLogl[s_n, 1]= n\n",
    "    EstimatedLogl[s_n, 2]= l\n",
    "    logL =  np.zeros(nn)\n",
    "    for i in range(nn):\n",
    "        QRE_lamda=QREs[n,l][i]\n",
    "        for pos, node in enumerate(['a','b','c','d','e']):\n",
    "            for turn in range(6):\n",
    "                freq = data.loc[(data['.player.type']==node) & \n",
    "                 (data['.player.period']==turn) , 'date' ].sum()\n",
    "                logL[i] += freq*np.log(QRE_lamda[pos,turn])\n",
    "    logL = logL[~np.isnan(logL)]\n",
    "    max_l = np.argmax(logL)            \n",
    "    EstimatedLogl[s_n, 3]= lambd[max_l]\n",
    "    EstimatedLogl[s_n, 4]= logL[max_l]            \n",
    "    outcome.loc[len(outcome.index)] = [ss, n, l, lambd[max_l], logL[max_l]  ]\n",
    "                \n",
    "np.set_printoptions(suppress=True)\n",
    "print('LogL')\n",
    "print(EstimatedLogl.round(3))\n",
    "\n",
    "\n",
    "#     for l,waitingcost in enumerate(['l','h']):\n",
    "#         logL =  np.zeros(nn)\n",
    "#         for i in range(nn):\n",
    "#             QRE_lamda=QREs[n,l][i]\n",
    "#             for pos, node in enumerate(['a','b','c','d','e']):\n",
    "#                 for turn in range(6):\n",
    "#                     freq = ByIndividuals.loc[(ByIndividuals['network']==network) & \n",
    "#                        (ByIndividuals['waiting_cost']==waitingcost) &\n",
    "#                       (ByIndividuals['.player.type']==node) & \n",
    "#                      (ByIndividuals['.player.period']==turn) , 'date' ].sum()\n",
    "#                     logL[i] += freq*np.log(QRE_lamda[pos,turn])\n",
    "#         logL = logL[~np.isnan(logL)]\n",
    "#         max_l = np.argmax(logL)\n",
    "#         EstimatedLogl[n,l] = logL[max_l]\n",
    "#         EstimatedL[n,l] = lambd[max_l]\n",
    "# EstimatedL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "17617952",
   "metadata": {},
   "outputs": [],
   "source": [
    "outcome.to_csv(datafolder2+\"05-QRE-Calculation-Normalize-Indiv-Estimation.csv\",index=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "be596d7c",
   "metadata": {},
   "outputs": [],
   "source": [
    "outcome['Network'] = outcome['Network'].replace({0:'nc', 1:'c'})\n",
    "outcome['WaitingCost'] = outcome['WaitingCost'].replace({0:'l', 1:'h'})\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "bead36ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ParticipantCode</th>\n",
       "      <th>Network</th>\n",
       "      <th>WaitingCost</th>\n",
       "      <th>EstimatedL</th>\n",
       "      <th>EstimatedLogl</th>\n",
       "      <th>Treatment</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>129</th>\n",
       "      <td>z1pxbhxi</td>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>35.501872</td>\n",
       "      <td>-57.523582</td>\n",
       "      <td>nc-l</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>110</th>\n",
       "      <td>jttdu2x1</td>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>135.099352</td>\n",
       "      <td>-29.885545</td>\n",
       "      <td>nc-l</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>111</th>\n",
       "      <td>k90nedek</td>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>15.794012</td>\n",
       "      <td>-52.156601</td>\n",
       "      <td>nc-l</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>128</th>\n",
       "      <td>wvcq0ka1</td>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>76.634109</td>\n",
       "      <td>-39.190549</td>\n",
       "      <td>nc-l</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>126</th>\n",
       "      <td>vs2fh0eq</td>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>86.533831</td>\n",
       "      <td>-43.773118</td>\n",
       "      <td>nc-l</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>70lpvw7w</td>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>6.747544</td>\n",
       "      <td>-43.634328</td>\n",
       "      <td>c-h</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6t09y23e</td>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>8.959037</td>\n",
       "      <td>-38.227400</td>\n",
       "      <td>c-h</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>6ep3453x</td>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>8.262004</td>\n",
       "      <td>-40.658549</td>\n",
       "      <td>c-h</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>hlbiyt4b</td>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>4.500558</td>\n",
       "      <td>-48.254489</td>\n",
       "      <td>c-h</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1tkgpojc</td>\n",
       "      <td>c</td>\n",
       "      <td>h</td>\n",
       "      <td>3.827494</td>\n",
       "      <td>-49.578063</td>\n",
       "      <td>c-h</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>130 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    ParticipantCode Network WaitingCost  EstimatedL  EstimatedLogl Treatment\n",
       "129        z1pxbhxi      nc           l   35.501872     -57.523582      nc-l\n",
       "110        jttdu2x1      nc           l  135.099352     -29.885545      nc-l\n",
       "111        k90nedek      nc           l   15.794012     -52.156601      nc-l\n",
       "128        wvcq0ka1      nc           l   76.634109     -39.190549      nc-l\n",
       "126        vs2fh0eq      nc           l   86.533831     -43.773118      nc-l\n",
       "..              ...     ...         ...         ...            ...       ...\n",
       "4          70lpvw7w       c           h    6.747544     -43.634328       c-h\n",
       "3          6t09y23e       c           h    8.959037     -38.227400       c-h\n",
       "2          6ep3453x       c           h    8.262004     -40.658549       c-h\n",
       "10         hlbiyt4b       c           h    4.500558     -48.254489       c-h\n",
       "0          1tkgpojc       c           h    3.827494     -49.578063       c-h\n",
       "\n",
       "[130 rows x 6 columns]"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "outcome['Treatment'] = outcome['Network'] +'-'+ outcome['WaitingCost']\n",
    "outcome = outcome.sort_values(by=['Treatment'], ascending=False)\n",
    "outcome"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "8b6b3997",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "ax = outcome.hist(column='EstimatedL', by='Treatment',\n",
    "                    grid=False, figsize=(8,10), layout=(2,2), sharex=True,\n",
    "                    color='#86bf91', zorder=1, rwidth=.5)\n",
    "\n",
    "# ax = ax[0]\n",
    "\n",
    "for i,xx in enumerate(ax):\n",
    "    for j,x in enumerate(xx):\n",
    "    \n",
    "        # Despine\n",
    "        x.spines['right'].set_visible(False)\n",
    "        x.spines['top'].set_visible(False)\n",
    "        x.spines['left'].set_visible(False)\n",
    "\n",
    "        # Switch off ticks\n",
    "#         x.tick_params(axis=\"both\", which=\"both\", bottom=\"off\", top=\"off\", labelbottom=\"on\", left=\"off\", right=\"off\", labelleft=\"on\")\n",
    "        x.set_xticks(lambd)\n",
    "        x.set_xscale('log')\n",
    "    #     # Draw horizontal axis lines\n",
    "        vals = x.get_yticks()\n",
    "        for tick in vals:\n",
    "            x.axhline(y=tick, linestyle='dashed', alpha=0.4, color='#eeeeee', zorder=1)\n",
    "\n",
    "    #     # Set x-axis label\n",
    "        x.set_xlabel(\"$\\lambda$ distribution\", labelpad=20, weight='bold', size=12)\n",
    "\n",
    "    #     # Set y-axis label\n",
    "        if j == 0:\n",
    "            x.set_ylabel(\"Number of Subjects\", labelpad=50, weight='bold', size=12)\n",
    "\n",
    "    #     # Format y-axis label\n",
    "    #     x.yaxis.set_major_formatter(StrMethodFormatter('{x:,g}'))\n",
    "\n",
    "        x.tick_params(axis='x', rotation=0)\n",
    "\n",
    "\n",
    "plt.savefig(outputfolder+\"05-QRE-Calculation\\\\Normalize-Indvd-Lambda-Distr\"  , bbox_inches=\"tight\")  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "4838d1b7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "[<AxesSubplot:title={'center':'c-h'}> <AxesSubplot:title={'center':'c-l'}>]\n",
      "1\n",
      "[<AxesSubplot:title={'center':'nc-h'}>\n",
      " <AxesSubplot:title={'center':'nc-l'}>]\n"
     ]
    }
   ],
   "source": [
    "for i,x in enumerate(ax):\n",
    "    print(i)\n",
    "    print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "id": "4c8ea773",
   "metadata": {},
   "outputs": [],
   "source": [
    "# By Sessions, only later 15\n",
    "\n",
    "\n",
    "DataExperiment= data[(data['app_name']=='dcn') & (data['.subsession.round_number']>=15)]\n",
    "\n",
    "\n",
    "# Count any variable will be the same\n",
    "\n",
    "BySessions = DataExperiment.groupby(['network', 'waiting_cost','session.code',\n",
    "                                     '.player.type','.player.period']).count().reset_index()\n",
    "BySessions = BySessions[['network', 'waiting_cost','session.code',\n",
    "                                     '.player.type','.player.period','date']]\n",
    "\n",
    "QREs =np.array([[QRE_a_l, QRE_a_h], [QRE_b_l, QRE_b_h]])\n",
    "\n",
    "nn = 200\n",
    "Sessions = BySessions['session.code'].unique()\n",
    "outcome = pd.DataFrame(columns = [\"SessionCode\", \"Network\", \"WaitingCost\",\"EstimatedL\",\"EstimatedLogl\"])\n",
    "\n",
    "EstimatedLogl =  np.empty((len(Sessions),5))\n",
    "for s_n, ss in enumerate(Sessions):\n",
    "    EstimatedLogl[s_n, 0]= s_n\n",
    "    data_s = BySessions[BySessions['session.code']==ss]\n",
    "    if BySessions[BySessions['session.code']==ss].network.unique()[0]=='c': \n",
    "        n = 1\n",
    "        \n",
    "    else :\n",
    "        n = 0 \n",
    "    \n",
    "    if BySessions[BySessions['session.code']==ss].waiting_cost.unique()[0]=='l':\n",
    "        l = 0\n",
    "    else :\n",
    "        l = 1\n",
    "    EstimatedLogl[s_n, 1]= n\n",
    "    EstimatedLogl[s_n, 2]= l\n",
    "    logL =  np.zeros(nn)\n",
    "    for i in range(nn):\n",
    "        QRE_lamda=QREs[n,l][i]\n",
    "        for pos, node in enumerate(['a','b','c','d','e']):\n",
    "            for turn in range(6):\n",
    "                freq = data_s.loc[(data_s['.player.type']==node) & \n",
    "                 (data_s['.player.period']==turn) , 'date' ].sum()\n",
    "                logL[i] += freq*np.log(QRE_lamda[pos,turn])\n",
    "    logL = logL[~np.isnan(logL)]\n",
    "    max_l = np.argmax(logL)            \n",
    "    EstimatedLogl[s_n, 3]= lambd[max_l]\n",
    "    EstimatedLogl[s_n, 4]= logL[max_l]            \n",
    "                \n",
    "                    \n",
    "#     for l,waitingcost in enumerate(['l','h']):\n",
    "#         logL =  np.zeros(nn)\n",
    "#         for i in range(nn):\n",
    "#             QRE_lamda=QREs[n,l][i]\n",
    "#             for pos, node in enumerate(['a','b','c','d','e']):\n",
    "#                 for turn in range(6):\n",
    "#                     freq = BySessions.loc[(BySessions['network']==network) & \n",
    "#                        (BySessions['waiting_cost']==waitingcost) &\n",
    "#                       (BySessions['.player.type']==node) & \n",
    "#                      (BySessions['.player.period']==turn) , 'date' ].sum()\n",
    "#                     logL[i] += freq*np.log(QRE_lamda[pos,turn])\n",
    "#         logL = logL[~np.isnan(logL)]\n",
    "#         max_l = np.argmax(logL)\n",
    "#         EstimatedLogl[n,l] = logL[max_l]\n",
    "#         EstimatedL[n,l] = lambd[max_l]\n",
    "# EstimatedL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "id": "5d2f21f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   0.   ,    1.   ,    1.   ,    7.934, -219.579],\n",
       "       [   1.   ,    1.   ,    1.   ,    4.322, -257.881],\n",
       "       [   2.   ,    1.   ,    0.   ,    0.1  , -286.911],\n",
       "       [   3.   ,    1.   ,    0.   ,   14.565, -251.02 ],\n",
       "       [   4.   ,    1.   ,    0.   ,    1.773, -285.915],\n",
       "       [   5.   ,    1.   ,    0.   ,   12.387, -260.036],\n",
       "       [   6.   ,    1.   ,    0.   ,    0.216, -286.669],\n",
       "       [   7.   ,    0.   ,    1.   ,    8.959, -190.347],\n",
       "       [   8.   ,    0.   ,    1.   ,    8.959, -193.452],\n",
       "       [   9.   ,    0.   ,    0.   ,    4.88 , -285.247],\n",
       "       [  10.   ,    0.   ,    0.   ,   90.11 , -285.182],\n",
       "       [  11.   ,    0.   ,    0.   ,   49.086, -400.545],\n",
       "       [  12.   ,    0.   ,    0.   ,   79.801, -250.579]])"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.set_printoptions(suppress=True)\n",
    "EstimatedLogl.round(3)\n",
    "\n",
    "# Only later 15 rounds\n",
    "# Huge session differences, driven by individual differences? \n",
    "# array([[   0.   ,    1.   ,    1.   ,    7.934, -219.579],\n",
    "#        [   1.   ,    1.   ,    1.   ,    4.322, -257.881],\n",
    "#        [   2.   ,    1.   ,    0.   ,    0.1  , -286.911],\n",
    "#        [   3.   ,    1.   ,    0.   ,   14.565, -251.02 ],\n",
    "#        [   4.   ,    1.   ,    0.   ,    1.773, -285.915],\n",
    "#        [   5.   ,    1.   ,    0.   ,   12.387, -260.036],\n",
    "#        [   6.   ,    1.   ,    0.   ,    0.216, -286.669],\n",
    "#        [   7.   ,    0.   ,    1.   ,    8.959, -190.347],\n",
    "#        [   8.   ,    0.   ,    1.   ,    8.959, -193.452],\n",
    "#        [   9.   ,    0.   ,    0.   ,    4.88 , -285.247],\n",
    "#        [  10.   ,    0.   ,    0.   ,   90.11 , -285.182],\n",
    "#        [  11.   ,    0.   ,    0.   ,   49.086, -400.545],\n",
    "#        [  12.   ,    0.   ,    0.   ,   79.801, -250.579]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9e1b1512",
   "metadata": {},
   "outputs": [],
   "source": [
    "# By information source (only later 15 rounds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "26c56b90",
   "metadata": {},
   "outputs": [],
   "source": [
    "# By individual (only later 15 rounds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "3f750ce8",
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'p' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_9756/128723725.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     25\u001b[0m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mset_xscale\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'log'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     26\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 27\u001b[1;33m     \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlambd\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mp\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mj\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'Turn'\u001b[0m\u001b[1;33m+\u001b[0m\u001b[0mstr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mj\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     28\u001b[0m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlegend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     29\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'p' is not defined"
     ]
    },
    {
     "data": {
      "image/png": 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cQSBJHWcQSFLHGQSS1HEGgSR13EiDIMm+SS5MsiLJEROMs0+Sc5MsT3L6KOuRJK1pk1HNOMk84FPAM4CVwNlJTq6qC3rG2Qb4NLBvVV2a5P6jqkeSNNhQLYIkD0lyr/b/+yR5bbsRn8yewIqquriqbgVOAPbvG+dA4BtVdSlAVV05reolSets2ENDJwG3J9kF+DywM/DlKaZZAFzW072y7dfrocB9k5yW5JwkBw1ZjyRphgx7aOiOqlqd5AXAx6rqE0n+e4ppMqBfDVj+Y4GnAfcGzkxyVlVddLcZJYuBxQCLFi0asmRJ0jCGbRHcluRlwN8Bp7T97jnFNCuBHXu6FwKrBozz3ar6Y1VdDfwAeHT/jKpqSVWNVdXY/PnzhyxZkjSMYYPgEOCJwNFVdUmSnYEvTjHN2cCuSXZOsilwAHBy3zj/B9grySZJ7gM8HvjF8OVLktbVUIeGquqCJG8GFrXdlwDvm2Ka1UkOB04F5gFLq2p5ksPa4cdU1S+SfBf4OXAH8C9Vdf7avxxJ0nSlqv+w/YCRkucBHwI2raqdk+wBvLOqnj/i+tYwNjZWy5Ytm+3FStIGLck5VTU2aNiwh4aOpLkc9HqAqjqX5sohSdIGbtggWF1VN/T1m7opIUla7w17+ej5SQ4E5iXZFXgt8OPRlSVJmi3DtgheAzwCuAX4CvAH4PUjqkmSNIuGvWroT8Db2j9J0kZk0iBI8rGqen2SbzLgnMBcXDUkSZpZU7UIvtD++6FRFyJJmhuTBkFVndP+6+8ESNJGaqhzBEnOY81DQzcAy4B3V9U1M12YJGl2DHv56HeA27nr0dMH0Dxd9AbgWOB5M16ZJGlWDBsET66qJ/d0n5fkjKp6cpK/HUVhkqTZMex9BFskefx4R5I9gS3aztUzXpUkadYM2yJ4FbA0yfjG/0bgVUk2B947ksokSbNi2BvKzgYemWRrmieWXt8z+MRRFCZJmh3D/nj9A5J8Hjihqq5PsnuSV464NknSLBj2HMGxND8ws0PbfRE+a0iSNgrDBsF2VXUiza+IUVWraS4nlSRt4IYNgj8m2Zb2prIkT6C5h0CStIEb9qqhN9D88PxDkpwBzAdePLKqJEmzZtggWA7sDexGc0fxhQzfmpAkrceG3ZifWVWrq2p5VZ1fVbcBZ46yMEnS7Jjq9wgeCCwA7p3kMTStAYCtgPuMuDZJ0iyY6tDQs4CDgYXAR3r63wi8dUQ1SZJm0VS/R3AccFySF1bVSbNUkyRpFg37iImTkjyH5gfsN+vp/85RFSZJmh3DPmLiGOClwGtozhO8GNhphHVJkmbJsFcNPamqDgKuq6qjgCcCO46uLEnSbBk2CG5u//1Tkh2A24CdR1OSJGk2DXtD2TeTbAN8EPgpzaMmPjeqoiRJs2fKIEhyD+D77W8QnJTkFGCzqvJZQ5K0EZjy0FBV3QF8uKf7FkNAkjYew54j+F6SFybJ1KNKkjYk03n66ObA6iQ301xCWlW11cgqkyTNimFvKNty1IVIkubGsDeUfX+YfpKkDc+kQZBksyT3A7ZLct8k92v/HsRdv1882fT7JrkwyYokR0wy3uOS3J7kRdN+BZKkdTLVoaG/p/mR+h2Ac3r63wh8arIJk8xrx3kGsBI4O8nJVXXBgPHeD5w6rcolSTNiqkNDPwaeBPxjVT0YOAo4Hzgd+PIU0+4JrKiqi6vqVuAEYP8B470GOAm4cjqFS5JmxlRB8Fnglqr6RJKnAu8FjqP54folU0y7ALisp3tl2+9OSRYALwCOmWxGSRYnWZZk2VVXXTXFYiVJ0zFVEMyrqmvb/78UWFJVJ1XVO4Bdpph20D0H1df9MeDNVXX7ZDOqqiVVNVZVY/Pnz59isZKk6ZjqHMG8JJtU1WrgacDiaUy7krs/oXQhsKpvnDHghPY+te2AZydZXVX/PlXhkqSZMdXG/CvA6UmuBv4M/BAgyS40h4cmczawa5Kdgd8BBwAH9o5QVXc+wTTJscAphoAkza6pfqry6PZ+ge2B71XV+KGde9Cc5J1s2tVJDqe5GmgesLSqlic5rB0+6XkBSdLsyF3b9g3D2NhYLVu2bK7LkKQNSpJzqmps0LBhHzonSdpIGQSS1HEGgSR1nEEgSR1nEEhSxxkEktRxBoEkdZxBIEkdZxBIUscZBJLUcQaBJHWcQSBJHWcQSFLHGQSS1HEGgSR1nEEgSR1nEEhSxxkEktRxBoEkdZxBIEkdZxBIUscZBJLUcQaBJHWcQSBJHWcQSFLHGQSS1HEGgSR1nEEgSR1nEEhSxxkEktRxBoEkdZxBIEkdZxBIUscZBJLUcSMNgiT7JrkwyYokRwwY/vIkP2//fpzk0aOsR5K0ppEFQZJ5wKeA/YDdgZcl2b1vtEuAvavqUcC7gCWjqkeSNNgoWwR7Aiuq6uKquhU4Adi/d4Sq+nFVXdd2ngUsHGE9kqQBRhkEC4DLerpXtv0m8krgOyOsR5I0wCYjnHcG9KuBIyZ/RRMET5lg+GJgMcCiRYtmqj5JEqNtEawEduzpXgis6h8pyaOAfwH2r6prBs2oqpZU1VhVjc2fP38kxUpSV40yCM4Gdk2yc5JNgQOAk3tHSLII+Abwiqq6aIS1SJImMLJDQ1W1OsnhwKnAPGBpVS1Pclg7/Bjgn4BtgU8nAVhdVWOjqkmStKZUDTxsv94aGxurZcuWzXUZkrRBSXLORDva3lksSR1nEEhSxxkEktRxBoEkdZxBIEkdZxBIUscZBJLUcQaBJHWcQSBJHWcQSFLHGQSS1HEGgSR1nEEgSR1nEEhSxxkEktRxBoEkdZxBIEkdZxBIUscZBJLUcQaBJHWcQSBJHWcQSFLHGQSS1HEGgSR1nEEgSR1nEEhSxxkEktRxBoEkdZxBIEkdZxBIUscZBJLUcQaBJHWcQSBJHWcQSFLHGQSS1HEjDYIk+ya5MMmKJEcMGJ4kH2+H/zzJX46yHknSmkYWBEnmAZ8C9gN2B16WZPe+0fYDdm3/FgOfGVU9kqTBRtki2BNYUVUXV9WtwAnA/n3j7A8cX42zgG2SbD/CmiRJfTYZ4bwXAJf1dK8EHj/EOAuAy3tHSrKYpsUAcFOSK4Ab1qKm7YCr12I6rZ2tWbv3aX23vr6uuahr1MscxfxnYp7rOo+1nX5dtmE7TTRglEGQAf1qLcahqpYAS+6cKFlSVYv7x5uyoGRZVY1NdzqtnbV9n9Z36+vrmou6Rr3MUcx/Jua5rvNY37Zhozw0tBLYsad7IbBqLcYZ5JvrVppmycb6Pq2vr2su6hr1Mkcx/5mY57rOY736DKVqjR3wmZlxsglwEfA04HfA2cCBVbW8Z5znAIcDz6Y5bPTxqtpzJAVhi0DShm1U27CRHRqqqtVJDgdOBeYBS6tqeZLD2uHHAN+mCYEVwJ+AQ0ZVT2vJ1KNI0nprJNuwkbUIJEkbBu8slqSOMwgkqeMMAknquE4HQZLNkxyX5HNJXj7X9UjSsJI8OMnnk3x9Xee10QVBkqVJrkxyfl//QQ/A+xvg61V1KPD8WS9WknpMZ/vVPr7nlTOx3I0uCIBjgX17e0zyALyF3PWIi9tnsUZJGuRYht9+zZiNLgiq6gfAtX29J3oA3kqaMICNcF1I2rBMc/s1Y7qy8Zvo4XbfAF6Y5DOsZ7d8S1Jr4PYrybZJjgEek+Qt67KAUT50bn0y8OF2VfVHRn83sySti4m2X9cAh83EArrSIljbh9tJ0lwb+farK0FwNrBrkp2TbAocAJw8xzVJ0jBGvv3a6IIgyVeAM4HdkqxM8sqqWk3zlNNTgV8AJ/Y+BVWS1gdztf3yoXOS1HEbXYtAkjQ9BoEkdZxBIEkdZxBIUscZBJLUcQaBJHWcQSBJHWcQSFLHGQTSDEjyyCS/TfI/57oWaboMAmkGVNV5NM+AOWiua5GmyyCQZs6VwCPmughpugwCaea8D7hXkp3muhBpOgwCaQYk2RfYHPgWtgq0gTEIpHWUZDPgA8CrgfOAv5jbiqTpMQikdfd24Piq+g0GgTZABoG0DpLsBjwD+FjbyyDQBscfppGkjrNFIEkdZxBIUscZBJLUcQaBJHWcQSBJHWcQSFLHGQSS1HEGgSR13P8HoaVrHJ9+m3AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Step 4 a. Draw QRE Graphs (additional)\n",
    "# Node_positions = ['A', 'B', 'C','D','E']\n",
    "\n",
    "# # For each node\n",
    "# for i in range(5):\n",
    "#     fig, ax = plt.subplots()\n",
    "#     ax.set_xlabel('$\\lambda$')\n",
    "#     ax.set_ylabel('Strategies')\n",
    "#     handles, labels = ax.get_legend_handles_labels()\n",
    "#     ax.set_title(\"QRE for Node\"+ Node_positions[i])\n",
    "#     ax.set_ylim(0, 1)\n",
    "#     ax.set_xscale('log')\n",
    "#     for j in range(5):\n",
    "#         ax.plot(lambd,p[:,i,j], label='Turn'+str(j))\n",
    "#     ax.legend()\n",
    "\n",
    "# By Indegree\n",
    "i = 1 # Node B is always the indegree=3\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "ax.set_ylabel('Strategies')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "ax.set_title(\"QRE for Nodes with Multiple Information Souces\")\n",
    "ax.set_ylim(0, 1)\n",
    "ax.set_xscale('log')\n",
    "for j in range(5):\n",
    "    ax.plot(lambd,p[:,i,j], label='Turn'+str(j))\n",
    "ax.legend()\n",
    "\n",
    "i = 3 # Node E is always the indegree=1\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "ax.set_ylabel('Strategies')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "ax.set_title(\"QRE for Nodes with Single Information Source\")\n",
    "ax.set_ylim(0, 1)\n",
    "ax.set_xscale('log')\n",
    "for j in range(5):\n",
    "    ax.plot(lambd,p[:,i,j], label='Turn'+str(j))\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "76f52184",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_11364/1544125704.py:18: UserWarning: You have mixed positional and keyword arguments, some input may be discarded.\n",
      "  lgd = ax.legend(handles, labels = labels, loc = 0)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "ax.set_ylabel('Strategies')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "ax.set_title(\"QRE for game\")\n",
    "ax.set_ylim(0, 1)\n",
    "ax.set_xscale('log')\n",
    "for i in range(1):\n",
    "    ax.plot(lambd,p[:,i,0])\n",
    "    ax.plot(lambd,p[:,i,1],'o',markerfacecolor = \"none\")\n",
    "    ax.plot(lambd,p[:,i,2],'.',markerfacecolor = \"none\")\n",
    "    ax.plot(lambd,p[:,i,3],'.',markerfacecolor = \"none\")\n",
    "    labels.append(('Turn 0', Node_positions[i]))\n",
    "    labels.append(('Turn 1', Node_positions[i]))\n",
    "    labels.append(('Turn 2', Node_positions[i]))\n",
    "    labels.append(('Turn 3', Node_positions[i]))\n",
    "\n",
    "lgd = ax.legend(handles, labels = labels, loc = 0)         "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "00f43772",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_11364/794840202.py:18: UserWarning: You have mixed positional and keyword arguments, some input may be discarded.\n",
      "  lgd = ax.legend(handles, labels = labels, loc = 0)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "ax.set_ylabel('Strategies')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "ax.set_title(\"QRE for game\")\n",
    "ax.set_ylim(0, 1)\n",
    "ax.set_xscale('log')\n",
    "i=3\n",
    "ax.plot(lambd,p[:,i,0])\n",
    "ax.plot(lambd,p[:,i,1],'o',markerfacecolor = \"none\")\n",
    "ax.plot(lambd,p[:,i,2],'.',markerfacecolor = \"none\")\n",
    "ax.plot(lambd,p[:,i,3],'.',markerfacecolor = \"none\")\n",
    "labels.append(('Turn 0', Node_positions[i]))\n",
    "labels.append(('Turn 1', Node_positions[i]))\n",
    "labels.append(('Turn 2', Node_positions[i]))\n",
    "labels.append(('Turn 3', Node_positions[i]))\n",
    "\n",
    "lgd = ax.legend(handles, labels = labels, loc = 0)         "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "283ec9c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[0.16666667, 0.16666667, 0.16666667, 0.16666667, 0.16666667,\n",
       "         0.16666667],\n",
       "        [0.16666667, 0.16666667, 0.16666667, 0.16666667, 0.16666667,\n",
       "         0.16666667],\n",
       "        [0.16666667, 0.16666667, 0.16666667, 0.16666667, 0.16666667,\n",
       "         0.16666667],\n",
       "        [0.16666667, 0.16666667, 0.16666667, 0.16666667, 0.16666667,\n",
       "         0.16666667],\n",
       "        [0.16666667, 0.16666667, 0.16666667, 0.16666667, 0.16666667,\n",
       "         0.16666667]],\n",
       "\n",
       "       [[0.22918537, 0.19953418, 0.17371916, 0.15124399, 0.13167658,\n",
       "         0.11464073],\n",
       "        [0.19604177, 0.19740452, 0.18444531, 0.16058243, 0.13980684,\n",
       "         0.12171913],\n",
       "        [0.20450215, 0.20592371, 0.17928203, 0.15608716, 0.13589316,\n",
       "         0.11831178],\n",
       "        [0.21463548, 0.1868667 , 0.18199561, 0.15844967, 0.13795001,\n",
       "         0.12010253],\n",
       "        [0.21463548, 0.1868667 , 0.18199561, 0.15844967, 0.13795001,\n",
       "         0.12010253]],\n",
       "\n",
       "       [[0.29989483, 0.22677113, 0.17147727, 0.12966577, 0.09804922,\n",
       "         0.07414177],\n",
       "        [0.22607974, 0.22926127, 0.19731655, 0.14920463, 0.1128239 ,\n",
       "         0.08531392],\n",
       "        [0.2420884 , 0.24549522, 0.18563584, 0.14037204, 0.10614497,\n",
       "         0.08026352],\n",
       "        [0.27067283, 0.20467436, 0.1900688 , 0.14372411, 0.1086797 ,\n",
       "         0.0821802 ],\n",
       "        [0.27067283, 0.20467436, 0.1900688 , 0.14372411, 0.1086797 ,\n",
       "         0.0821802 ]],\n",
       "\n",
       "       ...,\n",
       "\n",
       "       [[       nan,        nan,        nan,        nan,        nan,\n",
       "                nan],\n",
       "        [       nan,        nan,        nan,        nan,        nan,\n",
       "                nan],\n",
       "        [       nan,        nan,        nan,        nan,        nan,\n",
       "                nan],\n",
       "        [       nan,        nan,        nan,        nan,        nan,\n",
       "                nan],\n",
       "        [       nan,        nan,        nan,        nan,        nan,\n",
       "                nan]],\n",
       "\n",
       "       [[       nan,        nan,        nan,        nan,        nan,\n",
       "                nan],\n",
       "        [       nan,        nan,        nan,        nan,        nan,\n",
       "                nan],\n",
       "        [       nan,        nan,        nan,        nan,        nan,\n",
       "                nan],\n",
       "        [       nan,        nan,        nan,        nan,        nan,\n",
       "                nan],\n",
       "        [       nan,        nan,        nan,        nan,        nan,\n",
       "                nan]],\n",
       "\n",
       "       [[       nan,        nan,        nan,        nan,        nan,\n",
       "                nan],\n",
       "        [       nan,        nan,        nan,        nan,        nan,\n",
       "                nan],\n",
       "        [       nan,        nan,        nan,        nan,        nan,\n",
       "                nan],\n",
       "        [       nan,        nan,        nan,        nan,        nan,\n",
       "                nan],\n",
       "        [       nan,        nan,        nan,        nan,        nan,\n",
       "                nan]]])"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a4bf5de",
   "metadata": {},
   "source": [
    "# Method 3: Agent Extensive Form Estimation\n",
    "\n",
    "- [Return](#Content)\n",
    "\n",
    "In the extensive form game, assume agent is different at each turn. The probability of making a guess at each turn is based on payoffs between making a guess now and the maximal payoff from waiting. \n",
    "\n",
    "I only changed the payoff matrix but leave the probability matrix as the following. However, the probability is updated differently, for each node at each turn, I will assume the probability of guess at this turn is 0.5 and then update the probability based on the payoff tradeoff. \n",
    "\n",
    "\n",
    "Probability is defined as a matrix of 5*6 (5 nodes, deciding at 6 turns). It is assumed that each subject with a given lambda will pre-determine the probability of makig a prediction at a certain turn, the probability doesn't change based on what new information is updated as time goes by (Not sure what is a more formal/proper way to describe this)\n",
    "\n",
    "\n",
    "Comment: Got very interesting results!!!\n",
    "\n",
    "The normal form equilibrium is not the bayesian perfect nash equilibrium ... (Maybe because how we use the max to derive the optimal rule...)\n",
    "\n",
    "NOTE: NETWORK B EXPECTED PAYOFF UPDATED ONLY FROM HERE!!!!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5926d0bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Step 1: Define Payoffs for Deciding at each turn; The payoff depends on others' probability of making a prediction \n",
    "\n",
    "# Step 2: Write out the policy iteration \n",
    "\n",
    "# Step 3: for different lambda value, derive the results\n",
    "\n",
    "# Step 4: Based on the estimation result, do two things \n",
    "# A. Draw QRE for each node for each treatment, show the difference, describe\n",
    "# B. Estimate MLE based on realized/observed frequencies in each treatment\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "id": "0b28f696",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 1. \n",
    "def payoff(pOther,network, cost):\n",
    "    '''This is for the normal form estimation \n",
    "        pOther = matrix(5,6); each row is for each node; each column is for each turn\n",
    "        '''\n",
    "    diff_pay = 100\n",
    "    q = 0.7\n",
    "    if cost=='h':\n",
    "        c = 8\n",
    "    elif cost == 'l':\n",
    "        c = 1\n",
    "    \n",
    "    if network == 'a':\n",
    "        #In network a, I only consider the pay for A and B, at turn 0 \n",
    "        pay =  np.empty((5,6),dtype=float)\n",
    "        pay[:,0] = ProbCorrect_Bayesian(1,q)*diff_pay\n",
    "        \n",
    "        # indegree = 1, node A / E\n",
    "        pay_1 = ProbCorrect_Bayesian(2,q)*diff_pay - c\n",
    "        pay[0,1] = pay_1 \n",
    "        pay[4,1] = pay_1 \n",
    "        j = 2\n",
    "        while j <= 5:        \n",
    "            pay[0,j] = ProbCorrect_Bayesian(2,q)*diff_pay - j*c\n",
    "            pay[4,j] = ProbCorrect_Bayesian(2,q)*diff_pay - j*c\n",
    "            j += 1\n",
    "        \n",
    "        # indegree = 3, node B\n",
    "        pay_1 = ProbCorrect_Bayesian(4,q)*diff_pay - c\n",
    "        pi_b = pOther[0,0]*ProbCorrect_Bayesian(4,q)*diff_pay + (1- pOther[0,0])*ProbCorrect_Bayesian(5,q)*diff_pay \n",
    "        pay[1,1] = pay_1\n",
    "        j = 2\n",
    "        while j <= 5:        \n",
    "            pay[1,j] = pi_b - j*c\n",
    "            j += 1\n",
    "\n",
    "        # indegree = 2, node C\n",
    "        pay_1 = ProbCorrect_Bayesian(3,q)*diff_pay - c\n",
    "        pay[2,1] = pay_1\n",
    "        pi_c = pOther[0, 0]*pOther[1,0]*ProbCorrect_Bayesian(3,q)*diff_pay + ((1-pOther[0, 0])*pOther[1,0] + pOther[0, 0]*(1-pOther[1,0]))*ProbCorrect_Bayesian(4,q)*diff_pay + (1-pOther[0, 0])*(1-pOther[1,0])*ProbCorrect_Bayesian(3,q)*diff_pay\n",
    "        j = 2\n",
    "        while j <= 5:        \n",
    "            pay[2,j] = pi_c - j*c\n",
    "            j += 1\n",
    "            \n",
    "        # indegree = 1, node D (position 3)\n",
    "        pay_1 = ProbCorrect_Bayesian(2,q)*diff_pay - c\n",
    "        pay[3,1] = pay_1 \n",
    "        pi_d = pOther[0,0]*ProbCorrect_Bayesian(2,q)*diff_pay + (1- pOther[0,0])*ProbCorrect_Bayesian(3,q)*diff_pay \n",
    "        j = 2\n",
    "        while j <= 5:        \n",
    "            pay[3,j] = pi_d - j*c\n",
    "            j += 1\n",
    "        \n",
    "   \n",
    "        \n",
    "    elif network == 'b':\n",
    "         # We know there are 5 nodes, pay matrix is 5X6 ( 6 period)\n",
    "        pay =  np.empty((5,6),dtype=float)\n",
    "        pay[:,0] = ProbCorrect_Bayesian(1,q)*diff_pay\n",
    "\n",
    "        # Note: since here the payoff is about turn 0,1,2, need to do the max in the \n",
    "        # indegree = 2, node A\n",
    "        pay_1 = ProbCorrect_Bayesian(3,q)*diff_pay - c\n",
    "        pi_a = pOther[1,0]*ProbCorrect_Bayesian(3,q)*diff_pay + (1-pOther[1,0])*ProbCorrect_Bayesian(5,q)*diff_pay        \n",
    "        pay[0,1] = pay_1\n",
    "        j = 2\n",
    "        while j <= 5:        \n",
    "            pay[0,j] = pi_a - j*c\n",
    "            j += 1\n",
    "\n",
    "        # indegree = 3, node B\n",
    "        pay_1 = ProbCorrect_Bayesian(4,q)*diff_pay - c\n",
    "        pi_b = pOther[0,0]*ProbCorrect_Bayesian(4,q)*diff_pay + (1- pOther[0,0])*ProbCorrect_Bayesian(5,q)*diff_pay \n",
    "        pay[1,1] = pay_1\n",
    "        j = 2\n",
    "        while j <= 5:        \n",
    "            pay[1,j] = pi_b - j*c\n",
    "            j += 1\n",
    "\n",
    "\n",
    "        # indegree = 1, node C or D or E, (position 2,3)\n",
    "        pay_1 = ProbCorrect_Bayesian(2,q)*diff_pay - c\n",
    "        pay[2:5,1] = pay_1\n",
    "        # Since in bayesian updating, having 3 or 4 signals carry the same informaiton value, can group these points together\n",
    "        pi_e0 =  pOther[0,0]*ProbCorrect_Bayesian(2,q)*diff_pay + (1-pOther[0,0])*ProbCorrect_Bayesian(3,q)*diff_pay \n",
    "        pay[2:5,2] = pi_e0 - 2*c\n",
    "        pi_e =  pOther[0,0]*ProbCorrect_Bayesian(2,q)*diff_pay + (pOther[0,1] + (1- pOther[0,0] -pOther[0,1])*pOther[1,0])*ProbCorrect_Bayesian(3,q)*diff_pay  +(1- pOther[0,0] -pOther[0,1])*(1-pOther[1,0])*ProbCorrect_Bayesian(5,q)*diff_pay \n",
    "        \n",
    "        j = 3\n",
    "        while j <= 5:        \n",
    "            pay[2:5,j] = pi_e - j*c\n",
    "            j += 1\n",
    "#     pay_avg = np.sum(pay,axis=1)\n",
    "#     return pay/pay_avg[:,None]\n",
    "    return pay/70\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "id": "3ae3f3d6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Step 2\n",
    "def policy_iter(l,p_ini,network, waitingcost, tol = 1e-10):\n",
    "    \n",
    "    error = 1\n",
    "    pOthers = np.ones((5,6))* p_ini\n",
    "    \n",
    "    nrep = 1\n",
    "    while error > tol:\n",
    "        \n",
    "        mixed_payoff = payoff(pOthers,network, waitingcost)\n",
    "        ## Previous code\n",
    "#         add_error = np.exp(l*mixed_payoff)\n",
    "\n",
    "#         node_avg =  np.sum(add_error,axis=1)\n",
    "#         sigma = add_error / node_avg[:,None]\n",
    "        ## Here update the probability sequentially, using backward induction \n",
    "        # Backward induction, from prob guess at turn 4, turn 5 =1-sum(p0:p4):\n",
    "        sigma = np.zeros((5,6))\n",
    "        p_guess_byTurn = np.zeros((5,5))\n",
    "        for i in range(5):\n",
    "            temp = np.max(mixed_payoff[:, i+1:6],axis=1)\n",
    "            payoff_relevent = np.zeros((5,2))\n",
    "            payoff_relevent[:,0] = mixed_payoff[:,i]\n",
    "            payoff_relevent[:,1] = temp\n",
    "\n",
    "            payoff_error = np.exp(l*payoff_relevent)\n",
    "            node_avg =  np.sum(payoff_error,axis=1)\n",
    "            pi = payoff_error / node_avg[:,None] # (guess, wait)\n",
    "            \n",
    "            p_guess_byTurn[:,i] = pi[:,0]\n",
    "            \n",
    "        sigma[:,0] = p_guess_byTurn[:,0]\n",
    "        wait_prob = 1-p_guess_byTurn[:,0]\n",
    "        for i in range(1,5):\n",
    "            sigma[:,i] =    wait_prob * p_guess_byTurn[:,i]\n",
    "            wait_prob *= 1-p_guess_byTurn[:,i]\n",
    "\n",
    "        sigma[:,5] = 1-np.sum(sigma, axis=1)\n",
    "\n",
    "\n",
    "        error = np.max(np.sum(np.abs(sigma-pOthers), axis=1))\n",
    "        pOthers = sigma\n",
    "\n",
    "        nrep += 1\n",
    "        \n",
    "    print(\"Number of Iterations:\",nrep)\n",
    "    return pOthers\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "id": "edc11829",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Step 3\n",
    "\n",
    "# lambd = []\n",
    "n = 200\n",
    "lambd = np.logspace(-1, 2.5, n, endpoint=True)\n",
    "# for i in range(n):\n",
    "#     lambd.append(1.0173182**i - 1)\n",
    "\n",
    "def QRE_Outcome(network, waitingCost):\n",
    "    '''Contains both the prob and graphs'''\n",
    "    \n",
    "    p = np.empty((n,5,6))\n",
    "    for i in range(n):\n",
    "#         print(\"Round:\", i+1)\n",
    "        Result = policy_iter(lambd[i],1/6,network,waitingCost)\n",
    "        p[i] = Result\n",
    "    \n",
    "    return p\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "d765ac0e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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   ],
   "source": [
    "# Obtain the QRE and output QRE figures for extensive form\n",
    "\n",
    "QRE_a_l = QRE_Outcome('a', 'l')\n",
    "QRE_a_h = QRE_Outcome('a', 'h')\n",
    "QRE_b_l = QRE_Outcome('b', 'l')\n",
    "QRE_b_h = QRE_Outcome('b', 'h')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "id": "959be366",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculate the average waiting turns for each treatment, ndoes with 1 or multiple information \n",
    "turns = np.array([0,1,2,3,4,5])\n",
    "QREs = [QRE_a_l, QRE_a_h, QRE_b_l, QRE_b_h]\n",
    "TreatmentName = ['NC_l','NC_h', 'C_l', 'C_h']\n",
    "Network = ['nc', 'nc', 'c','c']\n",
    "Cost = ['l','h','l','h']\n",
    "\n",
    "avg_turn = np.empty((4,n,5))\n",
    "for t in range(4):\n",
    "    for i in range(n):\n",
    "        QRE = QREs[t]\n",
    "        x = QRE[i]*turns\n",
    "        avg_turn[t][i] = x.sum(axis=1)\n",
    "\n",
    "\n",
    "fig, axes = plt.subplots(nrows=1, ncols=3,  sharex=True,  sharey=True,   constrained_layout=True, figsize=(10,4))\n",
    "fig.set_constrained_layout_pads( w_pad=1 / 100)\n",
    "\n",
    "linestyle = {'c':'-', 'nc':':'}\n",
    "markerstyle = {'l': '>', 'h': 'o' }\n",
    "y_max = 5\n",
    "y_step = 1\n",
    "\n",
    "# Defining custom 'xlim' and 'ylim' values.\n",
    "# custom_xlim = (1, 11)\n",
    "custom_ylim = (0, y_max)\n",
    "# custom_xtick = np.arange(1,11,step=1)\n",
    "custom_ytick = np.arange(0,y_max,step=y_step)\n",
    "# custom_xticklabel = [1,5,10]\n",
    "\n",
    "plt.setp(axes, yticks= custom_ytick, ylim=custom_ylim)\n",
    "\n",
    "for t in range(4):\n",
    "    \n",
    "    if t==3:\n",
    "        axes[0].plot(lambd,avg_turn[t].mean(axis=1), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]],  markersize=2)\n",
    "    else: \n",
    "        axes[0].plot(lambd,avg_turn[t].mean(axis=1), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]])\n",
    "    axes[0].set_title('All nodes', fontsize=15) \n",
    "    \n",
    "    if t<=1:\n",
    "        axes[1].plot(lambd,avg_turn[t, :, [0,3,4]].mean(axis=0), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]])\n",
    "    elif t==3:\n",
    "        axes[1].plot(lambd,avg_turn[t, :, [2,3,4]].mean(axis=0), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]], markersize=2)\n",
    "    else : \n",
    "        axes[1].plot(lambd,avg_turn[t, :, [2,3,4]].mean(axis=0), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]])\n",
    "    axes[1].set_title('Nodes with $InDegree=1$', fontsize=15) \n",
    "    \n",
    "    \n",
    "    if t<=1:\n",
    "        axes[2].plot(lambd,avg_turn[t, :, [1,2]].mean(axis=0), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]])\n",
    "    elif t==3:\n",
    "        axes[2].plot(lambd,avg_turn[t, :, [0,1]].mean(axis=0), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]], markersize=2)\n",
    "    else : \n",
    "        axes[2].plot(lambd,avg_turn[t, :, [0,1]].mean(axis=0), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]])\n",
    "\n",
    "    axes[2].set_title('Nodes with $InDegree>1$', fontsize=15) \n",
    "    \n",
    "    axes[1].set_xlabel('$\\lambda$', fontsize=15)\n",
    "    axes[0].set_ylabel('Average Waiting Turns', fontsize=15)\n",
    "    axes[0].set_xscale('log')\n",
    "handles, labels = axes[0].get_legend_handles_labels()\n",
    "fig.legend(handles, labels, bbox_to_anchor=(.5,-0.05), loc=\"center\" , ncol=4, frameon=False, prop={'size':15})\n",
    "fig.savefig(\"..\\\\Output_Figures\\\\05-QRE-Calculation\\\\\"+\"QRE_Extensive_AvgTurns\"  , bbox_inches=\"tight\")  \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7693875f",
   "metadata": {},
   "source": [
    "# Estimate lambda extensive\n",
    "\n",
    "- [Return](#Content)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "id": "04a53f48",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0        1.0\n",
       "1        2.0\n",
       "2        3.0\n",
       "3        4.0\n",
       "4        5.0\n",
       "        ... \n",
       "5295     9.0\n",
       "5296     9.0\n",
       "5297    10.0\n",
       "5298    10.0\n",
       "5299    10.0\n",
       "Name: match, Length: 5300, dtype: float64"
      ]
     },
     "execution_count": 188,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['match']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "id": "5515a3cd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[32.73975136,  8.60346442],\n",
       "       [ 3.5297073 ,  5.97560538]])"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "\n",
    "# Step 4 b. Use the calculated QRE to estimate logL\n",
    "# datafolder = \"C:\\\\Users\\\\xinxi\\\\Purdue\\\\EffectiveSocialLearningProject\\\\DataAnalysis\\\\RawData\\\\Session_Formal\"\n",
    "datafolder = \"..\\\\RawData\\\\Session_Formal\"\n",
    "datafolder2 = \"..\\\\ImportedData\\\\\"\n",
    "outputfolder = \"..\\\\Output_Figures\\\\\" \n",
    "\n",
    "# Import data\n",
    "\n",
    "data  = pd.read_csv(datafolder2+\"02-Experiment-Clean-Data.csv\")\n",
    "\n",
    "for col in data.columns:\n",
    "    if type(data[col].unique()[1]) == str:\n",
    "        data[col] = data[col].str.lower()\n",
    "\n",
    "# Change the rounds into matches  \n",
    "data.loc[data['app_name']=='pdcn', 'match'] = data['.subsession.round_number']\n",
    "condition = data['app_name']=='dcn'\n",
    "data.loc[condition, 'match'] = ((data.loc[condition, '.subsession.round_number'] -1)/ 3).astype(int) +1 \n",
    "condition = (data['app_name']=='dcn') & (data['date']=='03/19/2021')\n",
    "data.loc[condition, 'match'] = ((data.loc[condition, '.subsession.round_number'] -1)/ 4).astype(int) +1 \n",
    "# data['match'] = data['.subsession.round_number']\n",
    "data[['match', 'app_name', '.subsession.round_number']]\n",
    "\n",
    "# DataExperiment= data[data['app_name']=='dcn'] \n",
    "DataExperiment= data[(data['app_name']=='dcn') & (data['match']>=6)]\n",
    "\n",
    "\n",
    "# Count any variable will be the same\n",
    "\n",
    "BySessions = DataExperiment.groupby(['network', 'waiting_cost','session.code',\n",
    "                                     '.player.type','.player.period']).count().reset_index()\n",
    "BySessions = BySessions[['network', 'waiting_cost','session.code',\n",
    "                                     '.player.type','.player.period','date']]\n",
    "\n",
    "ByIndividuals = DataExperiment.groupby(['network', 'waiting_cost','participant.code',\n",
    "                                     '.player.type','.player.period']).count().reset_index()\n",
    "ByIndividuals = ByIndividuals[['network', 'waiting_cost','participant.code',\n",
    "                                     '.player.type','.player.period','date']]\n",
    "\n",
    "# BySessions['session.code'].unique()\n",
    "ByIndividuals\n",
    "# BySessions.pivot(index=['network', 'waiting_cost','session.code','.player.type'], columns='.player.period')\n",
    "\n",
    "# By treatments\n",
    "\n",
    "QREs =np.array([[QRE_a_l, QRE_a_h], [QRE_b_l, QRE_b_h]])\n",
    "\n",
    "nn = 200\n",
    "EstimatedL =  np.empty((2,2))\n",
    "EstimatedLogl =  np.empty((2,2))\n",
    "for n,network in enumerate(['nc', 'c']):\n",
    "    for l,waitingcost in enumerate(['l','h']):\n",
    "        logL =  np.zeros(nn)\n",
    "        for i in range(nn):\n",
    "            QRE_lamda=QREs[n,l][i]\n",
    "            for pos, node in enumerate(['a','b','c','d','e']):\n",
    "                for turn in range(6):\n",
    "                    freq = BySessions.loc[(BySessions['network']==network) & \n",
    "                       (BySessions['waiting_cost']==waitingcost) &\n",
    "                      (BySessions['.player.type']==node) & \n",
    "                     (BySessions['.player.period']==turn) , 'date' ].sum()\n",
    "                    logL[i] += freq*np.log(QRE_lamda[pos,turn])\n",
    "        logL = logL[~np.isnan(logL)]\n",
    "        max_l = np.argmax(logL)\n",
    "        EstimatedLogl[n,l] = logL[max_l]\n",
    "        EstimatedL[n,l] = lambd[max_l]\n",
    "EstimatedL\n",
    "\n",
    "# Normalize the payoffs by dividing 70 gives me reasonable lambda \n",
    "EstimatedL\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "id": "ecd72b8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1058.5,  -358.1],\n",
       "       [-1330. ,  -451.7]])"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.set_printoptions(suppress=True)\n",
    "# EstimatedL.round(3)\n",
    "EstimatedLogl.round(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c1b87402",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.set_printoptions(suppress=True)\n",
    "EstimatedL.round(3)\n",
    "EstimatedLogl.round(1)\n",
    "\n",
    "# For all 30 rounds\n",
    "# array([[27.843,  7.934],\n",
    "#        [ 3.39 ,  5.976]])\n",
    "# For latter 15 rounds\n",
    "\n",
    "# array([[32.74 ,  8.603],\n",
    "#        [ 3.53 ,  5.976]])\n",
    "\n",
    "EstimatedLogl  # because logL also depends on how many observations I have\n",
    "\n",
    "# For all 30 rounds\n",
    "# array([[-2142.1,  -746.3],\n",
    "#        [-2663. ,  -907.9]])\n",
    "# For latter 15 rounds\n",
    "# array([[-1250.66311514,  -383.79953918],\n",
    "#        [-1419.69653271,  -483.66594404]])\n",
    "\n",
    "# By treatments and information sources: multiple sources \n",
    "\n",
    "QREs =np.array([[QRE_a_l, QRE_a_h], [QRE_b_l, QRE_b_h]])\n",
    "\n",
    "nn = 200\n",
    "EstimatedL =  np.empty((2,2))\n",
    "EstimatedLogl =  np.empty((2,2))\n",
    "for n,network in enumerate(['nc', 'c']):\n",
    "    for l,waitingcost in enumerate(['l','h']):\n",
    "        logL =  np.zeros(nn)\n",
    "        for i in range(nn):\n",
    "            QRE_lamda=QREs[n,l][i]\n",
    "            if n=='nc':\n",
    "                list_infor = ['b','c']\n",
    "            else :\n",
    "                list_infor = ['b','a']\n",
    "            for pos, node in enumerate(list_infor):\n",
    "                for turn in range(6):\n",
    "                    freq = BySessions.loc[(BySessions['network']==network) & \n",
    "                       (BySessions['waiting_cost']==waitingcost) &\n",
    "                      (BySessions['.player.type']==node) & \n",
    "                     (BySessions['.player.period']==turn) , 'date' ].sum()\n",
    "                    logL[i] += freq*np.log(QRE_lamda[pos,turn])\n",
    "        logL = logL[~np.isnan(logL)]\n",
    "        max_l = np.argmax(logL)\n",
    "        EstimatedLogl[n,l] = logL[max_l]\n",
    "        EstimatedL[n,l] = lambd[max_l]\n",
    "print(EstimatedL)\n",
    "print(EstimatedLogl)\n",
    "\n",
    "# 30 rounds\n",
    "# [[8.95903651 6.74754405]\n",
    "#  [8.95903651 9.32930403]]\n",
    "# [[ -913.07553497  -327.3827763 ]\n",
    "#  [-1026.52455389  -324.81681414]]\n",
    "\n",
    "# By treatments and information sources: single sources \n",
    "\n",
    "QREs =np.array([[QRE_a_l, QRE_a_h], [QRE_b_l, QRE_b_h]])\n",
    "\n",
    "nn = 200\n",
    "EstimatedL =  np.empty((2,2))\n",
    "EstimatedLogl =  np.empty((2,2))\n",
    "for n,network in enumerate(['nc', 'c']):\n",
    "    for l,waitingcost in enumerate(['l','h']):\n",
    "        logL =  np.zeros(nn)\n",
    "        for i in range(nn):\n",
    "            QRE_lamda=QREs[n,l][i]\n",
    "            if n=='nc':\n",
    "                list_infor = ['a','d','e']\n",
    "            else :\n",
    "                list_infor = ['c','d','e']\n",
    "            for pos, node in enumerate(list_infor):\n",
    "                for turn in range(6):\n",
    "                    freq = BySessions.loc[(BySessions['network']==network) & \n",
    "                       (BySessions['waiting_cost']==waitingcost) &\n",
    "                      (BySessions['.player.type']==node) & \n",
    "                     (BySessions['.player.period']==turn) , 'date' ].sum()\n",
    "                    logL[i] += freq*np.log(QRE_lamda[pos,turn])\n",
    "        logL = logL[~np.isnan(logL)]\n",
    "        max_l = np.argmax(logL)\n",
    "        EstimatedLogl[n,l] = logL[max_l]\n",
    "        EstimatedL[n,l] = lambd[max_l]\n",
    "print(EstimatedL)\n",
    "print(EstimatedLogl)\n",
    "\n",
    "# 30 rounds:\n",
    "\n",
    "# [[11.89534067  8.95903651]\n",
    "#  [ 4.3219366   6.22257084]]\n",
    "# [[-1352.09390136  -442.24833978]\n",
    "#  [-1589.60767198  -542.3661108 ]]\n",
    "\n",
    "# BySessions['session.code'].unique()\n",
    "\n",
    "ss = \"hyi8cnuz\"\n",
    "BySessions[BySessions['session.code']==ss]\n",
    "\n",
    "# By Sessions\n",
    "\n",
    "QREs =np.array([[QRE_a_l, QRE_a_h], [QRE_b_l, QRE_b_h]])\n",
    "\n",
    "nn = 200\n",
    "Sessions = BySessions['session.code'].unique()\n",
    "outcome = pd.DataFrame(columns = [\"SessionCode\", \"Network\", \"WaitingCost\",\"EstimatedL\",\"EstimatedLogl\"])\n",
    "\n",
    "EstimatedLogl =  np.empty((len(Sessions),5))\n",
    "for s_n, ss in enumerate(Sessions):\n",
    "    EstimatedLogl[s_n, 0]= s_n\n",
    "    data = BySessions[BySessions['session.code']==ss]\n",
    "    if BySessions[BySessions['session.code']==ss].network.unique()[0]=='c': \n",
    "        n = 1\n",
    "        \n",
    "    else :\n",
    "        n = 0 \n",
    "    \n",
    "    if BySessions[BySessions['session.code']==ss].waiting_cost.unique()[0]=='l':\n",
    "        l = 0\n",
    "    else :\n",
    "        l = 1\n",
    "    EstimatedLogl[s_n, 1]= n\n",
    "    EstimatedLogl[s_n, 2]= l\n",
    "    logL =  np.zeros(nn)\n",
    "    for i in range(nn):\n",
    "        QRE_lamda=QREs[n,l][i]\n",
    "        for pos, node in enumerate(['a','b','c','d','e']):\n",
    "            for turn in range(6):\n",
    "                freq = data.loc[(data['.player.type']==node) & \n",
    "                 (data['.player.period']==turn) , 'date' ].sum()\n",
    "                logL[i] += freq*np.log(QRE_lamda[pos,turn])\n",
    "    logL = logL[~np.isnan(logL)]\n",
    "    max_l = np.argmax(logL)            \n",
    "    EstimatedLogl[s_n, 3]= lambd[max_l]\n",
    "    EstimatedLogl[s_n, 4]= logL[max_l]            \n",
    "                \n",
    "                    \n",
    "#     for l,waitingcost in enumerate(['l','h']):\n",
    "#         logL =  np.zeros(nn)\n",
    "#         for i in range(nn):\n",
    "#             QRE_lamda=QREs[n,l][i]\n",
    "#             for pos, node in enumerate(['a','b','c','d','e']):\n",
    "#                 for turn in range(6):\n",
    "#                     freq = BySessions.loc[(BySessions['network']==network) & \n",
    "#                        (BySessions['waiting_cost']==waitingcost) &\n",
    "#                       (BySessions['.player.type']==node) & \n",
    "#                      (BySessions['.player.period']==turn) , 'date' ].sum()\n",
    "#                     logL[i] += freq*np.log(QRE_lamda[pos,turn])\n",
    "#         logL = logL[~np.isnan(logL)]\n",
    "#         max_l = np.argmax(logL)\n",
    "#         EstimatedLogl[n,l] = logL[max_l]\n",
    "#         EstimatedL[n,l] = lambd[max_l]\n",
    "# EstimatedL\n",
    "\n",
    "np.set_printoptions(suppress=True)\n",
    "EstimatedLogl.round(3)\n",
    "\n",
    "# 30 rounds:\n",
    "# array([[   0.   ,    1.   ,    1.   ,    7.026, -430.157],\n",
    "#        [   1.   ,    1.   ,    1.   ,    4.88 , -473.363],\n",
    "#        [   2.   ,    1.   ,    0.   ,    0.1  , -537.888],\n",
    "#        [   3.   ,    1.   ,    0.   ,   13.987, -475.817],\n",
    "#        [   4.   ,    1.   ,    0.   ,    1.508, -536.496],\n",
    "#        [   5.   ,    1.   ,    0.   ,    8.262, -512.119],\n",
    "#        [   6.   ,    1.   ,    0.   ,    1.773, -536.055],\n",
    "#        [   7.   ,    0.   ,    1.   ,    8.262, -368.741],\n",
    "#        [   8.   ,    0.   ,    1.   ,    7.934, -382.004],\n",
    "#        [   9.   ,    0.   ,    0.   ,    0.789, -537.438],\n",
    "#        [  10.   ,    0.   ,    0.   ,    5.292, -534.66 ],\n",
    "#        [  11.   ,    0.   ,    0.   ,   45.267, -645.031],\n",
    "#        [  12.   ,    0.   ,    0.   ,   62.587, -482.719]])\n",
    "\n",
    "ByIndividuals\n",
    "\n",
    "# By Individuals\n",
    "\n",
    "\n",
    "QREs =np.array([[QRE_a_l, QRE_a_h], [QRE_b_l, QRE_b_h]])\n",
    "\n",
    "nn = 200\n",
    "Sessions = ByIndividuals['participant.code'].unique()\n",
    "outcome = pd.DataFrame(columns = [\"ParticipantCode\", \"Network\", \"WaitingCost\",\"EstimatedL\",\"EstimatedLogl\"])\n",
    "\n",
    "EstimatedLogl =  np.empty((len(Sessions),5))\n",
    "for s_n, ss in enumerate(Sessions):\n",
    "    print(s_n)\n",
    "    EstimatedLogl[s_n, 0]= s_n\n",
    "    data = ByIndividuals[ByIndividuals['participant.code']==ss]\n",
    "    if ByIndividuals[ByIndividuals['participant.code']==ss].network.unique()[0]=='c': \n",
    "        n = 1\n",
    "        \n",
    "    else :\n",
    "        n = 0 \n",
    "    \n",
    "    if ByIndividuals[ByIndividuals['participant.code']==ss].waiting_cost.unique()[0]=='l':\n",
    "        l = 0\n",
    "    else :\n",
    "        l = 1\n",
    "    EstimatedLogl[s_n, 1]= n\n",
    "    EstimatedLogl[s_n, 2]= l\n",
    "    logL =  np.zeros(nn)\n",
    "    for i in range(nn):\n",
    "        QRE_lamda=QREs[n,l][i]\n",
    "        for pos, node in enumerate(['a','b','c','d','e']):\n",
    "            for turn in range(6):\n",
    "                freq = data.loc[(data['.player.type']==node) & \n",
    "                 (data['.player.period']==turn) , 'date' ].sum()\n",
    "                logL[i] += freq*np.log(QRE_lamda[pos,turn])\n",
    "    logL = logL[~np.isnan(logL)]\n",
    "    max_l = np.argmax(logL)            \n",
    "    EstimatedLogl[s_n, 3]= lambd[max_l]\n",
    "    EstimatedLogl[s_n, 4]= logL[max_l]            \n",
    "    outcome.loc[len(outcome.index)] = [ss, n, l, lambd[max_l], logL[max_l]  ]\n",
    "                \n",
    "np.set_printoptions(suppress=True)\n",
    "print('LogL')\n",
    "print(EstimatedLogl.round(3))\n",
    "\n",
    "\n",
    "#     for l,waitingcost in enumerate(['l','h']):\n",
    "#         logL =  np.zeros(nn)\n",
    "#         for i in range(nn):\n",
    "#             QRE_lamda=QREs[n,l][i]\n",
    "#             for pos, node in enumerate(['a','b','c','d','e']):\n",
    "#                 for turn in range(6):\n",
    "#                     freq = ByIndividuals.loc[(ByIndividuals['network']==network) & \n",
    "#                        (ByIndividuals['waiting_cost']==waitingcost) &\n",
    "#                       (ByIndividuals['.player.type']==node) & \n",
    "#                      (ByIndividuals['.player.period']==turn) , 'date' ].sum()\n",
    "#                     logL[i] += freq*np.log(QRE_lamda[pos,turn])\n",
    "#         logL = logL[~np.isnan(logL)]\n",
    "#         max_l = np.argmax(logL)\n",
    "#         EstimatedLogl[n,l] = logL[max_l]\n",
    "#         EstimatedL[n,l] = lambd[max_l]\n",
    "# EstimatedL\n",
    "\n",
    "outcome.to_csv(datafolder2+\"05-QRE-Calculation-Normalize-Indiv-Estimation.csv\",index=False)\n",
    "\n",
    "outcome['Network'] = outcome['Network'].replace({0:'nc', 1:'c'})\n",
    "outcome['WaitingCost'] = outcome['WaitingCost'].replace({0:'l', 1:'h'})\n",
    "\n",
    "\n",
    "outcome['Treatment'] = outcome['Network'] +'-'+ outcome['WaitingCost']\n",
    "outcome = outcome.sort_values(by=['Treatment'], ascending=False)\n",
    "outcome\n",
    "\n",
    "\n",
    "ax = outcome.hist(column='EstimatedL', by='Treatment',\n",
    "                    grid=False, figsize=(8,10), layout=(2,2), sharex=True,\n",
    "                    color='#86bf91', zorder=1, rwidth=.5)\n",
    "\n",
    "# ax = ax[0]\n",
    "\n",
    "for i,xx in enumerate(ax):\n",
    "    for j,x in enumerate(xx):\n",
    "    \n",
    "        # Despine\n",
    "        x.spines['right'].set_visible(False)\n",
    "        x.spines['top'].set_visible(False)\n",
    "        x.spines['left'].set_visible(False)\n",
    "\n",
    "        # Switch off ticks\n",
    "#         x.tick_params(axis=\"both\", which=\"both\", bottom=\"off\", top=\"off\", labelbottom=\"on\", left=\"off\", right=\"off\", labelleft=\"on\")\n",
    "        x.set_xticks(lambd)\n",
    "        x.set_xscale('log')\n",
    "    #     # Draw horizontal axis lines\n",
    "        vals = x.get_yticks()\n",
    "        for tick in vals:\n",
    "            x.axhline(y=tick, linestyle='dashed', alpha=0.4, color='#eeeeee', zorder=1)\n",
    "\n",
    "    #     # Set x-axis label\n",
    "        x.set_xlabel(\"$\\lambda$ distribution\", labelpad=20, weight='bold', size=12)\n",
    "\n",
    "    #     # Set y-axis label\n",
    "        if j == 0:\n",
    "            x.set_ylabel(\"Number of Subjects\", labelpad=50, weight='bold', size=12)\n",
    "\n",
    "    #     # Format y-axis label\n",
    "    #     x.yaxis.set_major_formatter(StrMethodFormatter('{x:,g}'))\n",
    "\n",
    "        x.tick_params(axis='x', rotation=0)\n",
    "\n",
    "\n",
    "plt.savefig(outputfolder+\"05-QRE-Calculation\\\\Normalize-Indvd-Lambda-Distr\"  , bbox_inches=\"tight\")  \n",
    "\n",
    "for i,x in enumerate(ax):\n",
    "    print(i)\n",
    "    print(x)\n",
    "\n",
    "# By Sessions, only later 15\n",
    "\n",
    "\n",
    "DataExperiment= data[(data['app_name']=='dcn') & (data['.subsession.round_number']>=15)]\n",
    "\n",
    "\n",
    "# Count any variable will be the same\n",
    "\n",
    "BySessions = DataExperiment.groupby(['network', 'waiting_cost','session.code',\n",
    "                                     '.player.type','.player.period']).count().reset_index()\n",
    "BySessions = BySessions[['network', 'waiting_cost','session.code',\n",
    "                                     '.player.type','.player.period','date']]\n",
    "\n",
    "QREs =np.array([[QRE_a_l, QRE_a_h], [QRE_b_l, QRE_b_h]])\n",
    "\n",
    "nn = 200\n",
    "Sessions = BySessions['session.code'].unique()\n",
    "outcome = pd.DataFrame(columns = [\"SessionCode\", \"Network\", \"WaitingCost\",\"EstimatedL\",\"EstimatedLogl\"])\n",
    "\n",
    "EstimatedLogl =  np.empty((len(Sessions),5))\n",
    "for s_n, ss in enumerate(Sessions):\n",
    "    EstimatedLogl[s_n, 0]= s_n\n",
    "    data_s = BySessions[BySessions['session.code']==ss]\n",
    "    if BySessions[BySessions['session.code']==ss].network.unique()[0]=='c': \n",
    "        n = 1\n",
    "        \n",
    "    else :\n",
    "        n = 0 \n",
    "    \n",
    "    if BySessions[BySessions['session.code']==ss].waiting_cost.unique()[0]=='l':\n",
    "        l = 0\n",
    "    else :\n",
    "        l = 1\n",
    "    EstimatedLogl[s_n, 1]= n\n",
    "    EstimatedLogl[s_n, 2]= l\n",
    "    logL =  np.zeros(nn)\n",
    "    for i in range(nn):\n",
    "        QRE_lamda=QREs[n,l][i]\n",
    "        for pos, node in enumerate(['a','b','c','d','e']):\n",
    "            for turn in range(6):\n",
    "                freq = data_s.loc[(data_s['.player.type']==node) & \n",
    "                 (data_s['.player.period']==turn) , 'date' ].sum()\n",
    "                logL[i] += freq*np.log(QRE_lamda[pos,turn])\n",
    "    logL = logL[~np.isnan(logL)]\n",
    "    max_l = np.argmax(logL)            \n",
    "    EstimatedLogl[s_n, 3]= lambd[max_l]\n",
    "    EstimatedLogl[s_n, 4]= logL[max_l]            \n",
    "                \n",
    "                    \n",
    "#     for l,waitingcost in enumerate(['l','h']):\n",
    "#         logL =  np.zeros(nn)\n",
    "#         for i in range(nn):\n",
    "#             QRE_lamda=QREs[n,l][i]\n",
    "#             for pos, node in enumerate(['a','b','c','d','e']):\n",
    "#                 for turn in range(6):\n",
    "#                     freq = BySessions.loc[(BySessions['network']==network) & \n",
    "#                        (BySessions['waiting_cost']==waitingcost) &\n",
    "#                       (BySessions['.player.type']==node) & \n",
    "#                      (BySessions['.player.period']==turn) , 'date' ].sum()\n",
    "#                     logL[i] += freq*np.log(QRE_lamda[pos,turn])\n",
    "#         logL = logL[~np.isnan(logL)]\n",
    "#         max_l = np.argmax(logL)\n",
    "#         EstimatedLogl[n,l] = logL[max_l]\n",
    "#         EstimatedL[n,l] = lambd[max_l]\n",
    "# EstimatedL\n",
    "\n",
    "np.set_printoptions(suppress=True)\n",
    "EstimatedLogl.round(3)\n",
    "\n",
    "# Only later 15 rounds\n",
    "# Huge session differences, driven by individual differences? \n",
    "# array([[   0.   ,    1.   ,    1.   ,    7.934, -219.579],\n",
    "#        [   1.   ,    1.   ,    1.   ,    4.322, -257.881],\n",
    "#        [   2.   ,    1.   ,    0.   ,    0.1  , -286.911],\n",
    "#        [   3.   ,    1.   ,    0.   ,   14.565, -251.02 ],\n",
    "#        [   4.   ,    1.   ,    0.   ,    1.773, -285.915],\n",
    "#        [   5.   ,    1.   ,    0.   ,   12.387, -260.036],\n",
    "#        [   6.   ,    1.   ,    0.   ,    0.216, -286.669],\n",
    "#        [   7.   ,    0.   ,    1.   ,    8.959, -190.347],\n",
    "#        [   8.   ,    0.   ,    1.   ,    8.959, -193.452],\n",
    "#        [   9.   ,    0.   ,    0.   ,    4.88 , -285.247],\n",
    "#        [  10.   ,    0.   ,    0.   ,   90.11 , -285.182],\n",
    "#        [  11.   ,    0.   ,    0.   ,   49.086, -400.545],\n",
    "#        [  12.   ,    0.   ,    0.   ,   79.801, -250.579]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6dcae2c8",
   "metadata": {},
   "source": [
    "# Method 4: Agent Extensive Form Estimation Linear\n",
    "\n",
    "- [Return](#Content)\n",
    "\n",
    "In the extensive form game, assume agent is different at each turn. The probability of making a guess at each turn is based on payoffs between making a guess now and the maximal payoff from waiting. \n",
    "\n",
    "I only changed the payoff matrix but leave the probability matrix as the following. However, the probability is updated differently, for each node at each turn, I will assume the probability of guess at this turn is 0.5 and then update the probability based on the payoff tradeoff. \n",
    "\n",
    "\n",
    "Probability is defined as a matrix of 5*6 (5 nodes, deciding at 6 turns). It is assumed that each subject with a given lambda will pre-determine the probability of makig a prediction at a certain turn, the probability doesn't change based on what new information is updated as time goes by (Not sure what is a more formal/proper way to describe this)\n",
    "\n",
    "The change here is I make the payoff to be linear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5926d0bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Step 1: Define Payoffs for Deciding at each turn; The payoff depends on others' probability of making a prediction \n",
    "\n",
    "# Step 2: Write out the policy iteration \n",
    "\n",
    "# Step 3: for different lambda value, derive the results\n",
    "\n",
    "# Step 4: Based on the estimation result, do two things \n",
    "# A. Draw QRE for each node for each treatment, show the difference, describe\n",
    "# B. Estimate MLE based on realized/observed frequencies in each treatment\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "id": "0b28f696",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Step 1. \n",
    "def payoff(pOther,network, cost):\n",
    "    '''This is for the normal form estimation \n",
    "        pOther = matrix(5,6); each row is for each node; each column is for each turn\n",
    "        '''\n",
    "    diff_pay = 100\n",
    "    q = 0.7\n",
    "    if cost=='h':\n",
    "        c = 8\n",
    "    elif cost == 'l':\n",
    "        c = 1\n",
    "    \n",
    "    if network == 'a':\n",
    "        #In network a, I only consider the pay for A and B, at turn 0 \n",
    "        pay =  np.empty((5,6),dtype=float)\n",
    "        pay[:,0] = ProbCorrect_Bayesian(1,q)*diff_pay\n",
    "        \n",
    "        # indegree = 1, node A / E\n",
    "        pay_1 = ProbCorrect_Bayesian(2,q)*diff_pay - c\n",
    "        pay[0,1] = pay_1 \n",
    "        pay[4,1] = pay_1 \n",
    "        j = 2\n",
    "        while j <= 5:        \n",
    "            pay[0,j] = ProbCorrect_Bayesian(2,q)*diff_pay - j*c\n",
    "            pay[4,j] = ProbCorrect_Bayesian(2,q)*diff_pay - j*c\n",
    "            j += 1\n",
    "        \n",
    "        # indegree = 3, node B\n",
    "        pay_1 = ProbCorrect_Bayesian(4,q)*diff_pay - c\n",
    "        pi_b = pOther[0,0]*ProbCorrect_Bayesian(4,q)*diff_pay + (1- pOther[0,0])*ProbCorrect_Bayesian(5,q)*diff_pay \n",
    "        pay[1,1] = pay_1\n",
    "        j = 2\n",
    "        while j <= 5:        \n",
    "            pay[1,j] = pi_b - j*c\n",
    "            j += 1\n",
    "\n",
    "        # indegree = 2, node C\n",
    "        pay_1 = ProbCorrect_Bayesian(3,q)*diff_pay - c\n",
    "        pay[2,1] = pay_1\n",
    "        pi_c = pOther[0, 0]*pOther[1,0]*ProbCorrect_Bayesian(3,q)*diff_pay + ((1-pOther[0, 0])*pOther[1,0] + pOther[0, 0]*(1-pOther[1,0]))*ProbCorrect_Bayesian(4,q)*diff_pay + (1-pOther[0, 0])*(1-pOther[1,0])*ProbCorrect_Bayesian(3,q)*diff_pay\n",
    "        j = 2\n",
    "        while j <= 5:        \n",
    "            pay[2,j] = pi_c - j*c\n",
    "            j += 1\n",
    "            \n",
    "        # indegree = 1, node D (position 3)\n",
    "        pay_1 = ProbCorrect_Bayesian(2,q)*diff_pay - c\n",
    "        pay[3,1] = pay_1 \n",
    "        pi_d = pOther[0,0]*ProbCorrect_Bayesian(2,q)*diff_pay + (1- pOther[0,0])*ProbCorrect_Bayesian(3,q)*diff_pay \n",
    "        j = 2\n",
    "        while j <= 5:        \n",
    "            pay[3,j] = pi_d - j*c\n",
    "            j += 1\n",
    "        \n",
    "   \n",
    "        \n",
    "    elif network == 'b':\n",
    "         # We know there are 5 nodes, pay matrix is 5X6 ( 6 period)\n",
    "        pay =  np.empty((5,6),dtype=float)\n",
    "        pay[:,0] = ProbCorrect_Bayesian(1,q)*diff_pay\n",
    "\n",
    "        # Note: since here the payoff is about turn 0,1,2, need to do the max in the \n",
    "        # indegree = 2, node A\n",
    "        pay_1 = ProbCorrect_Bayesian(3,q)*diff_pay - c\n",
    "        pi_a = pOther[1,0]*ProbCorrect_Bayesian(3,q)*diff_pay + (1-pOther[1,0])*ProbCorrect_Bayesian(5,q)*diff_pay        \n",
    "        pay[0,1] = pay_1\n",
    "        j = 2\n",
    "        while j <= 5:        \n",
    "            pay[0,j] = pi_a - j*c\n",
    "            j += 1\n",
    "\n",
    "        # indegree = 3, node B\n",
    "        pay_1 = ProbCorrect_Bayesian(4,q)*diff_pay - c\n",
    "        pi_b = pOther[0,0]*ProbCorrect_Bayesian(4,q)*diff_pay + (1- pOther[0,0])*ProbCorrect_Bayesian(5,q)*diff_pay \n",
    "        pay[1,1] = pay_1\n",
    "        j = 2\n",
    "        while j <= 5:        \n",
    "            pay[1,j] = pi_b - j*c\n",
    "            j += 1\n",
    "\n",
    "\n",
    "        # indegree = 1, node C or D or E, (position 2,3)\n",
    "        pay_1 = ProbCorrect_Bayesian(2,q)*diff_pay - c\n",
    "        pay[2:5,1] = pay_1\n",
    "        # Since in bayesian updating, having 3 or 4 signals carry the same informaiton value, can group these points together\n",
    "        pi_e0 =  pOther[0,0]*ProbCorrect_Bayesian(2,q)*diff_pay + (1-pOther[0,0])*ProbCorrect_Bayesian(3,q)*diff_pay \n",
    "        pay[2:5,2] = pi_e0 - 2*c\n",
    "        pi_e =  pOther[0,0]*ProbCorrect_Bayesian(2,q)*diff_pay + (pOther[0,1] + (1- pOther[0,0] -pOther[0,1])*pOther[1,0])*ProbCorrect_Bayesian(3,q)*diff_pay  +(1- pOther[0,0] -pOther[0,1])*(1-pOther[1,0])*ProbCorrect_Bayesian(5,q)*diff_pay \n",
    "        \n",
    "        j = 3\n",
    "        while j <= 5:        \n",
    "            pay[2:5,j] = pi_e - j*c\n",
    "            j += 1\n",
    "#     pay_avg = np.sum(pay,axis=1)\n",
    "#     return pay/pay_avg[:,None]\n",
    "    return pay/70\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "id": "3ae3f3d6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Step 2\n",
    "def policy_iter(l,p_ini,network, waitingcost, tol = 1e-10):\n",
    "    \n",
    "    error = 1\n",
    "    pOthers = np.ones((5,6))* p_ini\n",
    "    \n",
    "    nrep = 1\n",
    "    while error > tol:\n",
    "        \n",
    "        mixed_payoff = payoff(pOthers,network, waitingcost)\n",
    "        ## Previous code\n",
    "#         add_error = np.exp(l*mixed_payoff)\n",
    "\n",
    "#         node_avg =  np.sum(add_error,axis=1)\n",
    "#         sigma = add_error / node_avg[:,None]\n",
    "        ## Here update the probability sequentially, using backward induction \n",
    "        # Backward induction, from prob guess at turn 4, turn 5 =1-sum(p0:p4):\n",
    "        sigma = np.zeros((5,6))\n",
    "        p_guess_byTurn = np.zeros((5,5))\n",
    "        for i in range(5):\n",
    "            temp = np.max(mixed_payoff[:, i+1:6],axis=1)\n",
    "            payoff_relevent = np.zeros((5,2))\n",
    "            payoff_relevent[:,0] = mixed_payoff[:,i]\n",
    "            payoff_relevent[:,1] = temp\n",
    "\n",
    "            payoff_error = np.exp(l*payoff_relevent)\n",
    "            node_avg =  np.sum(payoff_error,axis=1)\n",
    "            pi = payoff_error / node_avg[:,None] # (guess, wait)\n",
    "            \n",
    "            p_guess_byTurn[:,i] = pi[:,0]\n",
    "            \n",
    "        sigma[:,0] = p_guess_byTurn[:,0]\n",
    "        wait_prob = 1-p_guess_byTurn[:,0]\n",
    "        for i in range(1,5):\n",
    "            sigma[:,i] =    wait_prob * p_guess_byTurn[:,i]\n",
    "            wait_prob *= 1-p_guess_byTurn[:,i]\n",
    "\n",
    "        sigma[:,5] = 1-np.sum(sigma, axis=1)\n",
    "\n",
    "\n",
    "        error = np.max(np.sum(np.abs(sigma-pOthers), axis=1))\n",
    "        pOthers = sigma\n",
    "\n",
    "        nrep += 1\n",
    "        \n",
    "    print(\"Number of Iterations:\",nrep)\n",
    "    return pOthers\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "id": "edc11829",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Step 3\n",
    "\n",
    "# lambd = []\n",
    "n = 200\n",
    "lambd = np.logspace(-1, 2.5, n, endpoint=True)\n",
    "# for i in range(n):\n",
    "#     lambd.append(1.0173182**i - 1)\n",
    "\n",
    "def QRE_Outcome(network, waitingCost):\n",
    "    '''Contains both the prob and graphs'''\n",
    "    \n",
    "    p = np.empty((n,5,6))\n",
    "    for i in range(n):\n",
    "#         print(\"Round:\", i+1)\n",
    "        Result = policy_iter(lambd[i],1/6,network,waitingCost)\n",
    "        p[i] = Result\n",
    "    \n",
    "    return p\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "d765ac0e",
   "metadata": {},
   "outputs": [
    {
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   ],
   "source": [
    "# Obtain the QRE and output QRE figures for extensive form\n",
    "\n",
    "QRE_a_l = QRE_Outcome('a', 'l')\n",
    "QRE_a_h = QRE_Outcome('a', 'h')\n",
    "QRE_b_l = QRE_Outcome('b', 'l')\n",
    "QRE_b_h = QRE_Outcome('b', 'h')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "id": "959be366",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculate the average waiting turns for each treatment, ndoes with 1 or multiple information \n",
    "turns = np.array([0,1,2,3,4,5])\n",
    "QREs = [QRE_a_l, QRE_a_h, QRE_b_l, QRE_b_h]\n",
    "TreatmentName = ['NC_l','NC_h', 'C_l', 'C_h']\n",
    "Network = ['nc', 'nc', 'c','c']\n",
    "Cost = ['l','h','l','h']\n",
    "\n",
    "avg_turn = np.empty((4,n,5))\n",
    "for t in range(4):\n",
    "    for i in range(n):\n",
    "        QRE = QREs[t]\n",
    "        x = QRE[i]*turns\n",
    "        avg_turn[t][i] = x.sum(axis=1)\n",
    "\n",
    "\n",
    "fig, axes = plt.subplots(nrows=1, ncols=3,  sharex=True,  sharey=True,   constrained_layout=True, figsize=(10,4))\n",
    "fig.set_constrained_layout_pads( w_pad=1 / 100)\n",
    "\n",
    "linestyle = {'c':'-', 'nc':':'}\n",
    "markerstyle = {'l': '>', 'h': 'o' }\n",
    "y_max = 5\n",
    "y_step = 1\n",
    "\n",
    "# Defining custom 'xlim' and 'ylim' values.\n",
    "# custom_xlim = (1, 11)\n",
    "custom_ylim = (0, y_max)\n",
    "# custom_xtick = np.arange(1,11,step=1)\n",
    "custom_ytick = np.arange(0,y_max,step=y_step)\n",
    "# custom_xticklabel = [1,5,10]\n",
    "\n",
    "plt.setp(axes, yticks= custom_ytick, ylim=custom_ylim)\n",
    "\n",
    "for t in range(4):\n",
    "    \n",
    "    if t==3:\n",
    "        axes[0].plot(lambd,avg_turn[t].mean(axis=1), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]],  markersize=2)\n",
    "    else: \n",
    "        axes[0].plot(lambd,avg_turn[t].mean(axis=1), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]])\n",
    "    axes[0].set_title('All nodes', fontsize=15) \n",
    "    \n",
    "    if t<=1:\n",
    "        axes[1].plot(lambd,avg_turn[t, :, [0,3,4]].mean(axis=0), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]])\n",
    "    elif t==3:\n",
    "        axes[1].plot(lambd,avg_turn[t, :, [2,3,4]].mean(axis=0), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]], markersize=2)\n",
    "    else : \n",
    "        axes[1].plot(lambd,avg_turn[t, :, [2,3,4]].mean(axis=0), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]])\n",
    "    axes[1].set_title('Nodes with $InDegree=1$', fontsize=15) \n",
    "    \n",
    "    \n",
    "    if t<=1:\n",
    "        axes[2].plot(lambd,avg_turn[t, :, [1,2]].mean(axis=0), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]])\n",
    "    elif t==3:\n",
    "        axes[2].plot(lambd,avg_turn[t, :, [0,1]].mean(axis=0), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]], markersize=2)\n",
    "    else : \n",
    "        axes[2].plot(lambd,avg_turn[t, :, [0,1]].mean(axis=0), label=str(TreatmentName[t]),\n",
    "               linestyle=linestyle[Network[t]], marker=markerstyle[Cost[t]])\n",
    "\n",
    "    axes[2].set_title('Nodes with $InDegree>1$', fontsize=15) \n",
    "    \n",
    "    axes[1].set_xlabel('$\\lambda$', fontsize=15)\n",
    "    axes[0].set_ylabel('Average Waiting Turns', fontsize=15)\n",
    "    axes[0].set_xscale('log')\n",
    "handles, labels = axes[0].get_legend_handles_labels()\n",
    "fig.legend(handles, labels, bbox_to_anchor=(.5,-0.05), loc=\"center\" , ncol=4, frameon=False, prop={'size':15})\n",
    "fig.savefig(\"..\\\\Output_Figures\\\\05-QRE-Calculation\\\\\"+\"QRE_Extensive_AvgTurns\"  , bbox_inches=\"tight\")  \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "261e7125",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}