05-QRE-Calculation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "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": 4,
   "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(\"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": "2a33d67c",
   "metadata": {},
   "source": [
    "# First method: sequantial probability. \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": 42,
   "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": 43,
   "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": 43,
     "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": 53,
   "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": 54,
   "id": "8b1fe500",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Round: 1\n",
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      "Round: 45\n",
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      "Round: 50\n",
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      "Round: 60\n",
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      "Round: 61\n",
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      "Round: 62\n",
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      "Round: 63\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: 68\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: 81\n",
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      "Round: 82\n",
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      "Round: 83\n",
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      "Round: 84\n",
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      "Round: 85\n",
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     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_32/3109127715.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_32/3109127715.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_32/3109127715.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_32/3109127715.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_32/2405291984.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",
      "Round: 175\n",
      "[70. 69.]\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": 55,
   "id": "d8288681",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "       [6.55952697e-01, 3.44047303e-01],\n",
       "       [6.62354263e-01, 3.37645737e-01],\n",
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       "       [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",
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       "       [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": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "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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     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_32/3109127715.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_32/3109127715.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_32/3109127715.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_32/3109127715.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_32/1600054940.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"
     ]
    },
    {
     "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": 57,
   "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",
      "[70.    81.692]\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",
      "[70.    81.692]\n",
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      "Round: 84\n",
      "[70.    79.546]\n",
      "[70.    81.692]\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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      "Number of Iterations: 3\n",
      "Round: 106\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[70.    79.546]\n",
      "[70.    81.692]\n",
      "Number of Iterations: 3\n",
      "Round: 107\n",
      "[70.    79.546]\n",
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      "[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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      "[70.    79.546]\n",
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      "Round: 114\n",
      "[70.    79.546]\n",
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      "Round: 115\n",
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      "Round: 116\n",
      "[70.    79.546]\n",
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      "[70.    79.546]\n",
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      "[70.    79.546]\n",
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     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_32/3109127715.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_32/3109127715.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_32/3109127715.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_32/3109127715.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_32/699999969.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": 58,
   "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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     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_32/3109127715.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_32/3109127715.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_32/3109127715.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_32/3109127715.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_32/1953066089.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"
     ]
    },
    {
     "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",
    "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": 116,
   "id": "fd51067d",
   "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 \n",
    "        pay_1 = ProbCorrect_Bayesian(2,q)*diff_pay - c\n",
    "        pay[0,1] = pay_1 \n",
    "        j = 2\n",
    "        while j <= 5:        \n",
    "            pay[0,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/E (position 3)\n",
    "        pay_1 = ProbCorrect_Bayesian(2,q)*diff_pay - c\n",
    "        pay[3:5,1] = 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[3:5,j] = pi_d - j*c\n",
    "            j += 1\n",
    "        \n",
    "   \n",
    "        \n",
    "    if 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_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 = 2\n",
    "        while j <= 5:        \n",
    "            pay[2:5,j] = pi_e - j*c\n",
    "            j += 1\n",
    "\n",
    "    return pay\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "id": "448a563f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[70.  , 69.  , 68.  , 67.  , 66.  , 65.  ],\n",
       "       [70.  , 77.4 , 80.81, 79.81, 78.81, 77.81],\n",
       "       [70.  , 77.4 , 76.4 , 75.4 , 74.4 , 73.4 ],\n",
       "       [70.  , 69.  , 75.  , 74.  , 73.  , 72.  ],\n",
       "       [70.  , 69.  , 75.  , 74.  , 73.  , 72.  ]])"
      ]
     },
     "execution_count": 212,
     "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": 213,
   "id": "de367360",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[70.  , 77.4 , 80.81, 79.81, 78.81, 77.81],\n",
       "       [70.  , 77.4 , 80.81, 79.81, 78.81, 77.81],\n",
       "       [70.  , 69.  , 77.94, 76.94, 75.94, 74.94],\n",
       "       [70.  , 69.  , 77.94, 76.94, 75.94, 74.94],\n",
       "       [70.  , 69.  , 77.94, 76.94, 75.94, 74.94]])"
      ]
     },
     "execution_count": 213,
     "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\n",
    "# node_avg =  np.sum(x,axis=1)\n",
    "# node_avg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "36d66217",
   "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": 170,
   "id": "357f072d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Step 3\n",
    "lambd = []\n",
    "n = 200\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",
    "    # 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(\"05-QRE-Calculation\\\\\"+\"QRE\"+network+\"-\"+waitingCost+\"-mSource\", bbox_inches=\"tight\")  \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(6):\n",
    "        ax.plot(lambd,p[:,i,j], label='Turn'+str(j))\n",
    "    ax.legend()\n",
    "    fig.savefig(\"05-QRE-Calculation\\\\\"+\"QRE\"+network+\"-\"+waitingCost+\"-sSource\", bbox_inches=\"tight\")  \n",
    "\n",
    "    \n",
    "    return p\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "id": "f81f2224",
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    {
     "name": "stderr",
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     "text": [
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_11364/1030355559.py:12: RuntimeWarning: overflow encountered in exp\n",
      "  add_error = np.exp(l*mixed_payoff)\n",
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_11364/1030355559.py:15: RuntimeWarning: invalid value encountered in true_divide\n",
      "  sigma = add_error / node_avg[:,None]\n"
     ]
    },
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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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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Nt1Vwu92t3WjLcNttt3HjjTeSm5tLbGwsL7/8sr9DF6Lb+mzbZ5z90dksLVzKrZNu5bWZr0kSOESSCALk8ssv57333msajogw7rO9YMECTjjhBC6++GJGjx7NggULmDZtGueddx7Dhg3jkksuQWuN1ppvv/2W8847D4DLLruMDz/8MBhvRYgupcHVwH2L7+O2H25jUMwgPjjjA34z4jeYTf7tkqE36XFNQ/d9sp4NBVV+XeaIlCjuPd1/95xeunQp69ato3///ixYsICVK1eyfv16UlJSOProo/npp58YNmwYMTExWCzGJkpLS2P37sO6j7cQ3d7Oqp3ctOAmNpdv5rejfssfxv0Bq0lOnT5cPS4RdAfZ2dkHnO6ZnZ1NWppxr/KsrCx27NjB0KEHV3HlwLDozZYWLuWGBTdgUiaemf4Mx6UdF+yQeowelwj8ued+OCwWCx6PBzDOanA49t+DOzw8/IBpQ0JCmv43m824XC4SEhKoqKjA5XJhsVjIz88nJeWA+30L0Wt8kPsBf1n8FzKiMnh6+tOkRaYFO6QeRY4RBEhmZibLly8H4KOPPsLpdHZqfqUUJ5xwQtNxhtdee40zzzzT73EK0ZV5tIe5y+dy76J7ye6bzRuz35AkEACSCALkqquuYuHChWRnZ7NkyZKDagEd8fDDD/P3v/+dQYMGUVpaypVXXhmASIXomtweN/cuupdX1r3CBUMv4JnpzxBpiwx2WD1SwO5ZHCgt3Y9g48aNDB8+PEgRBV9vf/+i53G6ndzx4x18ueNLrh17LdeOvVaOkR0mpdRyrfXElsb1uGMEQojurcHVwE0Lb+L7/O+5acJNXD7q8mCH1ONJIhBCdBkOt4MbFtzAot2L+POUP3P+0PODHVKvIIlACNEluDwubv3+Vn7a/RNzps7h3CHnBjukXkMOFgshgs6jPdz90918k/cNt026TZLAESaJQAgRVFprHvj5Af637X/8cdwf+fWIXwc7pF5HEoEQIqieW/Mc7255lytHXclVY64Kdji9kiQCPygtLSUrK4usrCySk5NJTU1tGva9oriznn76aQYNGoRSipKSEj9GLETX8NHWj5i3ah5nDDyD/xv/f8EOp9eSg8V+sK8baoA5c+YQERHBzTff3O58brcbs7n1HhOPPvpoTjvtNKZNm+anSIXoOn4u/Jk5i+Ywue9k5kydI9cJBJHUCALkcLuhBhg3bhyZmZnBCF+IgMotz+XG724kMzqTudPmYjVLD6LB1PNqBJ/fDkVr/bvM5NEw629+W1xHuqE+5phj/LY+IbqS8oZyrv/2ekItoTx70rPSbUQXIDWCIGitG2qTydTUDbUQPZHL4+KWhbdQXFfMUyc+RXJ4crBDEvTEGoEf99wPx+F2Qy1ET/R4zuMsKVrCg8c8yKiEUcEOR3hJjSBADrcbaiF6mo+2fsSbG9/k18N/zRkDzwh2OMKHJIIA8Uc31E899RRpaWnk5+czZswYfve73wUgUiECb33Jeu5ffD+Tkydz08Sbgh2OaEa6oe4Bevv7F11bZWMlF3x6AR7t4e3T3ibWHhvskHol6YZaCBEUWmv+/NOf2VO3h9dmviZJoIuSpiEhRMC8vuF1vtv1HX+a8CfGJI4JdjiiFZIIhBABsWrvKp5Y/gTT06fz6+HSkVxXJolACOF3lY2V3PL9LfQJ78P9R98v3Ud0cXKMQAjhV1pr7lt8HyX1Jbw5602ibFHBDkm0Q2oEQgi/+nDrh3y18yuuH3c9IxNGBjsc0QFSI/CD0tJSpk+fDkBRURFms5nExETA6FfIZrMd0nIvueQScnJysFqtZGdn8/zzz2O1SudcouvKq8rjoaUPkZ2czeUjLw92OKKDAlojUErNVEptVkptVUrd3sL4aKXUJ0qp1Uqp9UqpKwIZT6Ds64Z61apVXHPNNdx4441Nw20lAbfb3eZyL7nkEjZt2sTatWupr6/npZde8nfoQviN0+Pk9h9ux2qy8uAxD2JS0uDQXQRsSymlzMAzwCxgBHCRUmpEs8l+D2zQWo8FpgGPK6UObfe5i/FHN9SzZ89GKYVSiuzsbPLz84PyXoToiOdWP8fakrXcM/Ue6Uyumwlk01A2sFVrvQ1AKfUf4Exgg880GohUxikFEUAZcFg9rj289GE2lW06nEUcZFjcMG7Lvs1vy+tsN9ROp5M33niDJ5980m8xCOFPy/cs56W1L3HmwDOZkTkj2OGITgpk3S0V2OUznO99zdfTwHCgAFgL/J/W2tN8QUqpq5VSOUqpnOLi4kDFe8R0thvq6667juOOO45jjz32CEcqRPuqHdXc+cOdpISncMfkO4IdjjgEgawRtHTicPOOjWYAq4ATgYHAV0qpH7TWVQfMpPULwAtg9DXU1kr9ued+OPzVDfV9991HcXExzz//fIAjFuLQPLLsEaMLiVmvEW7tfOeKIvgCWSPIB/r5DKdh7Pn7ugL4QBu2AtuBYQGM6YjxRzfUL730El9++SVvvfUWJpMceBNdzw/5P/Dh1g+5YtQVjE0cG+xwxCEKZOmyDBislOrvPQB8IfBxs2nygOkASqk+wFBgWwBjOmL80Q31Nddcw549e5g6dSpZWVncf//9AYhUiENT7ajmvsX3MTB6INeOvTbY4YjDENBuqJVSs4EnADPwitb6QaXUNQBa6+eUUinAq0BfjKakv2mt32xrmdIN9cF6+/sXwTFn0Rz+u/W/vDnrTUYnjg52OKIdQeuGWmv9GfBZs9ee8/m/ADglkDEIIfxvccFi3s99nytGXiFJoAeQhmchRKfUOmuZs2gOmVGZXJd1XbDDEX4gXUwIITpl7vK5FNYW8vqs17Fb7MEOR/iB1AiEEB22tHApb29+m1+P+DVZSVnBDkf4iSQCIUSH1DnruHfRvaRHpnP9uOuDHY7wI2kaEkJ0yFMrnyK/Jp9/zvgnoZbQYIcj/EgSgR8EqhvqK6+8kpycHLTWDBkyhFdffbWp8zohjqQVe1bw743/5qJhFzExucUzEEU3Jk1DfhCobqjnzp3L6tWrWbNmDenp6Tz99NP+Dl2IdtW76rln0T2kRKRww/gbgh2OCABJBAHij26oo6KMW/xpramvr5f7voqgeHrl0+ys2sl9R91HmDUs2OGIAOhxTUNFf/0rjRv92w11yPBhJN95p9+W15luqK+44go+++wzRowYweOPP+63GIToiFV7V/HGhjc4f8j5TO47OdjhiACRGkEQdKYb6n/+858UFBQwfPhw3n777SBEK3qrRncj9ywybjLzp4l/CnY4IoB6XI3An3vuh8Nf3VDve+2CCy7g0Ucf5YoruuXdPEU3NG/VPLZXbuf5k56X7qV7OKkRBMjhdkOttWbr1q1N/3/yyScMG9YjeugW3cC6knW8uv5Vzhl8DkelHhXscESA9bgaQVdx1VVXceaZZ5Kdnc306dM73Q211prLLruMqqoqtNaMHTuWZ599NkDRCrGfw+3g7h/vJjE0kZsn3hzscMQRENBuqANBuqE+WG9//8K/nlrxFC+ufZF50+dxbJrcHrWnaKsbamkaEkI02VC6gVfWvcIZA8+QJNCLSCIQQgDgdDv5809/Js4ex62Tbg12OOIIkmMEQggAXlr7ElvKt/DUCU8RHRId7HDEESQ1AiEEm8s288KaF5jdfzYnpJ8Q7HDEESaJQIhezukxmoSiQqK4I/uOYIcjgkCahoTo5f657p9sLNvI3GlzibHHBDscEQRSI/CD0tJSsrKyyMrKIjk5mdTU1KZh3yuKD9X1118v3U+LgNhavpXnVj/HjMwZnJRxUrDDEUEiNQI/2NcNNcCcOXOIiIjg5pvbvxDH7XZjNpvbnCYnJ4eKigo/RCnEgVweF3/+6c9EWCO4c3LX6JpFBIfUCALEH91Qu91ubrnlFh555JGgvAfRs726/lXWla7jzil3EmePC3Y4Ioh6XI3gh3e2ULKrxq/LTOgXwbHnD/Hb8jraDfXTTz/NGWecQd++ff22biEAcstzmbdqHidnnMzMzJnBDkcEWY9LBN1Ba91QA03dUA8YMIB3332XBQsWBClK0VP5NgndNfmuYIcjuoAelwj8ued+OA63G+qVK1eydetWBg0aBEBdXR2DBg1q6pFUiEP1z3X/ZH3peh47/jHiQ+ODHY7oAuQYQYAcbjfUp556KkVFRezYsYMdO3YQFhYmSUActtzyXOatnscpGacwI3NGsMMRXYQkggC56qqrWLhwIdnZ2SxZsqTT3VAL4W9Oj5O7f7qbKFsUd02RJiGxn3RD3QP09vcvOuaFNS/wj5X/4PHjH+eUzFOCHY44wqQbaiF6uS3lW3h29bPMyJwhSUAcRBKBED2c0+Pk7h+NJiG5cEy0pMedNSSEONCLa15kY9lG/j7t73LhmGiR1AiE6MHWFK/hhTUvcPqA0zk54+RghyO6KEkEQvRQdc467vzxTpLCkrhjsnQvLVoX0ESglJqplNqslNqqlLq9lWmmKaVWKaXWK6UWBjIeIXqTvy//O3lVeTx4zINE2iKDHY7owgJ2jEApZQaeAU4G8oFlSqmPtdYbfKaJAeYBM7XWeUqppEDFE0ilpaVMnz4dgKKiIsxmM4mJiYDRr5DNZjuk5V5++eUsXLiQ6GjjtoGvvvoqWVlZfolZ9Gzf53/P25vf5rIRlzEpeVKwwxFdXIcSgVJqIJCvtW5USk0DxgCva60r2pgtG9iqtd7mXcZ/gDOBDT7TXAx8oLXOA9Ba7+3sG+gKAtkN9aOPPsp5553njzBFL1HeUM49P93D4NjB/HH8H4MdjugGOto09D7gVkoNAl4G+gP/bmeeVGCXz3C+9zVfQ4BYpdQCpdRypdSlHYyny/NHN9RCdJbWmvsW30eVo4qHjnkIm/nQaqOid+lo05BHa+1SSp0NPKG1/odSamU786gWXmtewlmACcB0IBRYrJT6WWu95YAFKXU1cDVAenp6myv97tUX2LtzWzuhdU5SxgBOuPxqvy2vo91QA9x1113cf//9TJ8+nb/97W8HdFAnRHMfbv2Qb/K+4U8T/sTQuKHBDkd0Ex2tETiVUhcBlwGfel+ztjNPPtDPZzgNKGhhmi+01rVa6xLge2Bs8wVprV/QWk/UWk/c1/benbXWDbXJZGrqhhrgoYceYtOmTSxbtoyysjIefvjhIEUsuoNtFdt4aOlDZCdnc+mIHlO5FkdAR2sEVwDXAA9qrbcrpfoDb7YzzzJgsHfa3cCFGMcEfH0EPK2UsgA2YDIwt6PBt8Sfe+6H43C7oQaabkgTEhLCFVdcwWOPPRbosEU31eBq4Jbvb8FutvPQsQ9hNrV97EkIXx2qEXjP9LkNWOEd3q61/ls787iAPwBfAhuBd7TW65VS1yilrvFOsxH4AlgDLAVe0lqvO9Q305UcbjfUAIWFhYCRSD788ENGjRrl1xhFz/FYzmNsKd/CA8c8QFJYtzz5TgRRR88aOh14DGOvvb9SKgu4X2t9Rlvzaa0/Az5r9tpzzYYfBR7tRMzdwlVXXcWZZ55JdnY206dPP6RuqC+55BKKi4vRWpOVlcVzzz3X/kyi1/l659dNp4oel3ZcsMMR3VCHuqFWSi0HTgQWaK3HeV9bq7UeHeD4DiLdUB+st7//3qygpoDzPjmPjMgMXp/1OlZze4fuRG/lj26oXVrrymavyTmOQgSR0+Pk1u9vRWvNI8c/IklAHLKOHixep5S6GDArpQYDfwQWBS4sIUR75q2ax+ri1Tx63KP0i+zX/gxCtKKjNYLrgZFAI/AWUAXcEKCYhBDtWLhrIS+tfYlzB5/LzP4zgx2O6OY6VCPQWtcBd3kfXZLWGqVauoatZ5OrkHufXdW7uOPHOxgeN5zbs1vsy1GITmkzESilntBa36CU+oQWjgm0d9bQkWK32yktLSU+Pr5XJQOtNaWlpdjt9mCHIo6QBlcDf1rwJwAen/Y4dotse3H42qsRvOF97tJXMqWlpZGfn09xcXGwQzni7HY7aWlpwQ5DHAFaax74+QE2lW3imenPyHEB4TdtJgKt9XLvc5e+T4DVaj2gywYheqL3ct/jo18+4v+N+X9yvYDwq45eULaWg5uGKoEc4AGtdam/AxNC7Ldizwr+uuSvHJ1yNNeOvTbY4YgepqOnj34OuNnf9fSFGL2LVgKvAqf7PTIhBACFNYXcuOBGUiNSefi4h6UfIeF3HU0ER2utj/YZXquU+klrfbRS6teBCEwIYdx3+I/f/RGH28FTJz5FdEh0sEMSPVBHryOIUEpN3jeglMoGIryDLr9HJYTAoz3c/dPdbC7bzCPHPcKA6AHBDkn0UB2tEfwOeEUpta/wrwZ+p5QKBx4KSGRC9HLPr36er3Z+xU0TbuLYtGODHY7owTp6QdkyYLRSKhqjo7oKn9HvBCIwIXqzT375hHmr53HGwDO4bORlwQ5H9HAdahpSSvVRSr0M/EdrXaGUGqGUujLAsQnRKy0pXMI9i+4hOzmbOVPn9KqLJEVwdPQYwasYN5hJ8Q5vQfoaEsLvtpZv5cbvbiQjMoO5J8yVHkXFEdHRRJCgtX4H8EDT3cfcAYtKiF5ob91erv3mWuwWO8+e9CxRtqhghyR6iY4eLK5VSsXjvahMKTUF4xoCIYQf1Dhq+MM3f6CysZLXZr5G34i+wQ5J9CIdTQR/Aj4GBiqlfgISgV8FLCohepEGVwPXf3s9ueW5PHXiUwyPl7vNiSOro4lgPXA8MBTjiuLNdLxZSQjRCqfHyU0Lb2L5nuX87di/yWmiIig6Wpgv1lq7tNbrtdbrtNZOYHEgAxOip3N73Nz14118n/89d0+5m9kDZgc7JNFLtXc/gmQgFQhVSo3DqA0ARAFhAY5NiB5La81fl/yVz7d/zg3jb+D8oecHOyTRi7XXNDQDuBxIA/7u83o1cGeAYhKiR9NaM3f5XN7Z8g6/HfVbrhwtl+SI4GrvfgSvAa8ppc7VWr9/hGISosfalwT+uf6fXDD0Am4Yf0OwQxKiw11MvK+UOhXjBvZ2n9fvD1RgQvQ0Wmsey3mM1ze8zoVDL+TOyXfKVcOiS+jojWmewzgmcALwEnAesDSAcQnRo2iteWTZI7y58U0uHnYxt2ffLklAdBkdPWvoKK31pUC51vo+YCogN0wVogO01jy87GHe3Pgmvx7+a0kCosvp6HUEDd7nOqVUClAKyE2ChWiH2+PmwSUP8u6Wd7l0xKXcPPFmSQKiy+loIvhEKRUDPAqswOhq4sVABSVET+BwO7j9h9v5audX/G707/jjuD9KEhBdUruJQCllAr7x3oPgfaXUp4Bday19DQnRihpHDTd8dwNLipZwy8RbuHTkpcEOSYhWtZsItNYepdTjGMcF0Fo3Ao2BDkyI7qq0vpRrv76W3PJc/nrMXzl94OnBDkmINnX0YPF8pdS5Suq1QrRpd81uLvviMrZXbufJE5+UJCC6hc70PhoOuJRSDRhdTWittXSYLoTXmuI1/PHbP+LwOHjxlBfJSsoKdkhCdEhHLyiLDHQgQnRnn2//nLt/vJuksCRenv4yA2MGBjskITqso/cs/qYjrwnR22iteXbVs9z6/a2MShjFv0/9tyQB0e20mQiUUnalVByQoJSKVUrFeR+Z7L9/cVvzz1RKbVZKbVVK3d7GdJOUUm6l1HmdfgdCBEmju5HbfriNeavnccbAM3jxlBeJtccGOywhOq29pqH/h3GT+hRguc/r1cAzbc2olDJ7pzkZyAeWKaU+1lpvaGG6h4EvOxW5EEFUUl/C/333f6wpXsMN42/gt6N+K9cIiG6rvaahRcBRwM1a6wHAfcA6YCHw73bmzQa2aq23aa0dwH+AM1uY7nrgfWBvZwIXIliW71nOrz75FbnlucydNpcrR18pSUB0a+0lgueBRq31P5RSxwEPAa9h3Lj+hXbmTQV2+Qzne19ropRKBc4GnmtrQUqpq5VSOUqpnOLi4nZWK0RgaK15bf1rXPnllURYI/jX7H9xUsZJwQ5LiMPWXtOQWWtd5v3/AuAF730J3ldKrWpn3pZ2kXSz4SeA27TW7rb2qLTWL+BNPBMnTmy+DCECrsZRwz2L7uGrnV9xUvpJ/OXovxBhiwh2WEL4RbuJQCll0Vq7gOnA1Z2YN58DeyhNAwqaTTMR+I83CSQAs5VSLq31h+0FLsSRsrV8KzcuuJFd1bu4eeLNXDriUmkKEj1Ke4X5W8BCpVQJUA/8AKCUGoTRPNSWZcBgpVR/YDdwIXCx7wRa66YeTJVSrwKfShIQXYXWmk+2fcIDPz9AmCWMF095kUnJk4IdlhB+196tKh/0Xi/QF5ivtd7XLGPCOMjb1rwupdQfMM4GMgOvaK3XK6Wu8Y5v87iAEMFU5ajigcUP8PmOz5nQZwKPHvcoiWGJwQ5LiIBQ+8v27mHixIk6Jycn2GGIHiynKIc7f7yT4rpirsu6jt+O+i1mkznYYQlxWJRSy7XWE1sa19G+hoTo8ZweJ8+uepaX171MWkQar896ndGJo4MdlhABJ4lACCCvKo/bvr+NdaXrOHvQ2dyefTth1rBghyXEESGJQPRqHu3hvS3v8VjOY1hNVh4//nFOyTwl2GEJcURJIhC91q6qXdy7+F6WFS1jct/JPHD0AySHJwc7LCGOOEkEotdxe9z8e9O/eWrFU1hMFu476j7OHnS2XBsgei1JBKJX2VaxjXsW3cPq4tUcn3Y8d0+5W2oBoteTRCB6BZfHxavrX2XeqnmEWcN46NiHOLX/qVILEAJJBKIXWFu8lr/8/Bc2lm3k5IyTuXPynSSEJgQ7LCG6DEkEoscqbyjnyRVP8kHuBySEJvD3aX/n5IyTgx2WEF2OJALR47g9bt7PfZ8nVzxJnbOOy0ZexjVjryHcGh7s0ITokiQRiB5lbfFaHljyABtKNzApeRJ3Zt/JoNhBwQ5LiC5NEoHoEZo3Az187MPM6j9LDgYL0QGSCES35vK4eH/L+/xj1T+ocdRw6YhLuWbsNXLTGCE6QRKB6Ja01vyw+wcez3mcbZXbmNhnIndOvpPBsYODHZoQ3Y4kAtHtbCrbxGM5j7GkcAnpkek8Me0JTkw/UZqBhDhEkghEt5Ffnc+zq5/lk18+ISokituzb+f8IedjNVuDHZoQ3ZokAtHlFdcV88KaF3gv9z1MmLhs5GVcNeYqomxRwQ5NiB5BEoHosioaKnhl/Su8tfEtXB4X5ww+h6vHXE2f8D7BDk2IHkUSgehyyhvKeWPDG7y16S1qnbWcOuBUrht7Hf2i+gU7NCF6JEkEossorivmtfWv8c6Wd2hwNXBSxklcO/ZaORNIiACTRCCCrrCmkFfWvcIHuR/g1m5m95/N70b/jgExA4IdWhOtNZ6aGlwlJbhLS3GVluEuL8dTV7f/UV+HrqtDO51N8+yjTGZUqB1TWBim0DBMoaGYo6MwJyRgSUjAkpiIJT4eU2hosN6i6MUkEYigWV+6njc3vMkX278ABWcOPJMrR10ZlCYg7Xbj2rMHR34+zl35OHfn7/+/qAh3aSna4Wh1fmXfV8iHoqxW2Hcqq/dZu13ouno89fV46urA42lxOebEBGwZGdgyM7FlZBAyeDCho0ZhSZDeUkXgSCIQR5Tb42bBrgW8vuF1VuxdQZgljAuHXcilIy6lb0TfgK9fezw4d++mMTeXxi25xnNuLo7t25v25AEwmbAk98GW1o/w7GzMCfFY4hOwJMRjjos3nmPjMIWHYwq1o8zmjsegNdrhwF1Ribu0BFdJCa7iElzFe3Hk7cKxYwc13y3AXVraNI8lORn7qJGEZWURNmUq9uHDOrVOIdoiiUAcEbXOWv6b+1/+tfFf5NfkkxqRyi0Tb+HswWcTaYsMyDq1w0HDllwa1q2lfu1ao+DfuhVdX980jTUlhZDBgwk/9hhs6RlY01KxpaVh7dsXZbMFJC6lFCokBFOfJKx9klqdzl1VRePmzdSvX0/DuvU0rF1LzdffAGCKjiY8O5uI448jYvp0LLGxAYlV9A7Ktx2zO5g4caLOyckJdhiiA7TWrC9dz/u57/P59s+pddYyLmkcvxnxG07odwIWk//2Q7THg2PHThrWrqF+7Trq166hceOmpuYcc0wMIcOHETJ4MCGDB2MfPBjboEGYI7pXn0TOvXupW7KE2sU/U7t4Ma7CQjCbCZs0iagZpxA1axbmmJhghym6IKXUcq31xBbHSSIQ/lbZWMmn2z7lg9wP2FK+hVBLKCdnnMxFwy5iVMIov6zD09BA/eo11C3PoT5nOfVr1+KprgZAhYZiHzmC0NFjCB09CvuYMVhTU3tcFxRaaxrWb6D6q6+onj8fx/btKJuNyJNOIuZX5xE2eTLKZAp2mKKLkEQgAs6jPSwrWsb7ue/zzc5vcHgcjIwfyTmDz2FW/1mH3fzjrqykbsUK6pcvpy5nOfXr14PTCUoZB1THjSN0zGjso0YTMnAAytK7Wj211jRu2kTF+x9Q+ckneCorsWakE3/55USfdZacjSQkEYjA0FqzrmQd83fOZ/6O+RTUFhBpi+S0AadxzuBzGBY37JCX7dyzh7qcnKaCvzE3F7QGq5XQkSMJmziB0AkTCBs/HnN0tB/fVffnaWykev5XlL3xBg1r1mCOiSH24ouJu/Q30mzUi0kiEH6zr91//o75zN85n901u7EoC1NSpjC7/2xOzjgZu8Xe6WU6tu9oauapW74cZ34+ACosjLCsLEInTiBswkRCx4yWvdsO0lpTv3w5pS+/Qs1332GKjCTuisuJu/QyzBFy287eRhKBOCxaazaUbuDLHV8eVPjPyJzBCf1OIDqk43vl2uGgYeNG6laspH7FcupWrGw6VdIcG7t/b3/CROM0yV7WzBMIDZs3U/zkU9R8+y3m2FgSrruO2IsulM+2F5FEIDqtsrGSJYVLWFSwiEUFiyisLcSiLExOmcyMjBmcmH5ihwt/d1UV9atWedv4V1C/di26oQEAa79+hI0fZxT8Eydi69+/xx3U7UrqV69m79/nUrdkCSGDB9PnrjsJnzIl2GGJI0ASgWiX0+NkTfEaFhcsZnHBYtaVrsOjPURYI8hOzmZav2kdKvy11rgKCqhbsaKp4G9q3zebsQ8fTuj4cYSNn0Do+HFYk1o/j14Ehtaa6q+/Zu/fHsa5ezeRM2eSfNedWBITgx2aCCBJBOIgWmvyqvOa9viXFS2j1lmLSZkYnTCao1KOYmrKVEYljMJqav3GL576eho2bjIu2lq1irrlK3Dt2QOAKTyc0Kwso+CfMIHQ0aMxhUvbdFfhaWyk7JVXKHn2OVRoKH1uvZXoc86WGlkPJYlAUOOoYUPpBtaVrmNdyTrWlqylqLYIgNSIVI5KOYqjUo4iu292qzd82X+l7jrq162lYe06GrduBbcbAEufPoRNGE/o+AmETRhPyJAh0g1CN9C4bTuF9/yZ+pzlhB99NH3/+tc2r3gW3VPQEoFSaibwJGAGXtJa/63Z+EuA27yDNcC1WuvVbS1TEkH7HG4Hm8s2NxX660rWsb1yOxpjW6dGpDIqYRST+kxiaspU+kX2O2gv0F1dbfTDs3kzDVu20LB+A42bfK7UjY7GPno09lEjCR09GvuoUVj7yA1juivt8VDx9tvseeRRTCEh9H3wASKnTw92WMKPgpIIlFJmYAtwMpAPLAMu0lpv8JnmKGCj1rpcKTULmKO1ntzWciURHMjtcbO9cvsBhf7m8s24PC4A4uxxjE4YzciEkcZz/Ehi7fv7pdFOJ43bt9O4eQuNW4xHQ+4WXAWFTdOYIiKwjxiBfdQo40rdUaOwpqX5vQnB49E46l001rlw1BsPp8ONy+HB7XTjcnpwOTx43NpIaj5fXWVSmC0mLFYTZqsJs8VESJjF52ElJNSCMkmzR1sat22n4OabadiwgZgLLqDP7bfJ6bo9RLASwVSMgn2Gd/gOAK31Q61MHwus01qntrXc3pgItNaU1Jews2onedV55FXlkVedx86qneyq3kW9y+hELdwazsj4kYxKGGU84keRHJ4MgLusDMfOPBx5O3Hm5eHYsZPGrVtp3L7duEIXwGIhpH9/QoYOJWTIEEKGDMY+ZAiWvn0PqdDXWuNsdFNX6aCuyvfR2PR/vfe5sd6Fs8Htt8+sJSazIizaRnh0COExIUTG24lOCCU6MZTopDCi4u2SKDCaAIufeorSl1/B1r8/qXPnYh86JNhhicPUViII5EnEqcAun+F8oK29/SuBzwMYT5e2r7DfV9A3L/T3FfYAFpOFtIg00qPSyU7OZnj8cEbGj6RfYziuvF04duThWLgOR95nbM/biXNnHp7a2v0rM5mw9u1LyKBBRBx/vLfQH0JI/8wO9bjpcribFeyOZgW7t6CvdOByHtzvvlIQGmUjzPuI7RuOPcyKLcxCSKgFW6ixF28LtWCxmbBYzVisJiw2MxabCZNZeZejwPjD49G4nR7cLg8upwe300NjnYvGOqf32UVdVSO1lQ5qKxopL6xl57pS3D7xWe1mEtIiSEiLJKFfBAlpEcSlhGOx9q7jHMpmI+nmmwk/5hgKbrmVHRdeSN8H/kL0qacGOzQRIIFMBC3tWrVY/VBKnYCRCI5pZfzVwNUA6enp/orviGt0N1LeUM7umt0H7dXnVeVR56prmtaiLKRFGoX9pKSJDCCBdEckSXUWoqo96KISXGuLce7ZhXPXIhx5efziPTffWIDF6E45I52wCROxpadjS++HNT0dW2rqQQW+2+2htspJXWFVK4W791HZiKOVPXd7hLWpcE8eEE1YlI3QKBvhUTbCokKaCn97hBVTIPa8O3dBM9qjqa10UFVSR3lRHaX5NZTk17BpcSHOBcZ7VCZFXEo4qUNiSB0SS8rgGOzhrZ9F1ZOET5lC5vvvsfvGP1Fw0800rFlL0s03GTfeET1K0JuGlFJjgP8Cs7TWW9pbbldpGvJoD1WNVZQ1llHRUEF5QznljeVUNFZQ1mC81nyc7149gBUzg03JDHUnkemMIqUhlMQ6C1FVLkIq6nAXl+AqLsZVXAwu10ExmKOjsSQlYe3XzyjoM9KNgj4jA3NSHxobNA01TuprHN5nJw01Duqrjf/rq/cX8A01zoOWD2CzmwmLDmkq4H335Pc/QgiNsmI294yeLrVHU1lST8muGkryq9mzvYrCXyqN2oOChLQIUofEkjo0lrRhsVhtPbvGoJ1O9jzyKOVvvEHYpEmkzv273DGtGwrWMQILxsHi6cBujIPFF2ut1/tMkw58C1yqtV7UkeUGKhHUu+oPKLzLGsqoaPQp4Ju9VumoxKM9mDya0EYI83nEuGwkuMOIc9uJcdmIdlmJcJgIawR7o4fQaie2smp0WUXLBXxMDJbERMxJSaiEZHRcHzwxSbgjY/GEx+AKicRtDcXpUjTWuYzCvcbZVNjX1zhorHO1Uv8ymkBCvXvvoZG2Awr65g9LDy/kOsrt9LBnRxW7t5Sze0s5Rb9U4XZ5sFhN9BsRR/+xiWSOiSc0IjA3s+kKKj/+mMJ77sUcF0u/557DPkSOG3QnwTx9dDbwBMbpo69orR9USl0DoLV+Tin1EnAusNM7i6u1QPfJHJmp7/7P3YcUj9vjNgryxnIq6supri6lsbIcR1UF5rpGQh36gAI9rFET3mgi2mUl2mkl3GkivBHsDZqQBheWeifmxv170h5lwmOy4jFZcZtseMzG/x5bKDo8Gh0WiQ6NQEfE4I6IxR0WjTskEpc1FJcpBKe24HSbcDS4aax34ah3oz1tbx+TSWGPsBIaaTWeI4yml33/h0ZYsUdaCd03LtyK2dr5PXetNR63C7fLhcflxu1y4nG7jWHv6+C9+5bJhMlkMm7Y7jNsttmw2kIwW63d/qIll9NN4dZKtq8uYfvqYmrKG1EK+g6KYeD4RAZN6ENYVM9LCvXr1pN/7bV46upIfeIJIo5tsTVXdEE96oKyQVGR+rHJ4w9pXqUVdrcNm8uG1W1BK2+BbbLiMVtxm6x4vMNus/d/WyjaForHZsdjseOx2JrmcSsLHsy4tQm3R+HRbRduxmetATfgAe3BGgJWu8IWApYQhdUGFpvCYgWLFcz7HmaN2aIxmb0Pk0aZNWi3t0D2KZhdrgMKaN/X9xfmLtxuNx6X0/vcbJzvfG7jf79RCqstBEtICNaQECy2EOwRkdgjIgiNiDKeI6OwR0QSERdHRFwCkfEJhEZGdckEorWmOK+a7atL2LaqmLKCWpRJkT4yjqGTk+k/JqFH1aycRUXsuuZaGnNzSb77LmIvuijYIYkO6FGJoF9Cqr7p1GsOYwlGAWwUyN5n7QE8aJ9xyqRRyoNSGqU0KO8wxv9N83rn0fuWofcPa4/vsxvtOfgMGn8zWyyYLFbMZjMmiwWTxWK8Zt73bD5w2OL7urXF8Qe91jRu/zwms3GOvvZ48Hi879n72DfsdjpwNjbicjQ2PbscDhwN9TTW1lBfXU1DTQ0NNdU4GxsOfm9WKxFx8UQnJhHbN9XnkUJ0UjKmLnIVc+nuGjYvKWLL0j3UVjRis5sZNCGJkcelkpTR8lXb3Y2ntpbdN91MzYIFxF12KUm33ipXkXdxPSsRxMXoG04+9pDnN5nNKJPJ21xhNgqxfc8W77PZ93UTymzG5J1eNY0zNU2jmk2/bx0tjVMmU6sFbnsFcvPxTa9ZLJjNFuN9dcE95kPhcjior6mitqyM6rISqktLqSkrobq0hMo9RZQV5tPoc0qsxWojISOTpIwBJGYOIMn7sAToBvQd4fFoCraUs3lJEVuX78Xl8JCUEcnI41IZPKlPtz/IrN1u9j7yCGWvvU7ECSeQ+vhjmMLCgh2WaEWPSgRd5awhEVxaa+qrqygvLKC8IJ+SXTsp3rmNvdu30VBbAxi1o6QBg0gZMpzUIcNJHT6SsKjg3M2ssd7F5p+LWPf9bsoLawkJszBsal/GnJhGVHz3vnK37N//Zs8DD2IfPYp+zz2HJTa2/ZnEEdejEsHQUWP1s+/NP6R5TUoRF24jPiKE+HAb9l52oVBvoLWmurSYPdu2UrBlEwVbNrFnWy5u79XTiZkDyBidRcaosaSNGH3Eawxaawq3VrB24W5+WVEMwKAJSYw7OZ3E9MO7r3MwVX/9NbtvuhlrSgrpL72INbXNDgJEEPSsRJASqV+4MuuQ5nVjoljHsJcY9uhYqizxOEKTcEckY4nsQ0xkOIkR3kQRYSM+PITESOM5OjRAF0GJgHM5nezdvpW8dWvIW7uKgi0bcbtcWEPsZGaNZ/CkqfQfNwl7RMQRjau6rIE13+5i/Y8FOBvcpA6NYcKsTNKGxnbLJr665cvZde11mOx2+r34onRL0cX0qEQwPj1S/3DbhEOb2ePEXLcXW0MpJn3gWTAeFGVEU+QxksQeHUMxsU3/l6g4GkP7YApPID4qjPjw/QkjISKEBG/i2DcstY2uy9nYQP7G9fyS8zNbc5ZQW16GyWwmbcRoBk2awqCJU4iMP3IXTDXWu9jwQwGrv8mjttJB34HRTDqtP2nDul9CaNiyhV1XXY2nro5+854hbNKkYIckvHpUIvDLMQKPG2pLoLoQqosOeNbVRbirjGFzXbFxlpDvrJgoN8Wyl1gK3TEUuqONZIGRMPZqI3k4QmKJi7A3JYz9ycJGamwYAxPD6RcXhrWHXI3bXWmPh6Jfctm6bDFbl/1MWUE+AClDhjPiuBMZetSx2MOPTE3B5XSz8adCln+xk9qKRiMhnNqftOHdKyE4CwrI+91VOPPzSXnsUaJOOSXYIQkkERw6twtq97aQMPY/dHUhqq7k4FkxU2WJp9QUxx4dw25XDHnOKPboGHZ4ktmi06g1RZIRH8aAxAgGJIYzMDGCgd7nmLCedzFSd1C6exdbly5m448LKM3Pw2y1MnDiFEYefyKZY8YfkVNU3U4PGxcVsPyLndSUN5I8IIrsMwbQb1hcwNftL67ycvKvuZb6NWtIvufPcq1BFyCJINBcDqjZsz9Z1OxpsbZBffkBs1VbE8mzZLDRnUpOXV/Wu9PYqlOox05cuI0BCUZS2JckBiSGkx4XhkVqEQGntWbv9l9Yv/AbNv60kIbqKsKiYxh+7AmMmT6TuJTAHwx1Oz1sXFzI8s93UFPeSL8RcUw9eyCJ/brHQWVPfT27b7iRmoULSbjuWhKuv75b1Wx6GkkEXYWzwUgIpb/A3g2wd6PxXLwJXMYFVBpFVWga+dYMNnnSWF7Xl5z6ZLbpvriwYDUr0uOMWsS+GsTotGgGJ0ViloPZAeF2Odm2MocNC79h24pleNxuMsaMY+wpsxk4PjvgtQSX0826hbvJ+XwHjbUuhkzuw+TTBxCV0PVPO9VOJ4X3zqHygw+I+dV5JN97L8oSyE6PRWskEXR1HjeU79ifHPasN55Lt4L3oLbHZKU6PJMCWyZbdD+W1yfzU1US29wJaEyE28yM7RfDuPQYxvWLJSs9hoSIkOC+rx6otqKctd98yepvvqCmtITI+ETGnDST0SeeQnhMYM+fb6xzsuLLnaz+Nh+tNaOnpTFxVmaX7xZba03xk09S+tzzREybRurcv8tdz4JAEkF35WqEklxvzWH9/hpERV7TJB5LGKUxI1lvGcm3dYP4qCSFSo/RMX+/uFDG9Ys1kkN6LCP6RmGzSLOSP3jcbn5ZsZTV8z9j55qVmC0Whh0zjYmnnU1Cv4yArrumvIEln2xn8+JCbGEWJp8+gJHHpmDq4k2G5W+9RdH9fyF0zBjSnntWLjw7wiQR9DSN1bB3k5EU9qyDXUugaK3Rx5EyUxc3gm1hY1jsHMyHZelsqDISg81iYlRKFOPSY8nqF8PkAXEkRXbybi7iIGUFu1n5xces++5rXI5G+mdNYOLp59Bv5JiAtomX7q7hh3dy2b25nLiUcI45f3CXP6BcNX8+BTffgjUlhX4vvYQtTS48O1IkEfQGDVWQvxTyfoadi2F3TtNxB1fsQAqjs1ilhvNldX++Kgqj0WVs9+F9ozhucALHDUlkQkasXP9wGOqrq1g9/zNWfvkpdZUVJGUOZOLpZzNkyjGYA9QurrVm+6oSfno/l6qSBgZkJXLUuYOITuy6TS91OTnsuu73qBAb6S+8gH348GCH1CtIIuiNXA4oXAU7FxnJIW8xNFQAoCOSqUycwCprFu9WDmN+vgWnW2O3mpjcP57jhiRy3OAEBiVFyFkeh8DlcLDhh+9Y/ul/KSvIJzI+kQmnnsmY6TOx2gNTA3M53az6ehfLv9iJx+0h66R0JszMwGbvmgdmG3NzybvqajzV1aQ9/Q/Cp04Ndkg9niQCAR6PcXZS3mLjsXMRVO02RiWOIC/+aL5zZ/HvwmRySxoB6Btt59jBCRw7OJHjBicSHda1D0p2NdrjYdvKHHI++YD8jeuwR0YxYfaZZM04NWAXqdWUN7L4w61sWbKHsGgbR509kCHZyagueEaZs6iIXVddTeOOHaQ89BDRp50a7JB6NEkE4mBaQ/FmyJ1vPPIWg8cFIdHUpR/PmtBsPqgaxuc7PFQ3uLCYFFMHxjNzVDInj+gjxxY6qWDLRpb89x22rViGLTSMcTNPZ/zsMwLWG2rRtkp+eHsLe3dW06d/FMdeMIQ+mV3vXgjuqiryr/s9dTk5JN70J+J/9zuphQaIJALRvoYq2LbAmxi+gpoiAHTfcRT2OZYvXON5bVs0O8vqUQomZsQyY2QyM0Ym0y9O+qDvqD3bf2Hpf99hy9JFWGw2xp40i4mnnU1EXLzf16U9mk0/F7L4w23UVzsYPrUvU84a2OVuoelpbKTwjjuo+uxzos88k+S/3I8piPeR6KkkEYjO0do4C2lfbSF/mXFGUkwGZRkz+YopvLojnk17jH7/R6VGMXNkMrNH92VA4pHtwbO7Ks3fxdIP32HjTwsxmUyMOuEUJp1xLtFJffy+Lke9i2Wf7WDNN7uw2ExMOq0/o09Iw9yFTjfVWlMybx4l/3ia0HHjSHv6H1ji/Z8cezNJBOLw1JbC5s9gw0dGrcHjhKg0KvvP4jvTVF7PT2LFrioAxqZFc9a4VE4bk0JipFzQ1p6KPUUs++g91i34GtAMP+YEss/6VUC6sCgvquXHd3PJW19GbHIYx5w/mPQRXauwrfriCwpuvwNzXCz9nn0W+9ChwQ6px5BEIPynvhw2f2EkhV++AbcDIvtSO3AW36qjeG57EuuLajCbFMcOTuCsrFROGdmHMFvXPHulq6guLSHnkw9Y882XuJ1Ohkw5muyzfkVS5gC/rkdrzc61pfzwbi5VxfVkjkngmF8NIjqx6zTv1a9bT/511+GuqaHv/ffLQWQ/kUQgAqOhymg62vChcVzB1QBRqZT1P41P3FN5ITeK3ZUNhNnMzBiZzFnjUjl6YLx0mteGusoKlv/vQ1bN/x+O+noGjJ9E9lnnkzrUv+fau50eVn2TR87nxumm405KZ3wXOt3UuWcvu2+8kfoVK4i56EL63HGHHDc4TJIIROA11sDmz2Hde7D1G/A40fGD2J06i3caJvPqFhtVDS4SIkI4Y2wKZ41LYXRqtJwh0oqG2hpWffk/ln/2EQ3VVaSNGMXks84nY8w4v35mtRWNLPqvcbppeLSNo84dxOBJfbrEdtFOJ3vnPkHZK69gHzWK1CfmYktLC3ZY3ZYkAnFk1ZXBxk+MpLD9B0Dj6TOa3KQZvFo5gfd/UTjcHgYkhnN2VipnjUuVM49a4WxoYM03X5Lz6QfUlJXSZ8AgJp91PoMmTUGZ/FezKvzFON20OK+avoOiOfrcwfTp3zVON63++msK7rgTlKLvgw8QdfLJwQ6pW5JEIIKnugjW/xfWvmd0ewG4UiezKno6z5eM4as8D2Ccjnr2+FROG50iF661wOV0suH7b1n20XtU7CkkLrUf2Weex7Cjj/db9xUej2bTokJ+/ugX6qudDByfyJQzBxLTJ/hJ2rFrF7tvuJGG9euJPvts+tx5B+bI7nFfhq5CEoHoGsq2w7r3jcfeDaDMNPQ7lp9Cj+epgmGsLtbYzCZOHJbE2eNTOWFokvSW2ozH7WbLzz+y5MN3KcnbQUR8AuNmnMbo6TMIjfBPwehocLHqqzxWfb0Ll9PDiKP7Mum0/oRHB/csMO1wUDxvHqUvvIgluQ8pf/0r4VOmBDWm7kQSgeh69mwwmo7WvQ/lO9BmG9VpJzDfdAxz8wawu1YRE2bltDF9OXtcGuPTY7pEu3VXobVm+8oclv/vv+StW4PFFsLI409k3KwziE/t55d11FU5yPl8B+u/343JpBgzvR/jTk4P+v0P6letouC223Hs3En0OeeQdMvN0qV1B0giEF2X1rB7hTcpfAA1RWhbBHv6nsiHrqk8k9ePaqeJjPgwzspK5ZzxqWTEhwc76i6leOd2Vnz+MRt/XIDb6aR/1gTGzz7TbweWK4vrWPLxdnKX7cEaYmbU8alknZQe1CuUPfX1lMybR+k/X8UcEUHSrbcSfdaZfj1u0tNIIhDdg8cNO38yjids+AgaKtD2WLYlncRbdRP55+5U3NpEVr8YThvTl9mj+5IS03W7Wz7S6iorWP3156ye/xm1FeXEpaQx+sRTGHH8dL/0aVS6u4bln+8gd/leLBYTI45NIeukdCLjgtfvVMPmLRTNmUP9ypXYR40i6ZZbCJ+cHbR4ujJJBKL7cTngl2+NmsKmz8BZizs8mXWxJ/Ja5Tj+W9wXjYmJGbGcOqYvs0b1JTlaOsID48DylsU/sOqrzyjcsgmT2cKgSVMYPX0GGaPGHvZec3lRLSu+2MnmpXsAGDgukbHT+9Gnf1RQmu+0x0Plxx9T/ORTuAoLiZg2jcQb/g/7sGFHPJauTBKB6N4ctbDlC1j7Pmz9CtwOXKEJbI4+mnerR/Of0oE0EMLYtGhOHtGHU0YmM1jupQBAya6drP12Phu+/5aGmmoiExIZdtRxDD3qOJIyBxzWZ1RVWs+6BbvZ8FMBjXUukjKjGHVcCgPHJwXlwjRPQwPlb75JyfMv4KmuJmLaNOL/39WEjRt3xGPpiiQRiJ6jvgK2fm30fZT7FTRW4THb2RU9ga8aR/JW2WB+0SlkxIdzwtAkjh+SyJQB8YTaeved11wOB7nLFrPx+2/ZuXYVHreb2JQ0IylMPYa41H6HnBQcDS42/1zEmu/yqdhThzXEzKCJSQw/KoXkAUe+luCuqqL8X/+i7LXXcVdUEDphArEXXkjkjFN69dXJkghEz+RyQN4io+lo69dQ9gsANfa+LLeM5dOqgfzoGEapJZHJ/eM4amACUwbEMSo1Gmsv7uairqqS3CWL2LRoIfkb14PWRPdJZsD4SQwYn03a8FFYrJ0/M0hrTdEvlWxcVEju8r24Gt1ExIUwcHwSg8Yn0Scz6ojeIMdTW0v5u+9S/u+3cOblYY6NJfqss4g67VTsI0b0uhqjJALRO5TvMI4r/PItbPseGisBqLD1ZakexsK6/qz2DGCXtT9jMhIZnx7LmLRoRqdF99ob7VSXlbBt+VK2rVhG3trVuJwOrPZQ0oaPpN+I0fQbMZqk/gMxmTtXo3I0uNi2sphfVuwlb2MZHpcmPNpG+sh4+o2Io9+wOOwRR+Y0VO3xULtoMeX/eYuaBQvB5cKWmUnkzBlEHHccoWPGoAJ0T+muRBKB6H08btiz3nvP5kXGc20xAE5lY6upP6scKWzxpJGr06gIH0jftExGp8UwOi2aYcmRJEfZe9Veo7Oxgbx1q9m+Modd69dSVpAPgC00lL6Dh9FnwCD6DBhE8oDBRCYkdvizaax3sWNNCdtXl5C/qYzGOhcoSEiLILl/NH0GRNEnM4qYpLCA1xhc5eVUz/+Kqv/9j7qcHPB4MEVGEn7UUYRPnUpo1lhCBg3qkYkhaIlAKTUTeBIwAy9prf/WbLzyjp8N1AGXa61XtLVMSQTikGgNFXmwe7nxKFiJ3rMB1VDeNEk14Wz2pJLrSWWn7kOJOREdlUpoQjqxfTJIT4wmMyGc5Cg7SVEhhFh69nGH2opydm1YS/6GtRTkbqZ01048bjcA9vAIYlPTiEvZ/4hNSSUqIRFrSOu1K49Hs3dHFXkbyijcWsGeHVU4G4xlhoRZSEiLIDY5nNi+YcZzchjh0SEBSRDuykpqFy+m5scfqf3hR1x7jLOglN2OfeRI7CNHEDJgILYB/QkZOBBzXFy33jEISiJQSpmBLcDJQD6wDLhIa73BZ5rZwPUYiWAy8KTWenJby5VEIPxGa6OWULwJ9m6C4k249mxE792EtbHsgEndWrGXWPboWEp1FBVEUGeOwh0SiycsDnNYLBZ7JNbQCGyhEYSERRIaHkVYRBThEVFEhIVhs5oJsZixWUzYzCasZtWtChaXw0Fx3nb2/LKV4p3bKSvMp7xgN7UV5QdMZw+PICIu3vtIICwqipDwCOwREdjDI4z/wyOwhYVhttioKXdRWtBA8c5aygrrKS+qw1HvalqeyaQIjwkhIi6EiFg7YVE27OFW7BFWQsIs2COs2MOsWEPMmK0mrDYzZpsJi8XU4QSitcaZl0f92nXUr1lNw5q1NGzahG5o2B9HeDiW5GSsfZKw9EnG0icJS3wC5qhITJFRmKOjMEVGYo6KwmS3o0JCUDYbqpPNaoESrEQwFZijtZ7hHb4DQGv9kM80zwMLtNZveYc3A9O01oWtLVcSgTgiGmugajdU5kNlPu6KfOpKduIsz4f6ciwNZYQ4Kwnx1HdocR6tcGLGjRkXJlze/92YcSkzHsx4lBk3FtzKjGZfAaYw/u3Y8P75OGC4tdf9wemG2kYzdY0m6p0mGp0mGpwmGpyKRqcJh1uhdcfWZ1Iak0ljUgqNCbTZeMaM9nkYjQzK+2jtwL9CKQ14mj6F/fSBH6PPOOUzDfvi1nr/JLrZog5HWx+LRXH8sG1YTEbHjDGhNlKP/Q1MvOLQVtVGIghkQ1gqsMtnOB9jr7+9aVKBAxKBUupq4GrvYI03YfhbNFAZ5OV1Zp6OTNvWNK2N68zrCUBJOzEEmj+326Euy5/b7VDHy3YL7HxdZLt9VwK/bSvOtmS0OkZrHZAH8CuM4wL7hn8D/KPZNP8DjvEZ/gaYEKiY2on3hWAvrzPzdGTatqZpbVxnXgdygrGtArXdDnVZ/txuhzpetptst8N5BPJk6nzAtxvENKDgEKY5Uj7pAsvrzDwdmbataVob19nXg82fcR3qsvy53Q51vGy3wM7Xo7dbII8RWDAOFk8HdmMcLL5Ya73eZ5pTgT+w/2DxU1pr6TGqm1BK5ehW2hxF1yXbrXsK5HYL2DECrbVLKfUH4EuMIzuvaK3XK6Wu8Y5/DvgMIwlsxTh99NCOgohgeSHYAYhDItutewrYdut2F5QJIYTwr97b4YoQQghAEoEQQvR6kgiEEKKXk0QgAkIpNUAp9bJS6r1gxyJap5QKV0q9ppR6USl1SbDjER3j79+XJAJxEKXUK0qpvUqpdc1en6mU2qyU2qqUur2tZWitt2mtrwxspKIlndx+5wDvaa2vAs444sGKJp3Zbv7+fUkiEC15FZjp+4K3E8FngFnACOAipdQIpdRopdSnzR5JRz5k4eNVOrj9MC7i3NfNi/sIxigO9iod325+1fM63RaHTWv9vVIqs9nL2cBWrfU2AKXUf4AztdGJ4GlHOETRhs5sP4yr+9OAVciOYVB1crttwI9kw4uOaq2DwBYppeKVUs8B4/b1PCuCqrXt9wFwrlLqWbpudxS9WYvbzd+/L6kRiI5qqcPcVq9G1FqXAtcELhzRSS1uP611LXJFf1fW2nbz6+9LagSio7pSB4Gi82T7dU9HZLtJIhAdtQwYrJTqr5SyARcCHwc5JtFxsv26pyOy3SQRiIMopd4CFgNDlVL5SqkrtdYujJ5ivwQ2Au/49iQrug7Zft1TMLebdDonhBC9nNQIhBCil5NEIIQQvZwkAiGE6OUkEQghRC8niUAIIXo5SQRCCNHLSSIQQoheThKBEEL0cpIIhPAD730Zdiqlrg12LEJ0liQCIfxAa70Wox+YS4MdixCdJYlACP/ZC4wMdhBCdJYkAiH8529AiFIqI9iBCNEZkgiE8AOl1EwgHPgfUisQ3YwkAiEOk1LKDjwCXAesBUYFNyIhOkcSgRCH727gda31DiQRiG5IEoEQh0EpNRQ4GXjC+5IkAtHtyI1phBCil5MagRBC9HKSCIQQopeTRCCEEL2cJAIhhOjlJBEIIUQvJ4lACCF6OUkEQgjRy0kiEEKIXu7/A1G7/NUQOZfuAAAAAElFTkSuQmCC\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": 209,
   "id": "57bd6135",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2e0b1c49220>"
      ]
     },
     "execution_count": 209,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "i =4\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_a_l[:,i,j], label='Turn'+str(j))\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "id": "cc3bf1aa",
   "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>...</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>272</th>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>vsmhjntd</td>\n",
       "      <td>d</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>273</th>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>vsmhjntd</td>\n",
       "      <td>e</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>274</th>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>vsmhjntd</td>\n",
       "      <td>e</td>\n",
       "      <td>1.0</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>275</th>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>vsmhjntd</td>\n",
       "      <td>e</td>\n",
       "      <td>2.0</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>276</th>\n",
       "      <td>nc</td>\n",
       "      <td>l</td>\n",
       "      <td>vsmhjntd</td>\n",
       "      <td>e</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>277 rows × 6 columns</p>\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",
       "..      ...          ...          ...          ...             ...   ...\n",
       "272      nc            l     vsmhjntd            d             3.0     5\n",
       "273      nc            l     vsmhjntd            e             0.0     2\n",
       "274      nc            l     vsmhjntd            e             1.0    28\n",
       "275      nc            l     vsmhjntd            e             2.0    25\n",
       "276      nc            l     vsmhjntd            e             3.0     5\n",
       "\n",
       "[277 rows x 6 columns]"
      ]
     },
     "execution_count": 173,
     "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(\"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",
    "\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",
    "# BySessions['session.code'].unique()\n",
    "BySessions\n",
    "# BySessions.pivot(index=['network', 'waiting_cost','session.code','.player.type'], columns='.player.period')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "id": "94336a95",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_11364/4085236405.py:17: RuntimeWarning: divide by zero encountered in log\n",
      "  logL[i] += freq*np.log(QRE_lamda[pos,turn])\n",
      "C:\\Users\\xinxi\\AppData\\Local\\Temp/ipykernel_11364/4085236405.py:17: RuntimeWarning: invalid value encountered in multiply\n",
      "  logL[i] += freq*np.log(QRE_lamda[pos,turn])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[0.10851324, 0.10851324],\n",
       "       [0.08964259, 0.08964259]])"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "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.empty(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": 207,
   "id": "54db8f40",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.10851324, 0.10851324],\n",
       "       [0.08964259, 0.08964259]])"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "EstimatedL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "id": "86394e93",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-3926.522598  ,  -751.95634386],\n",
       "       [-4909.60347814, -3170.7144038 ]])"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "EstimatedLogl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "id": "88ad0e91",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "34"
      ]
     },
     "execution_count": 188,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "network='nc'\n",
    "waitingcost = 'l'\n",
    "BySessions.loc[ (BySessions['network']==network) & \n",
    "           (BySessions['waiting_cost']==waitingcost) &\n",
    "          (BySessions['.player.type']==node) & \n",
    "         (BySessions['.player.period']==turn), 'date' ].sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "e13d7886",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2e0add766d0>"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "# 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": "7b0ff7bd",
   "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": "c749148d",
   "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": "6484e9f8",
   "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",
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       "                nan]],\n",
       "\n",
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       "        [       nan,        nan,        nan,        nan,        nan,\n",
       "                nan],\n",
       "        [       nan,        nan,        nan,        nan,        nan,\n",
       "                nan]]])"
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     "execution_count": 126,
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     "output_type": "execute_result"
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