ComputingQREForDirectedNetworkb_Matrix.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "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": "markdown",
   "metadata": {},
   "source": [
    "# This file is used to compute the QRE in network (b). \n",
    "## Note： this is the later version, where payoff and prob are both matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "outputfolder = \"C:\\\\Users\\\\xinxi\\\\Anaconda3\\\\Xinxin's Files\\\\Networks\\\\4O3I_Distance\\\\\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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(outputfolder+\"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",
   "metadata": {},
   "source": [
    "# Part 1: Preliminaries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# CRRA utility function\n",
    "def CRRA(x,gamma): #can use offset by xMin in case of negative values of x\n",
    "    if gamma == 1:\n",
    "        return np.log(x)\n",
    "    else:\n",
    "        return ((x)**(1-gamma) - 1)/(1-gamma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 2: Compute QRE at turn 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the payoff, assuming that the utility depends solely on the payoff\n",
    "# Estimate the prob of decising at turn 0,1,2,3,4, (5 is ignored because it should be 1-sum(previous 4))\n",
    "# pOther = matrix （5*5）\n",
    "#[A: decide at turn 0,1,2,3,4\n",
    "# B: ...\n",
    "# C: ... \n",
    "# D: ...\n",
    "# E: ...]\n",
    "# pOther is an array!\n",
    "# pOther[0,1] A decide at turn 0 p[0], decide at turn 1 p[1]\n",
    "# B decide at turn 0 p[5]\n",
    "\n",
    "# Calculate expected utility of action a given other players' mixing prob. (Turocy,for network)\n",
    "\n",
    "def payoff(pOther, 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",
    "    # 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",
    "    pay_2 = pOther[5]*ProbCorrect_Bayesian(3,q)*diff_pay + pOther[6]*ProbCorrect_Bayesian(5,q)*diff_pay + (1- pOther[5] - pOther[6])*ProbCorrect_Bayesian(5,q)*diff_pay - 2*c\n",
    "    pay[0,1] = pay_1\n",
    "    pay[0,2] = pay_2\n",
    "    j = 2\n",
    "    i = 1\n",
    "    while j < 5:        \n",
    "        j = j+ 1\n",
    "        pay[0,j] = pay_2 - i*c\n",
    "        i += 1\n",
    "    \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] = pay_1\n",
    "    pay[1,2] = pay_2\n",
    "    j = 2\n",
    "    i = 1\n",
    "    while j < 5:        \n",
    "        j = j+ 1\n",
    "        pay[1,j] = pay_2 - i*c\n",
    "        i += 1\n",
    "    \n",
    "    \n",
    "    # indegree = 1, node C or D, (position 2,3)\n",
    "    pay_1 = ProbCorrect_Bayesian(2,q)*diff_pay - c\n",
    "    pay_2 = pOther[0]*ProbCorrect_Bayesian(2,q)*diff_pay + (1-pOther[0])*ProbCorrect_Bayesian(4,q)*diff_pay - 2*c\n",
    "    pay_3 = pOther[0]*ProbCorrect_Bayesian(2,q)*diff_pay + (pOther[1] + (1-pOther[0]-pOther[1])*pOther[5])*ProbCorrect_Bayesian(4,q)*diff_pay +(1-pOther[0]-pOther[1])*(1-pOther[5])*ProbCorrect_Bayesian(5,q)*diff_pay - 3*c\n",
    "       \n",
    "    pay[2,1] = pay_1\n",
    "    pay[3,1] = pay_1\n",
    "    pay[2,2] = pay_2\n",
    "    pay[3,2] = pay_2\n",
    "    pay[2,3] = pay_3\n",
    "    pay[3,3] = pay_3\n",
    "    j = 3\n",
    "    i = 1\n",
    "    while j < 5:        \n",
    "        j = j+ 1\n",
    "        pay[2,j] = pay_3 - i*c\n",
    "        pay[3,j] = pay_3 - i*c\n",
    "        i += 1\n",
    "    \n",
    "    \n",
    "    # indegree = 1, node E, (position 4)\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 = pOther[0]*ProbCorrect_Bayesian(2,q)*diff_pay + (pOther[1] + (1-pOther[0]-pOther[1])*pOther[5])*ProbCorrect_Bayesian(3,q)*diff_pay + (1-pOther[0]-pOther[1])*(1-pOther[5])*ProbCorrect_Bayesian(5,q)*diff_pay - 3*c\n",
    "\n",
    "    pay[4,1] = pay_1\n",
    "    pay[4,2] = pay_2\n",
    "    pay[4,3] = pay_3\n",
    "    j = 3\n",
    "    i = 1\n",
    "    while j < 5:        \n",
    "        j = j+ 1\n",
    "        pay[4,j] = pay_3 - i*c\n",
    "        \n",
    "        i += 1\n",
    "\n",
    "    return pay\n",
    "    \n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ProbCorrect_Bayesian(4,0.7)*100 - 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pp = [0,0,0.3,0.01,0.01,0,0.3,0.3,0.01,0.01,0.3,0.3,0.3,0.01,0.01,0.3,0.3,0.3,0.01,0.01,0.3,0.3,0.3,0.01,0.01]\n",
    "payoff(pp,cost)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pp = [0,0,0.3,0.01,0.01,1,0.3,0.3,0.01,0.01,0.3,0.3,0.3,0.01,0.01,0.3,0.3,0.3,0.01,0.01,0.3,0.3,0.3,0.01,0.01]\n",
    "payoff(pp,cost)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assumptions:\n",
    "    * Five agents\n",
    "    * Five nodes, the prob of deciding at turn each turn 0 - 4\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 1: for all 5 turns, find the QRE (not converting!!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "#Define the function whose 0 we want to find  (Turocy)\n",
    "def F(p, l = 1,cost='h'): ## probability vector and value of lambda\n",
    "    # The part where it is about prob of deciding at turn 0\n",
    "\n",
    "    p_real = np.exp(p)\n",
    "    p = np.reshape(p, (5,5))\n",
    "   \n",
    "    p_5 = np.log(1- np.exp(p).sum(axis=1))\n",
    "    \n",
    "  \n",
    "\n",
    "    H =  np.empty((5,15),dtype=float)\n",
    "\n",
    "    # This version: the probability is the difference between prob of deciding at turn 0 vs the exact payoff of a future turn\n",
    "    \n",
    "    H[:,0]= p[:,0] - p[:,1] - l*(payoff(p_real, cost)[:,0]- payoff(p_real, cost)[:,1])\n",
    "    H[:,1]= p[:,0] - p[:,2] - l*(payoff(p_real, cost)[:,0]- payoff(p_real, cost)[:,2])\n",
    "    H[:,2]= p[:,0] - p[:,3] - l*(payoff(p_real, cost)[:,0]- payoff(p_real, cost)[:,3])\n",
    "    H[:,3]= p[:,0] - p[:,4] - l*(payoff(p_real, cost)[:,0]- payoff(p_real, cost)[:,4]) \n",
    "    H[:,10]= p[:,0] - p_5 - l*(payoff(p_real, cost)[:,0]- payoff(p_real, cost)[:,5])\n",
    "    \n",
    "    H[:,4]= p[:,1] - p[:,2] - l*(payoff(p_real, cost)[:,1]- payoff(p_real, cost)[:,2])\n",
    "    H[:,5]= p[:,1] - p[:,3] - l*(payoff(p_real, cost)[:,1]- payoff(p_real, cost)[:,3])\n",
    "    H[:,6]= p[:,1] - p[:,4] - l*(payoff(p_real, cost)[:,1]- payoff(p_real, cost)[:,4])\n",
    "    H[:,11]= p[:,1] - p_5 - l*(payoff(p_real, cost)[:,1]- payoff(p_real, cost)[:,5])\n",
    "    \n",
    "    H[:,7]= p[:,2] - p[:,3] - l*(payoff(p_real, cost)[:,2]- payoff(p_real, cost)[:,3])\n",
    "    H[:,8]= p[:,2] - p[:,4] - l*(payoff(p_real, cost)[:,2]- payoff(p_real, cost)[:,4])\n",
    "    H[:,12]= p[:,2] - p_5 - l*(payoff(p_real, cost)[:,2]- payoff(p_real, cost)[:,5])\n",
    "    \n",
    "    H[:,9]= p[:,3] - p[:,4] - l*(payoff(p_real, cost)[:,3]- payoff(p_real, cost)[:,4])\n",
    "    H[:,13]= p[:,3] - p_5 - l*(payoff(p_real, cost)[:,3]- payoff(p_real, cost)[:,5])\n",
    "    H[:,14]= p[:,4] - p_5 - l*(payoff(p_real, cost)[:,4]- payoff(p_real, cost)[:,5])\n",
    "    H = H.reshape(-1)\n",
    "    res =  np.dot(np.transpose(H),H) \n",
    "    return res\n",
    "\n",
    "\n",
    "cons = ({'type': 'ineq', 'fun' : lambda p: 1- np.sum(np.exp(p)[0:5]-0.00000001) } ,\n",
    "   {'type': 'ineq', 'fun' : lambda p: 1-np.sum(np.exp(p)[5:10]-0.00000001)  },\n",
    "    {'type': 'ineq', 'fun' : lambda p: 1- np.sum(np.exp(p)[10:15]-0.00000001) },\n",
    "    {'type': 'ineq', 'fun' : lambda p: 1- np.sum(np.exp(p)[15:20]-0.00000001) },\n",
    "    {'type': 'ineq', 'fun' : lambda p: 1- np.sum(np.exp(p)[20:25]-0.00000001) },\n",
    "   )\n",
    "\n",
    "\n",
    "\n",
    "cost='l'\n",
    "lSeq = np.arange(0,10,.25)\n",
    "QRE = np.zeros((len(lSeq),25))\n",
    "p0 = np.log([0.2,0.2,0.2,0.2,0.1, 0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1])\n",
    "\n",
    "\n",
    "for (i,l) in enumerate(lSeq):\n",
    "    res = minimize(F, p0, args=(l,cost,), method='SLSQP',constraints=cons)\n",
    "    p0 = res.x # use the new value as the new guess for next lambda\n",
    "    QRE[i] =  np.exp(res.x)\n",
    "    \n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE[:,0],lSeq, QRE[:,1],lSeq, QRE[:,2],lSeq, QRE[:,3],lSeq, QRE[:,4])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','2', '3','4'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node A for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE[:,5],lSeq, QRE[:,6],lSeq, QRE[:,7],lSeq, QRE[:,8],lSeq, QRE[:,9])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','2', '3','4'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node B for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE[:,10],lSeq, QRE[:,11],lSeq, QRE[:,12],lSeq, QRE[:,13],lSeq, QRE[:,14])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','2', '3','4'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node C for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE[:,15],lSeq, QRE[:,16],lSeq, QRE[:,17],lSeq, QRE[:,18],lSeq, QRE[:,19])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','2', '3','4'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node D for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE[:,20],lSeq, QRE[:,21],lSeq, QRE[:,22],lSeq, QRE[:,23],lSeq, QRE[:,24])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','2', '3','4'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node E for turn\")\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Prob of deciding at turn 0 for 5 nodes:\n",
    "[QRE[:,0], QRE[:,5],QRE[:,10],QRE[:,15], QRE[:,20]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 2: at turn 0, only find the prob of deciding at turn 0, find the QRE (not converting either)\n",
    "\n",
    "- Here define the QRE as deciding at turn 0 vs deciding at future turns, where the payoff of future turns will be the max of all future turns. \n",
    "- Advantage: clear tradeoff, \n",
    "- Disadvantage: A optimal to decide at turn 1? also E looks wierd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "#Define the function whose 0 we want to find  (Turocy)\n",
    "def F(p, l = 1,cost='h'): ## probability vector and value of lambda\n",
    "    # The part where it is about prob of deciding at turn 0\n",
    "\n",
    "    p_real = np.exp(p)\n",
    "    p = np.reshape(p, (5,5))\n",
    "   \n",
    "    p_5 = np.log(1- np.exp(p).sum(axis=1))\n",
    "\n",
    "    H =  np.empty((5,15),dtype=float)\n",
    "\n",
    "    # This version: the probability is the difference between prob of deciding at turn 0 vs later\n",
    "    \n",
    "    H[:,0]= p[:,0] - p[:,1] - l*(payoff(p_real, cost)[:,0]- np.max(payoff(p_real, cost)[:,1:] , axis=1))\n",
    "    H[:,1]= p[:,0] - p[:,2] - l*(payoff(p_real, cost)[:,0]- np.max(payoff(p_real, cost)[:,2:], axis=1))\n",
    "    H[:,2]= p[:,0] - p[:,3] - l*(payoff(p_real, cost)[:,0]- np.max(payoff(p_real, cost)[:,3:], axis=1))\n",
    "    H[:,3]= p[:,0] - p[:,4] - l*(payoff(p_real, cost)[:,0]- np.max(payoff(p_real, cost)[:,4:], axis=1))\n",
    "    H[:,10]= p[:,0] - p_5 - l*(payoff(p_real, cost)[:,0]- payoff(p_real, cost)[:,5])\n",
    "    \n",
    "    H[:,4]= p[:,1] - p[:,2] - l*(payoff(p_real, cost)[:,1]- np.max(payoff(p_real, cost)[:,2:], axis=1))\n",
    "    H[:,5]= p[:,1] - p[:,3] - l*(payoff(p_real, cost)[:,1]- np.max(payoff(p_real, cost)[:,3:], axis=1))\n",
    "    H[:,6]= p[:,1] - p[:,4] - l*(payoff(p_real, cost)[:,1]- np.max(payoff(p_real, cost)[:,4:], axis=1))\n",
    "    H[:,11]= p[:,1] - p_5 - l*(payoff(p_real, cost)[:,1]- payoff(p_real, cost)[:,5])\n",
    "    \n",
    "    H[:,7]= p[:,2] - p[:,3] - l*(payoff(p_real, cost)[:,2]- np.max(payoff(p_real, cost)[:,3:], axis=1))\n",
    "    H[:,8]= p[:,2] - p[:,4] - l*(payoff(p_real, cost)[:,2]- np.max(payoff(p_real, cost)[:,4:], axis=1))\n",
    "    H[:,12]= p[:,2] - p_5 - l*(payoff(p_real, cost)[:,2]- payoff(p_real, cost)[:,5])\n",
    "    \n",
    "    H[:,9]= p[:,3] - p[:,4] - l*(payoff(p_real, cost)[:,3]- np.max(payoff(p_real, cost)[:,4:], axis=1))\n",
    "    H[:,13]= p[:,3] - p_5 - l*(payoff(p_real, cost)[:,3]- payoff(p_real, cost)[:,5])\n",
    "    H[:,14]= p[:,4] - p_5 - l*(payoff(p_real, cost)[:,4]- payoff(p_real, cost)[:,5])\n",
    "    H = H.reshape(-1)\n",
    "    res =  np.dot(np.transpose(H),H) \n",
    "    return res\n",
    "\n",
    "\n",
    "cons = ({'type': 'ineq', 'fun' : lambda p: 1- np.sum(np.exp(p)[0:5]-0.00000001) } ,\n",
    "   {'type': 'ineq', 'fun' : lambda p: 1-np.sum(np.exp(p)[5:10]-0.00000001)  },\n",
    "    {'type': 'ineq', 'fun' : lambda p: 1- np.sum(np.exp(p)[10:15]-0.00000001) },\n",
    "    {'type': 'ineq', 'fun' : lambda p: 1- np.sum(np.exp(p)[15:20]-0.00000001) },\n",
    "    {'type': 'ineq', 'fun' : lambda p: 1- np.sum(np.exp(p)[20:25]-0.00000001) },\n",
    "   )\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "cost='l'\n",
    "lSeq = np.arange(0,10,.25)\n",
    "QRE_method2 = np.zeros((len(lSeq),25))\n",
    "# p0 = np.log([[0.2,0.2,0.2,0.2,0.1], [0.2,0.2,0.2,0.2,0.1],[0.2,0.2,0.2,0.2,0.1],[0.2,0.2,0.2,0.2,0.1],[0.2,0.2,0.2,0.2,0.1]])\n",
    "p0 = np.log([0.2,0.2,0.2,0.2,0.1, 0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1])\n",
    "\n",
    "for (i,l) in enumerate(lSeq):\n",
    "    res = minimize(F, p0, args=(l,cost,), method='SLSQP',constraints=cons)\n",
    "    p0 = res.x # use the new value as the new guess for next lambda\n",
    "    QRE_method2[i] =  np.exp(res.x)\n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE_method2[:,0],lSeq, QRE_method2[:,1],lSeq, QRE_method2[:,2],lSeq, QRE_method2[:,3],lSeq, QRE_method2[:,4])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','2', '3','4'], loc = 0)\n",
    "ax.set_title(\"QRE_method2 when cost=\"+str(cost)+\" Prob of decision at node A for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE_method2[:,5],lSeq, QRE_method2[:,6],lSeq, QRE_method2[:,7],lSeq, QRE_method2[:,8],lSeq, QRE_method2[:,9])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','2', '3','4'], loc = 0)\n",
    "ax.set_title(\"QRE_method2 when cost=\"+str(cost)+\" Prob of decision at node B for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE_method2[:,10],lSeq, QRE_method2[:,11],lSeq, QRE_method2[:,12],lSeq, QRE_method2[:,13],lSeq, QRE_method2[:,14])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','2', '3','4'], loc = 0)\n",
    "ax.set_title(\"QRE_method2 when cost=\"+str(cost)+\" Prob of decision at node C for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE_method2[:,15],lSeq, QRE_method2[:,16],lSeq, QRE_method2[:,17],lSeq, QRE_method2[:,18],lSeq, QRE_method2[:,19])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','2', '3','4'], loc = 0)\n",
    "ax.set_title(\"QRE_method2 when cost=\"+str(cost)+\" Prob of decision at node D for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE_method2[:,20],lSeq, QRE_method2[:,21],lSeq, QRE_method2[:,22],lSeq, QRE_method2[:,23],lSeq, QRE_method2[:,24])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','2', '3','4'], loc = 0)\n",
    "ax.set_title(\"QRE_method2 when cost=\"+str(cost)+\" Prob of decision at node E for turn\")\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 3 (on top of method 2) : at turn 0, only find the prob of deciding at turn 0 vs not \n",
    "\n",
    "### next, futher improve by estimating each node with the prob of deciding at turn 0, 1 vs future (see whether the results are different)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "#Define the function whose 0 we want to find  (Turocy)\n",
    "def F(p, l = 1,cost='h'): ## probability vector and value of lambda\n",
    "    # The part where it is about prob of deciding at turn 0\n",
    "\n",
    "    p_real = np.exp(p)\n",
    "\n",
    "    # node A\n",
    "    H1 = p[0] - p[1] -  l*(payoff(p_real, cost)[0,0]- np.max(payoff(p_real, cost)[0,1:] ))\n",
    "    H2 = p[0] - np.log(1- p_real[0] - p_real[1]) -  l*(payoff(p_real, cost)[0,0]- np.max(payoff(p_real, cost)[0,2:]))\n",
    "    H3 = p[1] - np.log(1- p_real[0] - p_real[1]) -  l*(payoff(p_real, cost)[0,1]- np.max(payoff(p_real, cost)[0,2:]))\n",
    "    # node B\n",
    "    H4 = p[5] - np.log(1-p_real[5]) - l*(payoff(p_real, cost)[1,0]- np.max(payoff(p_real, cost)[1,1:] ))\n",
    "#     # node C\n",
    "#     H5 = p[10] - (1-p_real[10]) - l*(payoff(p_real, cost)[2,0]- np.max(payoff(p_real, cost)[2,1:] ))\n",
    "#     # node D\n",
    "#     H6 = p[15] - (1-p_real[15]) - l*(payoff(p_real, cost)[3,0]- np.max(payoff(p_real, cost)[3,1:] ))\n",
    "#     # node E\n",
    "#     H5 = p[20] - (1-p_real[20]) - l*(payoff(p_real, cost)[4,0]- np.max(payoff(p_real, cost)[4,1:] ))\n",
    "    \n",
    "    H = np.array([H1, H2, H3, H4])\n",
    "    res =  np.dot(np.transpose(H),H) \n",
    "    return res\n",
    "\n",
    "\n",
    "cons = ({'type': 'ineq', 'fun' : lambda p: 1- np.exp(p[0])-np.exp(p[1]) } ,\n",
    "           {'type': 'ineq', 'fun' : lambda p: 1- np.exp(p[5])  },\n",
    "            {'type': 'ineq', 'fun' : lambda p: 1- np.exp(p[10])  },\n",
    "    {'type': 'ineq', 'fun' : lambda p: 1- np.exp(p[15])  },\n",
    "    {'type': 'ineq', 'fun' : lambda p: 1- np.exp(p[20])  },\n",
    "   \n",
    "   )\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "cost='l'\n",
    "lSeq = np.arange(0,10,.25)\n",
    "QRE = np.zeros((len(lSeq),25))\n",
    "QRE_turn0 = np.zeros((len(lSeq), 5))\n",
    "p0 = np.log([0.2,0.2,0.2,0.2,0.1, 0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1])\n",
    "for (i,l) in enumerate(lSeq):\n",
    "    res = minimize(F, p0, args=(l,cost,), method='SLSQP',constraints=cons)\n",
    "    p0 = res.x # use the new value as the new guess for next lambda\n",
    "    QRE[i] =  np.exp(res.x)\n",
    "    A_turn0 = QRE[i, 0]\n",
    "    B_turn0 = QRE[i, 5]\n",
    "    C_turn0 = 1/np.exp(l * payoff(QRE[i], cost)[2,0]- np.max(payoff(QRE[i], cost)[2,1:]))\n",
    "    D_turn0 = 1/np.exp(l * payoff(QRE[i], cost)[3,0]- np.max(payoff(QRE[i], cost)[3,1:]))\n",
    "    E_turn0 = 1/np.exp(l * payoff(QRE[i], cost)[4,0]- np.max(payoff(QRE[i], cost)[4,1:]))\n",
    "    QRE_turn0[i] = [A_turn0, B_turn0, C_turn0, D_turn0, E_turn0]\n",
    "    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE[:,0],lSeq, QRE[:,1],lSeq, 1- QRE[:,0]-QRE[:,1])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','>= 2'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node A for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE[:,5],lSeq, 1- QRE[:,5])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','>= 1'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node B for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE_turn0[:,0] ,lSeq, QRE_turn0[:,1], lSeq, QRE_turn0[:,2], lSeq, QRE_turn0[:,3], lSeq, QRE_turn0[:,4] )\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['A','B', 'C','D','E'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at turn 0 for node\")\n",
    "plt.show()  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "cost='h'\n",
    "lSeq = np.arange(0,10,.25)\n",
    "QRE = np.zeros((len(lSeq),25))\n",
    "p0 = np.log([0.2,0.2,0.2,0.2,0.1, 0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1])\n",
    "for (i,l) in enumerate(lSeq):\n",
    "    res = minimize(F, p0, args=(l,cost,), method='SLSQP',constraints=cons)\n",
    "    p0 = res.x # use the new value as the new guess for next lambda\n",
    "    QRE[i] =  np.exp(res.x)\n",
    "    A_turn0 = QRE[i, 0]\n",
    "    B_turn0 = QRE[i, 5]\n",
    "    C_turn0 = 1/np.exp(l * payoff(QRE[i], cost)[2,0]- np.max(payoff(QRE[i], cost)[2,1:]))\n",
    "    D_turn0 = 1/np.exp(l * payoff(QRE[i], cost)[3,0]- np.max(payoff(QRE[i], cost)[3,1:]))\n",
    "    E_turn0 = 1/np.exp(l * payoff(QRE[i], cost)[4,0]- np.max(payoff(QRE[i], cost)[4,1:]))\n",
    "    QRE_turn0[i] = [A_turn0, B_turn0, C_turn0, D_turn0, E_turn0]\n",
    "    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE[:,0],lSeq, QRE[:,1],lSeq, 1- QRE[:,0]-QRE[:,1])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','>= 2'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node A for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE[:,5],lSeq, 1- QRE[:,5])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','>= 1'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node B for turn\")\n",
    "plt.show()    \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "p0 = np.log([0.2,0.2,0.2,0.2,0.1, 0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1])\n",
    "res = minimize(F, p0, args=(10000,cost,), method='SLSQP',constraints=cons)\n",
    "QRE[i] =  np.exp(res.x)\n",
    "A_turn0 = QRE[i, 0]\n",
    "B_turn0 = QRE[i, 5]\n",
    "C_turn0 = 1/np.exp(l * payoff(QRE[i], cost)[2,0]- np.max(payoff(QRE[i], cost)[2,1:]))\n",
    "D_turn0 = 1/np.exp(l * payoff(QRE[i], cost)[3,0]- np.max(payoff(QRE[i], cost)[3,1:]))\n",
    "E_turn0 = 1/np.exp(l * payoff(QRE[i], cost)[4,0]- np.max(payoff(QRE[i], cost)[4,1:]))\n",
    "QRE_turn0 = [A_turn0, B_turn0, C_turn0, D_turn0, E_turn0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 4: based on method 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "#Define the function whose 0 we want to find  (Turocy)\n",
    "def F(p, l = 1,cost='h'): ## probability vector and value of lambda\n",
    "    # The part where it is about prob of deciding at turn 0\n",
    "\n",
    "    p_real = np.exp(p)\n",
    "\n",
    "    # node A\n",
    "    H1 = p[0] - p[1] -  l*(payoff(p_real, cost)[0,0]- payoff(p_real, cost)[0,1] )\n",
    "    H2 = p[0] - np.log(1- p_real[0] - p_real[1]) -  l*(payoff(p_real, cost)[0,0]- np.max(payoff(p_real, cost)[0,2:]))\n",
    "    H3 = p[1] - np.log(1- p_real[0] - p_real[1]) -  l*(payoff(p_real, cost)[0,1]- np.max(payoff(p_real, cost)[0,2:]))\n",
    "    # node B\n",
    "    H4 = p[5] - p[6] - l*(payoff(p_real, cost)[1,0]- payoff(p_real, cost)[1,1] )\n",
    "    H41 = p[5] - np.log(1-p_real[5] - p_real[6]) - l*(payoff(p_real, cost)[1,0]- np.max(payoff(p_real, cost)[1,2:] ))\n",
    "    H42 = p[6] - np.log(1-p_real[5] - p_real[6]) - l*(payoff(p_real, cost)[1,1]- np.max(payoff(p_real, cost)[1,2:] ))\n",
    "    # node C\n",
    "    H5 = p[10] - p[11] - l*(payoff(p_real, cost)[2,0]- payoff(p_real, cost)[2,1] )\n",
    "    H51 = p[10] - np.log(1-p_real[10]-p_real[11]) - l*(payoff(p_real, cost)[2,0]- np.max(payoff(p_real, cost)[2,2:] ))\n",
    "    H52 = p[11] - np.log(1-p_real[10]-p_real[11]) - l*(payoff(p_real, cost)[2,1]- np.max(payoff(p_real, cost)[2,2:] ))\n",
    "    # node D\n",
    "    H6 = p[15] - p[16] - l*(payoff(p_real, cost)[3,0]-payoff(p_real, cost)[3,1] )\n",
    "    H61 =  p[15] - np.log(1-p_real[15]-p_real[16]) - l*(payoff(p_real, cost)[3,0]- np.max(payoff(p_real, cost)[3,2:] ))\n",
    "    H62 =  p[16] - np.log(1-p_real[15]-p_real[16]) - l*(payoff(p_real, cost)[3,1]- np.max(payoff(p_real, cost)[3,2:] ))\n",
    "    # node E\n",
    "    H7 = p[20] - p[21]  - l*(payoff(p_real, cost)[4,0]- payoff(p_real, cost)[4,1] )\n",
    "    H71 = p[20] - np.log(1-p_real[20]-p_real[21]) - l*(payoff(p_real, cost)[4,0]- np.max(payoff(p_real, cost)[4,2:] ))\n",
    "    H72 = p[21] - np.log(1-p_real[20]-p_real[21]) - l*(payoff(p_real, cost)[4,1]- np.max(payoff(p_real, cost)[4,2:] ))\n",
    "    \n",
    "    H = np.array([H1, H2, H3, H4, H41, H42, H5, H51, H52, H6, H61, H62, H7, H71, H72])\n",
    "    res =  np.dot(np.transpose(H),H) \n",
    "    return res\n",
    "\n",
    "\n",
    "cons = ({'type': 'ineq', 'fun' : lambda p: 1- np.exp(p[0])-np.exp(p[1]) -1e-30  } ,\n",
    "           {'type': 'ineq', 'fun' : lambda p: 1- np.exp(p[5]) - np.exp(p[6]) - 1e-30},\n",
    "            {'type': 'ineq', 'fun' : lambda p: 1- np.exp(p[10]) -np.exp(p[11]) -1e-30 },\n",
    "    {'type': 'ineq', 'fun' : lambda p: 1- np.exp(p[15]) -np.exp(p[16]) -1e-30 },\n",
    "    {'type': 'ineq', 'fun' : lambda p: 1- np.exp(p[20]) -  np.exp(p[21]) -1e-30 },\n",
    "   \n",
    "   )\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Try something new, use the second position to denote 1-p[1]-p[2]\n",
    "## This is the eq at turn 0\n",
    "#Define the function whose 0 we want to find  (Turocy)\n",
    "def F(p, l = 1,cost='h'): ## probability vector and value of lambda\n",
    "    # The part where it is about prob of deciding at turn 0\n",
    "\n",
    "    p_real = np.exp(p)\n",
    "\n",
    "    # node A\n",
    "    H1 = p[0] - p[1] -  l*(payoff(p_real, cost)[0,0]- payoff(p_real, cost)[0,1] )\n",
    "    H2 = p[0] - p[2] -  l*(payoff(p_real, cost)[0,0]- np.max(payoff(p_real, cost)[0,2:]))\n",
    "    H3 = p[1] - p[2] -  l*(payoff(p_real, cost)[0,1]- np.max(payoff(p_real, cost)[0,2:]))\n",
    "    # node B\n",
    "    H4 = p[5] - p[6] - l*(payoff(p_real, cost)[1,0]- payoff(p_real, cost)[1,1] )\n",
    "    H41 = p[5] - p[7] - l*(payoff(p_real, cost)[1,0]- np.max(payoff(p_real, cost)[1,2:] ))\n",
    "    H42 = p[6] - p[7] - l*(payoff(p_real, cost)[1,1]- np.max(payoff(p_real, cost)[1,2:] ))\n",
    "    # node C\n",
    "    H5 = p[10] - p[11] - l*(payoff(p_real, cost)[2,0]- payoff(p_real, cost)[2,1] )\n",
    "    H51 = p[10] -p[12] - l*(payoff(p_real, cost)[2,0]- np.max(payoff(p_real, cost)[2,2:] ))\n",
    "    H52 = p[11] - p[12] - l*(payoff(p_real, cost)[2,1]- np.max(payoff(p_real, cost)[2,2:] ))\n",
    "    # node D\n",
    "    H6 = p[15] - p[16] - l*(payoff(p_real, cost)[3,0]-payoff(p_real, cost)[3,1] )\n",
    "    H61 =  p[15] - p[17] - l*(payoff(p_real, cost)[3,0]- np.max(payoff(p_real, cost)[3,2:] ))\n",
    "    H62 =  p[16] - p[17] - l*(payoff(p_real, cost)[3,1]- np.max(payoff(p_real, cost)[3,2:] ))\n",
    "    # node E\n",
    "    H7 = p[20] - p[21]  - l*(payoff(p_real, cost)[4,0]- payoff(p_real, cost)[4,1] )\n",
    "    H71 = p[20] - p[22] - l*(payoff(p_real, cost)[4,0]- np.max(payoff(p_real, cost)[4,2:] ))\n",
    "    H72 = p[21] - p[22] - l*(payoff(p_real, cost)[4,1]- np.max(payoff(p_real, cost)[4,2:] ))\n",
    "    \n",
    "    H = np.array([H1, H2, H3, H4, H41, H42, H5, H51, H52, H6, H61, H62, H7, H71, H72])\n",
    "    res =  np.dot(np.transpose(H),H) \n",
    "    return res\n",
    "\n",
    "\n",
    "cons = ({'type': 'eq', 'fun' : lambda p: 1- np.exp(p[0])-np.exp(p[1]) -np.exp(p[2])  } ,\n",
    "           {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[5]) - np.exp(p[6])  -np.exp(p[7])},\n",
    "            {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[10]) -np.exp(p[11])  -np.exp(p[12]) },\n",
    "    {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[15]) -np.exp(p[16]) -np.exp(p[17]) },\n",
    "    {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[20]) -  np.exp(p[21]) -np.exp(p[22]) },\n",
    "   \n",
    "   )\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "datafolder = \"C:\\\\Users\\\\xinxi\\\\Purdue\\\\EffectiveSocialLearningProject\\\\DataAnalysis\\\\ImportedData\\\\\"\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-11-d4fbf4df2ad3>:24: UserWarning: You have mixed positional and keyword arguments, some input may be discarded.\n",
      "  lgd = ax.legend(handles, labels = ['0','1','>= 2'], 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"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-11-d4fbf4df2ad3>:33: UserWarning: You have mixed positional and keyword arguments, some input may be discarded.\n",
      "  lgd = ax.legend(handles, labels = ['0','1','>=  2'], 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"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-11-d4fbf4df2ad3>:42: UserWarning: You have mixed positional and keyword arguments, some input may be discarded.\n",
      "  lgd = ax.legend(handles, labels = ['0','1','>= 2'], 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"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-11-d4fbf4df2ad3>:51: UserWarning: You have mixed positional and keyword arguments, some input may be discarded.\n",
      "  lgd = ax.legend(handles, labels = ['0','1','>= 2'], 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"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-11-d4fbf4df2ad3>:60: UserWarning: You have mixed positional and keyword arguments, some input may be discarded.\n",
      "  lgd = ax.legend(handles, labels = ['0','1','>= 2'], 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"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-11-d4fbf4df2ad3>:69: UserWarning: You have mixed positional and keyword arguments, some input may be discarded.\n",
      "  lgd = ax.legend(handles, labels = ['A','B', 'C','D','E'], 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": [
    "cost='l'\n",
    "lSeq = np.arange(0,10,.25)\n",
    "QRE = np.zeros((len(lSeq),25))\n",
    "QRE_turn0 = np.zeros((len(lSeq), 5))\n",
    "p0 = np.log([0.2,0.2,0.2,0.2,0.1, 0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1])\n",
    "for (i,l) in enumerate(lSeq):\n",
    "    res = minimize(F, p0, args=(l,cost,), method='SLSQP',constraints=cons)\n",
    "    p0 = res.x # use the new value as the new guess for next lambda\n",
    "    QRE[i] =  np.exp(res.x)\n",
    "#     A_turn0 = QRE[i, 0]\n",
    "#     B_turn0 = QRE[i, 5]\n",
    "#     C_turn0 = 1/np.exp(l * payoff(QRE[i], cost)[2,0]- np.max(payoff(QRE[i], cost)[2,1:]))\n",
    "#     D_turn0 = 1/np.exp(l * payoff(QRE[i], cost)[3,0]- np.max(payoff(QRE[i], cost)[3,1:]))\n",
    "#     E_turn0 = 1/np.exp(l * payoff(QRE[i], cost)[4,0]- np.max(payoff(QRE[i], cost)[4,1:]))\n",
    "#     QRE_turn0[i] = [A_turn0, B_turn0, C_turn0, D_turn0, E_turn0]\n",
    "QRE_l = QRE\n",
    "np.savetxt(datafolder+'QRE_bL.csv', QRE_l, delimiter=',')\n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE[:,0],lSeq, QRE[:,1],lSeq, QRE[:,2])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','>= 2'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node A for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE[:,5],lSeq, QRE[:,6],lSeq, QRE[:,7])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','>=  2'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node B for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE[:,10],lSeq, QRE[:,11],lSeq, QRE[:,12])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','>= 2'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node C for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE[:,15],lSeq, QRE[:,16],lSeq, QRE[:,17])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','>= 2'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node D for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE[:,20],lSeq, QRE[:,21],lSeq, QRE[:,22])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','>= 2'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node E for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE_turn0[:,0] ,lSeq, QRE_turn0[:,1], lSeq, QRE_turn0[:,2], lSeq, QRE_turn0[:,3], lSeq, QRE_turn0[:,4] )\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['A','B', 'C','D','E'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at turn 0 for node\")\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     fun: 9.900545666552578e-14\n",
       "     jac: array([ 4.22989558e-07, -5.78590885e-07,  1.25799005e-07, -0.00000000e+00,\n",
       "       -0.00000000e+00, -2.29526677e-07,  1.06119188e-07,  9.36051663e-08,\n",
       "       -0.00000000e+00, -0.00000000e+00,  3.96472331e-08,  2.53233480e-07,\n",
       "       -3.22683036e-07, -0.00000000e+00, -0.00000000e+00,  3.39714262e-07,\n",
       "       -7.89802357e-08, -3.50140994e-07, -0.00000000e+00, -0.00000000e+00,\n",
       "        7.75998217e-08,  1.83110899e-07, -3.50117688e-07, -0.00000000e+00,\n",
       "       -0.00000000e+00])\n",
       " message: 'Optimization terminated successfully'\n",
       "    nfev: 80\n",
       "     nit: 3\n",
       "    njev: 3\n",
       "  status: 0\n",
       " success: True\n",
       "       x: array([-1.13997000e+02, -4.18470001e+01,  5.38162376e-14, -1.60943791e+00,\n",
       "       -2.30258509e+00, -1.13997000e+02, -4.18470000e+01,  6.99738861e-14,\n",
       "       -1.60943791e+00, -2.30258509e+00, -1.04247000e+02, -1.13997000e+02,\n",
       "        6.34149720e-17, -1.60943791e+00, -2.30258509e+00, -1.04247000e+02,\n",
       "       -1.13997000e+02, -4.29023602e-17, -1.60943791e+00, -2.30258509e+00,\n",
       "       -1.04247000e+02, -1.13997000e+02, -4.90423023e-17, -1.60943791e+00,\n",
       "       -2.30258509e+00])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-13-452f1d9d959c>:26: UserWarning: You have mixed positional and keyword arguments, some input may be discarded.\n",
      "  lgd = ax.legend(handles, labels = ['0','1','>= 2'], 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"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-13-452f1d9d959c>:35: UserWarning: You have mixed positional and keyword arguments, some input may be discarded.\n",
      "  lgd = ax.legend(handles, labels = ['0','1','>=  2'], 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"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-13-452f1d9d959c>:44: UserWarning: You have mixed positional and keyword arguments, some input may be discarded.\n",
      "  lgd = ax.legend(handles, labels = ['0','1','>= 2'], 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"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-13-452f1d9d959c>:53: UserWarning: You have mixed positional and keyword arguments, some input may be discarded.\n",
      "  lgd = ax.legend(handles, labels = ['0','1','>= 2'], 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"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-13-452f1d9d959c>:62: UserWarning: You have mixed positional and keyword arguments, some input may be discarded.\n",
      "  lgd = ax.legend(handles, labels = ['0','1','>= 2'], loc = 0)\n"
     ]
    },
    {
     "data": {
      "image/png": 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FpEDENtCfWNvC/NpJTBxbGnUpIiI5EctA39rZzctNW3V3IhEpKLEM9D+sa8VddycSkcISy0B/am0zFeUlHFczMepSRERyJnaB7u48tbaFk2ZPoUSn+4tIAYld4q1v6WDT1nd1dyIRKTixC/Sn1uh0fxEpTLEL9A0tHVSWl1BbpdP9RaSwxC7Q2zp7qJ4wJuoyRERyLnaB3t7RzeRxOplIRApP7AK9raObKt0MWkQKUEaBbmZnmNlqM1tnZlenGT7RzH5rZn80s5VmdlH2S81Me2c3k8cp0EWk8AwZ6GZWDPwYOBOYC5xnZnNTRlsKrHL344DTgO+bWc5T1d3VQheRgpVJC30RsM7d17t7N7AMOCdlHAcqLLjw+ASgDejNaqUZ6OzuY1dvvwJdRApSJoE+A2hM6m4K+yW7CTgK2Ay8Alzu7v2pEzKzS81shZmtaG5u3s+SB9fW0Q3AZAW6iBSgTAI93e1+PKX7dOAlYDowH7jJzCoHvMj9Fnevd/f6qVOzf+JPe2cQ6FXahy4iBSiTQG8CapO6awha4skuAn7lgXXABuDI7JSYObXQRaSQZRLoy4E5ZjYr/KFzCXB/yjgNwAcBzOxg4AhgfTYLzcTuFroCXUQKUMlQI7h7r5l9EXgYKAZud/eVZnZZOPxm4FrgTjN7hWAXzVXu3jKCdafV1tEDaJeLiBSmIQMdwN0fAB5I6Xdz0vPNwEeyW9rwtXXsorjIqByb0WyJiMRKrM4UbevoYfK4MoKjJ0VECkusAr29o5uq8bqOi4gUplgFeptO+xeRAharQG/Xaf8iUsDiFeid3ToGXUQKVmwCvb/fae/soVqBLiIFKjaBvr2rh75+1z50ESlYsQn0xGn/2ocuIoUqNoGeOO1f+9BFpFDFJtB12r+IFLrYBHp7YpfLBAW6iBSm2AR6a4euhS4ihS02gd7e2U15aRFjy4qjLkVEJBKxCfS2jm61zkWkoMUm0Ns7dJaoiBS22AR6W6eu4yIihS02ga4Lc4lIoYtNoLd26NK5IlLYYhHoPX397OjqVQtdRApaLAJdp/2LiMQl0HXav4hIPAI9caXFybqfqIgUsFgEemKXS/X4MRFXIiISnVgEeqta6CIi8Qj0xJUWddiiiBSyWAR6W0c3FeUllBbHYnZERPZLLBKwXaf9i4jEI9DbdJaoiEg8Ar29s5tqtdBFpMCVRF1ANrTt7ObI91RGXYaIjJCenh6ampro6uqKupScKS8vp6amhtLSzI/eyyjQzewM4EagGLjV3a9LM85pwA1AKdDi7qdmXMUB0qVzReKtqamJiooKZs6ciZlFXc6Ic3daW1tpampi1qxZGb9uyF0uZlYM/Bg4E5gLnGdmc1PGmQT8BDjb3ecB5w6n+APxbncfXT392ocuEmNdXV1UV1cXRJgDmBnV1dXD/kaSyT70RcA6d1/v7t3AMuCclHE+CfzK3RsA3H3LsKo4AG3hWaJVOqlIJNYKJcwT9md+Mwn0GUBjUndT2C/Z4cBkM3vczF4ws08PUuClZrbCzFY0NzcPu9h0EicVVem0fxEpcJkEero/E57SXQIsBD4KnA78vZkdPuBF7re4e72710+dOnXYxabT1qEWuoiMvIceeogjjjiCww47jOuuG/Az4qiQSaA3AbVJ3TXA5jTjPOTuHe7eAjwJHJedEvetTaf9i8gI6+vrY+nSpTz44IOsWrWKu+++m1WrVkVd1gCZBPpyYI6ZzTKzMmAJcH/KOL8BTjazEjMbB/wJ8Fp2S01vTwtdgS4iI+P555/nsMMO49BDD6WsrIwlS5bwm9/8JuqyBhjysEV37zWzLwIPExy2eLu7rzSzy8LhN7v7a2b2EPAy0E9waOOrI1l4QntnN0UGleXa5SJSCL7x25Ws2rw9q9OcO72Sr/2feYMO37RpE7W1e3ZU1NTU8Nxzz2W1hmzI6Dh0d38AeCCl380p3d8Dvpe90jKTOO2/qKiwfgEXkdxxT/3ZcHQedZP3Z4rqwlwihWVfLemRUlNTQ2PjnoP9mpqamD59es7rGEreX8ulraNbN4cWkRF1/PHHs3btWjZs2EB3dzfLli3j7LPPjrqsAfK+hd7W0c2hUyZEXYaIxFhJSQk33XQTp59+On19fVx88cXMm5f7bwpDiUGg97DwELXQRWRkLV68mMWLF0ddxj7l9S4Xdw/3oesIFxGRvA707V299PW7TioSESHPAz1xHZfqCQp0EZG8DvRWnfYvIrJbXgd6u077FxHZLa8DPXEtdLXQRUTyPNDVQheRXLn44os56KCDOProo6MuZVB5Hehtnd2UlRQxrqw46lJEJOYuvPBCHnrooajL2Ke8DvT2jm6qx5eNyovkiEi8nHLKKVRVVUVdxj7l9ZmiiSstikgBefBqePuV7E7zPcfAmaPzLkTDkdct9LYOXWlRRCQhr1vo7Z09zJg8LuoyRCSXYtCSHin530Ifp+u4iIhAHgd6b18/297toWr8mKhLEZECcN5553HiiSeyevVqampquO2226IuaYC83eWy9d0eAF1pUURy4u677466hCHlbQu9LXEdF/0oKiICxCDQq3TYoogIkMeB3q4WuojIXvI20BMX5tJx6CIigbwN9HZdC11EZC95G+htHT1UjCmhrCRvZ0FEJKvyNg3bOnZp/7mI5KXf/e53LFy4kGOOOYaFCxfy6KOPZmW6eXsceltnjwJdRHKmvb2dyZMnZ2VaU6ZM4be//S3Tp0/n1Vdf5fTTT2fTpk0HPN28baG367R/Ecmh+vp6PvnJT/Loo4/i7gc0rQULFjB9+nQA5s2bR1dXF7t27TrgGvO3hd7RzZyDJ0Rdhojk2PXPX8/rba9ndZpHVh3JVYuu2uc4a9as4cEHH+Smm25i6dKlXHDBBVx44YW7g/mKK67gscceG/C6JUuWcPXVVw863V/+8pcsWLCAMWMO/DImeRvo7Z3BzS1ERHKhuLiYs846i7POOovm5ma+/OUvU1dXx9NPP82iRYv44Q9/OOxprly5kquuuopHHnkkKzXmZaB39fTR2d2nfegiBWiolvRI2rZtG/fccw933HEHpaWl3HbbbRx77LHA8FvoTU1NfPzjH+euu+5i9uzZWakvo0A3szOAG4Fi4FZ3T3tBYjM7HngW+Et3vy8rFaah0/5FJNfOP/98nnnmGc4991zuuusu5syZs9fw4bTQt27dykc/+lG+853vcNJJJ2WtxiF/FDWzYuDHwJnAXOA8M5s7yHjXAw9nrbpB6MJcIpJrn/jEJ1i9ejXXXXfdgDAfrptuuol169Zx7bXXMn/+fObPn8+WLVsOuMZMWuiLgHXuvh7AzJYB5wCrUsb7K+CXwPEHXNUQ2nXav4jk2Nlnn521aV1zzTVcc801WZteQiaHLc4AGpO6m8J+u5nZDODjwM37mpCZXWpmK8xsRXNz83Br3a1Np/2LiAyQSaBbmn6pB2HeAFzl7n37mpC73+Lu9e5eP3Xq1ExrHCBxHRcd5SIiskcmu1yagNqk7hpgc8o49cAyMwOYAiw2s153/4+sVJmirbOHIoPKsTqxSKRQuDthxhSE/Tl5KZMW+nJgjpnNMrMyYAlwf8obz3L3me4+E7gP+MJIhTkE13GZNK6M4qLCWbgihay8vJzW1tYDPkMzX7g7ra2tlJeXD+t1Q7bQ3b3XzL5IcPRKMXC7u680s8vC4fvcbz4S2jt6mKzT/kUKRk1NDU1NTRzIb2/5pry8nJqammG9JqPj0N39AeCBlH5pg9zdLxxWBfuhraNbR7iIFJDS0lJmzZoVdRmjXl5enKu9s1tHuIiIpMjLQG/r6KZ6ggJdRCRZ3gW6u6uFLiKSRt4F+o5dvfT0ufahi4ikyLtA182hRUTSy7tA332lRbXQRUT2kneBvmrVndTP/AplvRujLkVEZFTJu0DH+lg9tp9d21+IuhIRkVEl7wL9lPkfAWDb9pURVyIiMrrkXaBPmzqXEncat74RdSkiIqNK3gV6SVEJM6yMhs63oy5FRGRUybtAB6gtm0xDXyf09UZdiojIqJGXgV5XWUdjSTHeqt0uIiIJ+Rno1Uexs6iI9k3PR12KiMiokZeBXjttIQANb62IuBIRkdEjLwO9btJsABrbVkdciYjI6JGXgT5jwgyKgIadm6IuRURk1MjLQC8tLmVayQQa+jqga1vU5YiIjAp5GegAdeOn01hSAu+siroUEZFRIX8DvWoODaUlsEWXABARgTwO9Nrqo9hWXMy2t16KuhQRkVEhbwO9rqIOgMbmVyOuRERkdMjfQK8MAr1h+0bo74+4GhGR6OVtoNdU1GBAg/XCtoaoyxERiVzeBvqY4jEcPKYqPNJFP4yKiORtoAPUTZxFQ2mpAl1EhDwP9NqJM2koGwPv6IdREZG8DvS6yjraimCnWugiInke6IlDF3c2QndnxNWIiEQrrwO9tqIWgIbiImh+PeJqRESilVGgm9kZZrbazNaZ2dVphn/KzF4OH0+b2XHZL3WgRKA36odREZGhA93MioEfA2cCc4HzzGxuymgbgFPd/VjgWuCWbBeazrjScUwdO5WGMeUKdBEpeJm00BcB69x9vbt3A8uAc5JHcPen3b097HwWqMlumYOrrahl49gKHekiIgUvk0CfATQmdTeF/QbzWeDBdAPM7FIzW2FmK5qbmzOvch/qKutoLLaghe6elWmKiOSjTALd0vRLm5xm9n6CQL8q3XB3v8Xd6929furUqZlXuQ91FXU0ezedXe2w852sTFNEJB9lEuhNQG1Sdw2wOXUkMzsWuBU4x91bs1Pe0Gorwx9GS0q020VEClomgb4cmGNms8ysDFgC3J88gpnVAb8CLnD3Ndkvc3C7j0Uv1TVdRKSwlQw1grv3mtkXgYeBYuB2d19pZpeFw28GvgpUAz8xM4Bed68fubL32H0s+oRqBbqIFLQhAx3A3R8AHkjpd3PS80uAS7JbWmYqyiqoKq+iwfoU6CJS0PL6TNGE2opaGkvLoHk19HZHXY6ISCRiEeh1FXU0+C7o74HWtVGXIyISiVgEem1lLW/3bKfLDN5ZFXU5IiKRiEWgJ4502VRWrkMXRaRgxSrQG6oP0Q+jIlKw4hHolWGgVx6kQBeRghWLQJ84ZiKVZZU0jhkLOzZDZ1vUJYmI5FwsAh3CI12K+oMOtdJFpADFJtBrK2tp6N4WdCjQRaQAxSbQ6yrqeOvdLfSMq4YtCnQRKTzxCfTKOvq9n00HH64WuogUpPgEeuLQxUkzgkDftSPiikREcis2gb77htEHHQa9XfDyPRFXJCKSW7EJ9KryKsaXjqehCJh2HCy/TbekE5GCEptAN7Pg0MUdDXD852DLKtj4dNRliYjkTGwCHcLL6O5ohKP/HMonwfJboy5JRCRnYhXodZV1bNqxid6SMlhwPrx2P+x4O+qyRERyIl6BXlFHr/fyVsdbUH8x9PfCi3dFXZaISE7EKtB3H+myvRGqZ8PsD8CKO6CvN+LKRERGXqwCffdVF3c0BD2O/1xwsa7VD+zjVSIi8RCrQJ86dirlxeV7Av3w02FirX4cFZGCEKtANzNqK2uDXS4ARcVQfxFseAKa10RbnIjICItVoAN7jkVPWPBpKCqFFbdFV5SISA7ELtAPnXgoG7dv5NWW8N6iE6bCvI/BS/8G3R3RFiciMoJiF+jnzz2fg8cdzOWPXU7Luy1Bz+M/B7u2w8v3RluciMgIil2gV5VXccP7b2D7ru1c+fiV9PT1QO0iOPiY4MdRXd9FRGIqdoEOcFT1UXzjfd/gxS0vcv3y68EMFl0C77wKjc9HXZ6IyIiIZaADLD50MRcdfRH3rL6H+9bcB8ecC2MqYfk/R12aiMiIiG2gA1y+4HLeN/19fOu5b/HS1rUw/5Ow8j9gZ3PUpYmIZF2sA724qJjvnvJdpo2fxhWPX8E7x3wc+nvguZ9qX7qIxE6sAx1g4piJ3Pj+G+no6eCKP/6IXXM+Ak99H/5pIfz+h7DjnahLFBHJiowC3czOMLPVZrbOzK5OM9zM7Efh8JfN7L3ZL3X/zZk8h2//6bd5peUVvlU3B//YzVDxHvjvr8MPjoJln4I1D+siXiKS10qGGsHMioEfAx8GmoDlZna/u69KGu1MYE74+BPgp9/wDGYAAAWiSURBVOG/o8aHDvkQnz/28/zs5Z9RNKeMw084n6qFn6C64Tkmr/lvqtY8wMTx76F4waegZhGMqQgfE4IfU8dUQHFp1LMhIjKoIQMdWASsc/f1AGa2DDgHSA70c4C73N2BZ81skplNc/e3sl7xAfjC/C/QtLOJX6/7Nf3ev2dAdTlU11AETHrz3xiz4RcUhbvYDacIMMAwzIowLDEw8b+9WJp+IiIJHz/4BD7z0VuyPt1MAn0G0JjU3cTA1ne6cWYAewW6mV0KXApQV1c33FoPWJEVcd3J1/Gtk77Ftu5ttL3bRltXymPHJnZ1tUNfD/193XhfD97Xjff34H099Pf3hD+ohom/+8dVD/9L/bHV99kpIoWnevzBIzLdTAI9XXMzNZYyGQd3vwW4BaC+vj6yaCsuKqaqvIqq8qqoShARybpMfhRtAmqTumuAzfsxjoiIjKBMAn05MMfMZplZGbAEuD9lnPuBT4dHu5wAbBtt+89FROJuyF0u7t5rZl8EHgaKgdvdfaWZXRYOvxl4AFgMrAM6gYtGrmQREUknk33ouPsDBKGd3O/mpOcOLM1uaSIiMhyxP1NURKRQKNBFRGJCgS4iEhMKdBGRmDCP6DKyZtYMbNzPl08BWrJYTj4p1Hkv1PmGwp33Qp1v2Pe8H+LuU9MNiCzQD4SZrXD3+qjriEKhznuhzjcU7rwX6nzD/s+7drmIiMSEAl1EJCbyNdCzf93J/FGo816o8w2FO++FOt+wn/Oel/vQRURkoHxtoYuISAoFuohITORdoA91w+o4MrNaM3vMzF4zs5VmdnnUNeWamRWb2f+a2X9GXUuuhLdyvM/MXg+X/YlR15QrZnZFuK6/amZ3m1l51DWNBDO73cy2mNmrSf2qzOx3ZrY2/HdyptPLq0BPumH1mcBc4DwzmxttVTnRC1zp7kcBJwBLC2S+k10OvBZ1ETl2I/CQux8JHEeBzL+ZzQC+BNS7+9EEl+1eEm1VI+ZO4IyUflcD/+Puc4D/CbszkleBTtINq929G0jcsDrW3P0td38xfL6DYMOeEW1VuWNmNcBHgVujriVXzKwSOAW4DcDdu919a7RV5VQJMNbMSoBxxPQOaO7+JNCW0vsc4F/C5/8CfCzT6eVboA92M+qCYWYzgQXAc9FWklM3AH8H9EddSA4dCjQDd4S7mm41s/FRF5UL7r4J+EeggeBG89vc/ZFoq8qpgxN3fAv/PSjTF+ZboGd0M+q4MrMJwC+B/+fu26OuJxfM7Cxgi7u/EHUtOVYCvBf4qbsvADoYxlfvfBbuMz4HmAVMB8ab2fnRVpUf8i3QC/Zm1GZWShDmv3D3X0VdTw6dBJxtZm8S7GL7gJn9PNqScqIJaHL3xDex+wgCvhB8CNjg7s3u3gP8CnhfxDXl0jtmNg0g/HdLpi/Mt0DP5IbVsWNmRrAv9TV3/0HU9eSSu3/Z3WvcfSbB8n7U3WPfWnP3t4FGMzsi7PVBYFWEJeVSA3CCmY0L1/0PUiA/CIfuBz4TPv8M8JtMX5jRPUVHi8FuWB1xWblwEnAB8IqZvRT2+0p4r1eJr78CfhE2XtZTIDdfd/fnzOw+4EWCI7z+l5heBsDM7gZOA6aYWRPwNeA64F4z+yzBH7dzM56eTv0XEYmHfNvlIiIig1Cgi4jEhAJdRCQmFOgiIjGhQBcRiQkFuohITCjQRURiQoEuksTMjjGzjWb2f6OuRWS4FOgiSdz9FYJLDHw66lpEhkuBLjLQFmBe1EWIDJcCXWSg64AxZnZI1IWIDIcCXSSJmZ0BjAf+C7XSJc8o0EVC4Y2Ivwt8AXgFODraikSGR4Eussc1wF3u/iYKdMlDCnQRILyRxIcJ7l8KCnTJQ7oeuohITKiFLiISEwp0EZGYUKCLiMSEAl1EJCYU6CIiMaFAFxGJCQW6iEhM/H8+z0K4osQibAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-13-452f1d9d959c>:71: UserWarning: You have mixed positional and keyword arguments, some input may be discarded.\n",
      "  lgd = ax.legend(handles, labels = ['A','B', 'C','D','E'], 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": [
    "# The prob for this part is that 1- p[5] - p[6] goes too closely to 0 and cause the np.log not working properly \n",
    "\n",
    "\n",
    "cost='h'\n",
    "lSeq = np.arange(0,10,.25)\n",
    "QRE = np.zeros((len(lSeq),25))\n",
    "QRE_turn0 = np.zeros((len(lSeq), 5))\n",
    "p0 = np.log([0.2,0.2,0.2,0.2,0.1, 0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1])\n",
    "for (i,l) in enumerate(lSeq):\n",
    "    res = minimize(F, p0, args=(l,cost,), method='SLSQP',constraints=cons)\n",
    "    p0 = res.x # use the new value as the new guess for next lambda\n",
    "    QRE[i] =  np.exp(res.x)\n",
    "#     A_turn0 = QRE[i, 0]\n",
    "#     B_turn0 = QRE[i, 5]\n",
    "#     C_turn0 = 1/np.exp(l * payoff(QRE[i], cost)[2,0]- np.max(payoff(QRE[i], cost)[2,1:]))\n",
    "#     D_turn0 = 1/np.exp(l * payoff(QRE[i], cost)[3,0]- np.max(payoff(QRE[i], cost)[3,1:]))\n",
    "#     E_turn0 = 1/np.exp(l * payoff(QRE[i], cost)[4,0]- np.max(payoff(QRE[i], cost)[4,1:]))\n",
    "#     QRE_turn0[i] = [A_turn0, B_turn0, C_turn0, D_turn0, E_turn0]\n",
    "\n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE[:,0],lSeq, QRE[:,1],lSeq, QRE[:,2])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','>= 2'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node A for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE[:,5],lSeq, QRE[:,6],lSeq, QRE[:,7])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','>=  2'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node B for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE[:,10],lSeq, QRE[:,11],lSeq, QRE[:,12])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','>= 2'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node C for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE[:,15],lSeq, QRE[:,16],lSeq, QRE[:,17])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','>= 2'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node D for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE[:,20],lSeq, QRE[:,21],lSeq, QRE[:,22])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['0','1','>= 2'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node E for turn\")\n",
    "plt.show()    \n",
    "\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE_turn0[:,0] ,lSeq, QRE_turn0[:,1], lSeq, QRE_turn0[:,2], lSeq, QRE_turn0[:,3], lSeq, QRE_turn0[:,4] )\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['A','B', 'C','D','E'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at turn 0 for node\")\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# For estimation , a more fine l grid:\n",
    "cost='h'\n",
    "lSeq = np.arange(0,10,.01)\n",
    "QRE = np.zeros((len(lSeq),25))\n",
    "QRE_turn0 = np.zeros((len(lSeq), 5))\n",
    "p0 = np.log([0.2,0.2,0.2,0.2,0.1, 0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1])\n",
    "for (i,l) in enumerate(lSeq):\n",
    "    res = minimize(F, p0, args=(l,cost,), method='SLSQP',constraints=cons)\n",
    "    p0 = res.x # use the new value as the new guess for next lambda\n",
    "    QRE[i] =  np.exp(res.x)\n",
    "#     QRE_turn0[i] = [QRE[i][0], QRE[i][5],QRE[i][10],QRE[i][15],QRE[i][20]]\n",
    "#     QRE_NOTturn0[i] = [QRE[i][1]+QRE[i][2], QRE[i][6]+QRE[i][7],QRE[i][11]+QRE[i][12],QRE[i][16]+QRE[i][17],QRE[i][21]+QRE[i][22]]\n",
    "QRE_h = QRE\n",
    "np.savetxt(datafolder+'QRE_bH.csv', QRE_h, delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv(datafolder+\"Networkb_CostH\"+\".csv\", sep=\",\")\n",
    "Decide_0 = data.iloc[:,3:].to_numpy()==0 * 1\n",
    "Decide_1 = data.iloc[:,3:].to_numpy()==1 * 1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "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>session</th>\n",
       "      <th>g_id</th>\n",
       "      <th>round_id</th>\n",
       "      <th>A_period</th>\n",
       "      <th>B_period</th>\n",
       "      <th>C_period</th>\n",
       "      <th>D_period</th>\n",
       "      <th>E_period</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>115</th>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>26</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>116</th>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>27</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>117</th>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>28</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>118</th>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>29</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>119</th>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>30</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>120 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     session  g_id  round_id  A_period  B_period  C_period  D_period  E_period\n",
       "0          6     1         1         1         1         0         2         2\n",
       "1          6     1         2         1         1         0         3         2\n",
       "2          6     1         3         1         1         0         2         2\n",
       "3          6     1         4         0         1         2         1         2\n",
       "4          6     1         5         0         0         0         1         1\n",
       "..       ...   ...       ...       ...       ...       ...       ...       ...\n",
       "115        7     2        26         2         1         3         1         2\n",
       "116        7     2        27         2         1         3         2         2\n",
       "117        7     2        28         1         1         2         0         1\n",
       "118        7     2        29         1         2         2         1         1\n",
       "119        7     2        30         0         2         0         1         1\n",
       "\n",
       "[120 rows x 8 columns]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "QRE_h = QRE\n",
    "\n",
    "likeli_turn0 = np.zeros(len(QRE_h))\n",
    "\n",
    "for i in range(len(QRE_h)) :\n",
    "    l = np.array([QRE_h[i][0], QRE_h[i][5],QRE_h[i][10],QRE_h[i][15],QRE_h[i][20]])\n",
    "    l_no = np.array([QRE_h[i][1]+QRE_h[i][2], QRE_h[i][6]+QRE_h[i][7],QRE_h[i][11]+QRE_h[i][12],QRE_h[i][16]+QRE_h[i][17],QRE_h[i][21]+QRE_h[i][22]]\n",
    ")\n",
    "    l_1 = np.array([QRE_h[i][1], QRE_h[i][6],QRE_h[i][11],QRE_h[i][16],QRE_h[i][21]]\n",
    ")\n",
    "    likeli_turn0[i] = np.sum(np.dot(Decide_0,np.log(l))) + np.sum(np.dot(Decide_1, np.log(l_1)))\n",
    "#     likeli_turn0[i] = np.sum(np.dot(Decide_0,np.log(l))) + np.sum(np.dot(1- Decide_0,np.log(l_no))) \n",
    "    \n",
    "# np.savetxt(datafolder+'likeli_turn0_bH.csv', likeli_turn0, delimiter=',')    \n",
    "\n",
    "# Note: network b, cost H, with the second expression, linear relationship\n",
    "# Maybe only use the decision, not the wait "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.25"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lSeq[likeli_turn0.argmax()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Try a different range \n",
    "cost='h'\n",
    "lSeq = np.arange(0,50,.5)\n",
    "QRE = np.zeros((len(lSeq),25))\n",
    "QRE_turn0 = np.zeros((len(lSeq), 5))\n",
    "p0 = np.log([0.2,0.2,0.2,0.2,0.1, 0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1])\n",
    "for (i,l) in enumerate(lSeq):\n",
    "    res = minimize(F, p0, args=(l,cost,), method='SLSQP',constraints=cons)\n",
    "    p0 = res.x # use the new value as the new guess for next lambda\n",
    "    QRE[i] =  np.exp(res.x)\n",
    "#     QRE_turn0[i] = [QRE[i][0], QRE[i][5],QRE[i][10],QRE[i][15],QRE[i][20]]\n",
    "#     QRE_NOTturn0[i] = [QRE[i][1]+QRE[i][2], QRE[i][6]+QRE[i][7],QRE[i][11]+QRE[i][12],QRE[i][16]+QRE[i][17],QRE[i][21]+QRE[i][22]]\n",
    "QRE_h = QRE\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "likeli_turn0 = np.zeros(len(QRE_h))\n",
    "\n",
    "for i in range(len(QRE_h)) :\n",
    "    l = np.array([QRE_h[i][0], QRE_h[i][5],QRE_h[i][10],QRE_h[i][15],QRE_h[i][20]])\n",
    "    l_no = np.array([QRE_h[i][1]+QRE_h[i][2], QRE_h[i][6]+QRE_h[i][7],QRE_h[i][11]+QRE_h[i][12],QRE_h[i][16]+QRE_h[i][17],QRE_h[i][21]+QRE_h[i][22]]\n",
    ")\n",
    "#     likeli_turn0[i] = np.sum(np.dot(Decide_0,np.log(l)))\n",
    "    likeli_turn0[i] = np.sum(np.dot(Decide_0,np.log(l))) + np.sum(np.dot(1- Decide_0,np.log(l_no))) \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "likeli_turn0.argmax()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 3: For turn 1, \n",
    "\n",
    "Firstly redefine the payoff, as payoff is determined by subjects' behaviors at turn 0, "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Try something new, use the second position to denote 1-p[1]-p[2]\n",
    "## This is the eq at turn 1\n",
    "## can update the prob matrix in function F\n",
    "#Define the function whose 0 we want to find  (Turocy)\n",
    "def F_A0B0(p,  l = 1,cost='h'): ## probability vector and value of lambda\n",
    "    # The part where it is about prob of deciding at turn 0\n",
    "    \n",
    "    p_real = np.exp(p)\n",
    "    p_real[0]=p_real[5]=1\n",
    "    p_real[1:4]=0\n",
    "    p_real[6:9]=0\n",
    "    \n",
    "    # node C\n",
    "    H5 = p[11] - p[12] - l*(payoff(p_real, cost)[2,1]- payoff(p_real, cost)[2,2] )\n",
    "    H51 = p[11] -p[13] - l*(payoff(p_real, cost)[2,1]- np.max(payoff(p_real, cost)[2,3:] ))\n",
    "    H52 = p[12] - p[13] - l*(payoff(p_real, cost)[2,2]- np.max(payoff(p_real, cost)[2,3:] ))\n",
    "    # node D\n",
    "    H6 = p[16] - p[17] - l*(payoff(p_real, cost)[3,1]-payoff(p_real, cost)[3,2] )\n",
    "    H61 =  p[16] - p[18] - l*(payoff(p_real, cost)[3,1]- np.max(payoff(p_real, cost)[3,3:] ))\n",
    "    H62 =  p[17] - p[18] - l*(payoff(p_real, cost)[3,2]- np.max(payoff(p_real, cost)[3,3:] ))\n",
    "    # node E\n",
    "    H7 = p[21] - p[22]  - l*(payoff(p_real, cost)[4,1]- payoff(p_real, cost)[4,2] )\n",
    "    H71 = p[21] - p[23] - l*(payoff(p_real, cost)[4,1]- np.max(payoff(p_real, cost)[4,3:] ))\n",
    "    H72 = p[22] - p[23] - l*(payoff(p_real, cost)[4,2]- np.max(payoff(p_real, cost)[4,3:] ))\n",
    "    \n",
    "    H = np.array([H5, H51, H52, H6, H61, H62, H7, H71, H72])\n",
    "    res =  np.dot(np.transpose(H),H) \n",
    "    return res\n",
    "\n",
    "\n",
    "cons = (\n",
    "            {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[13]) -np.exp(p[11])  -np.exp(p[12]) },\n",
    "    {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[18]) -np.exp(p[16]) -np.exp(p[17]) },\n",
    "    {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[23]) -  np.exp(p[21]) -np.exp(p[22]) },\n",
    "   \n",
    "   )\n",
    "\n",
    "cost='h'\n",
    "lSeq = np.arange(0,10,.01)\n",
    "QRE_turn1_A0B0 = np.zeros((len(lSeq), 25))\n",
    "p0 = np.log([0.2,0.2,0.2,0.2,0.1, 0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1])\n",
    "for (i,l) in enumerate(lSeq):\n",
    "    res = minimize(F_A0B0, p0, args=(l,cost,), method='SLSQP',constraints=cons)\n",
    "    p0 = res.x # use the new value as the new guess for next lambda\n",
    "    QRE_turn1_A0B0[i] =  np.exp(res.x)\n",
    "np.savetxt(datafolder+'QRE_turn1_A0B0_bH.csv', QRE_turn1_A0B0, delimiter=',')\n",
    "\n",
    "cost='l'\n",
    "lSeq = np.arange(0,10,.01)\n",
    "QRE_turn1_A0B0 = np.zeros((len(lSeq), 25))\n",
    "p0 = np.log([0.2,0.2,0.2,0.2,0.1, 0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1])\n",
    "for (i,l) in enumerate(lSeq):\n",
    "    res = minimize(F_A0B0, p0, args=(l,cost,), method='SLSQP',constraints=cons)\n",
    "    p0 = res.x # use the new value as the new guess for next lambda\n",
    "    QRE_turn1_A0B0[i] =  np.exp(res.x)\n",
    "np.savetxt(datafolder+'QRE_turn1_A0B0_bL.csv', QRE_turn1_A0B0, delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "def F_A0B0(p,  l = 1,cost='h'): ## probability vector and value of lambda\n",
    "    # The part where it is about prob of deciding at turn 0\n",
    "    \n",
    "    p_real = np.exp(p)\n",
    "    p_real[0]=p_real[5]=1\n",
    "    p_real[1:4]=0\n",
    "    p_real[6:9]=0\n",
    "    \n",
    "    # node C\n",
    "    H5 = p[11] - p[12] - l*(payoff(p_real, cost)[2,1]- payoff(p_real, cost)[2,2] )\n",
    "    H51 = p[11] -p[13] - l*(payoff(p_real, cost)[2,1]- np.max(payoff(p_real, cost)[2,3:] ))\n",
    "    H52 = p[12] - p[13] - l*(payoff(p_real, cost)[2,2]- np.max(payoff(p_real, cost)[2,3:] ))\n",
    "    # node D\n",
    "    H6 = p[16] - p[17] - l*(payoff(p_real, cost)[3,1]-payoff(p_real, cost)[3,2] )\n",
    "    H61 =  p[16] - p[18] - l*(payoff(p_real, cost)[3,1]- np.max(payoff(p_real, cost)[3,3:] ))\n",
    "    H62 =  p[17] - p[18] - l*(payoff(p_real, cost)[3,2]- np.max(payoff(p_real, cost)[3,3:] ))\n",
    "    # node E\n",
    "    H7 = p[21] - p[22]  - l*(payoff(p_real, cost)[4,1]- payoff(p_real, cost)[4,2] )\n",
    "    H71 = p[21] - p[23] - l*(payoff(p_real, cost)[4,1]- np.max(payoff(p_real, cost)[4,3:] ))\n",
    "    H72 = p[22] - p[23] - l*(payoff(p_real, cost)[4,2]- np.max(payoff(p_real, cost)[4,3:] ))\n",
    "    \n",
    "    H = np.array([H5, H51, H52, H6, H61, H62, H7, H71, H72])\n",
    "    res =  np.dot(np.transpose(H),H) \n",
    "    return res\n",
    "\n",
    "\n",
    "cons = (\n",
    "            {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[13]) -np.exp(p[11])  -np.exp(p[12]) },\n",
    "    {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[18]) -np.exp(p[16]) -np.exp(p[17]) },\n",
    "    {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[23]) -  np.exp(p[21]) -np.exp(p[22]) },\n",
    "   \n",
    "   )\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Try something new, use the second position to denote 1-p[1]-p[2]\n",
    "## This is the eq at turn 1\n",
    "## can update the prob matrix in function F\n",
    "#Define the function whose 0 we want to find  (Turocy)\n",
    "def F_A0Bnot0(p,  l = 1,cost='h'): ## probability vector and value of lambda\n",
    "    # The part where it is about prob of deciding at turn 0\n",
    "   \n",
    "    p_real = np.exp(p)\n",
    "    p_real[0]=1\n",
    "    p_real[1:4]=0    \n",
    "    p_real[5]=0\n",
    "    # node B\n",
    "    H4 = p[6] - p[7] - l*(payoff(p_real, cost)[1,1]- payoff(p_real, cost)[1,2] )\n",
    "    H41 = p[6] - p[8] - l*(payoff(p_real, cost)[1,1]- np.max(payoff(p_real, cost)[1,3:] ))\n",
    "    H42 = p[7] - p[8] - l*(payoff(p_real, cost)[1,2]- np.max(payoff(p_real, cost)[1,3:] ))\n",
    "    # node C\n",
    "    H5 = p[11] - p[12] - l*(payoff(p_real, cost)[2,1]- payoff(p_real, cost)[2,2] )\n",
    "    H51 = p[11] -p[13] - l*(payoff(p_real, cost)[2,1]- np.max(payoff(p_real, cost)[2,3:] ))\n",
    "    H52 = p[12] - p[13] - l*(payoff(p_real, cost)[2,2]- np.max(payoff(p_real, cost)[2,3:] ))\n",
    "    # node D\n",
    "    H6 = p[16] - p[17] - l*(payoff(p_real, cost)[3,1]-payoff(p_real, cost)[3,2] )\n",
    "    H61 =  p[16] - p[18] - l*(payoff(p_real, cost)[3,1]- np.max(payoff(p_real, cost)[3,3:] ))\n",
    "    H62 =  p[17] - p[18] - l*(payoff(p_real, cost)[3,2]- np.max(payoff(p_real, cost)[3,3:] ))\n",
    "    # node E\n",
    "    H7 = p[21] - p[22]  - l*(payoff(p_real, cost)[4,1]- payoff(p_real, cost)[4,2] )\n",
    "    H71 = p[21] - p[23] - l*(payoff(p_real, cost)[4,1]- np.max(payoff(p_real, cost)[4,3:] ))\n",
    "    H72 = p[22] - p[23] - l*(payoff(p_real, cost)[4,2]- np.max(payoff(p_real, cost)[4,3:] ))\n",
    "    \n",
    "    H = np.array([H4, H41, H42, H5, H51, H52, H6, H61, H62, H7, H71, H72])\n",
    "    res =  np.dot(np.transpose(H),H) \n",
    "    return res\n",
    "\n",
    "\n",
    "cons = ({'type': 'eq', 'fun' : lambda p: 1- np.exp(p[8]) - np.exp(p[6])  -np.exp(p[7])},\n",
    "            {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[13]) -np.exp(p[11])  -np.exp(p[12]) },\n",
    "    {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[18]) -np.exp(p[16]) -np.exp(p[17]) },\n",
    "    {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[23]) -  np.exp(p[21]) -np.exp(p[22]) },\n",
    "   \n",
    "   )\n",
    "\n",
    "cost='h'\n",
    "lSeq = np.arange(0,10,.01)\n",
    "QRE_turn1_A0Bnot0 = np.zeros((len(lSeq), 25))\n",
    "p0 = np.log([0.2,0.2,0.2,0.2,0.1, 0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1])\n",
    "for (i,l) in enumerate(lSeq):\n",
    "    res = minimize(F_A0Bnot0, p0, args=(l,cost,), method='SLSQP',constraints=cons)\n",
    "    p0 = res.x # use the new value as the new guess for next lambda\n",
    "    QRE_turn1_A0Bnot0[i] =  np.exp(res.x)\n",
    "np.savetxt(datafolder+'QRE_turn1_A0Bnot0_bH.csv', QRE_turn1_A0Bnot0, delimiter=',')\n",
    "\n",
    "\n",
    "cost='l'\n",
    "lSeq = np.arange(0,10,.01)\n",
    "QRE_turn1_A0Bnot0 = np.zeros((len(lSeq), 25))\n",
    "p0 = np.log([0.2,0.2,0.2,0.2,0.1, 0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1])\n",
    "for (i,l) in enumerate(lSeq):\n",
    "    res = minimize(F_A0Bnot0, p0, args=(l,cost,), method='SLSQP',constraints=cons)\n",
    "    p0 = res.x # use the new value as the new guess for next lambda\n",
    "    QRE_turn1_A0Bnot0[i] =  np.exp(res.x)\n",
    "np.savetxt(datafolder+'QRE_turn1_A0Bnot0_bL.csv', QRE_turn1_A0Bnot0, delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[70.   , 70.4  , 67.692, 59.692, 51.692, 43.692],\n",
       "       [70.   , 70.4  , 62.4  , 54.4  , 46.4  , 38.4  ],\n",
       "       [70.   , 62.   , 54.   , 46.   , 38.   , 30.   ],\n",
       "       [70.   , 62.   , 54.   , 46.   , 38.   , 30.   ],\n",
       "       [70.   , 62.   , 54.   , 46.   , 38.   , 30.   ]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_real = np.exp(p0)\n",
    "p_real[0]=1\n",
    "p_real[1:4]=0    \n",
    "p_real[5]=0\n",
    "payoff(p_real, cost)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Try something new, use the second position to denote 1-p[1]-p[2]\n",
    "## This is the eq at turn 1\n",
    "## can update the prob matrix in function F\n",
    "#Define the function whose 0 we want to find  (Turocy)\n",
    "def F_Anot0Bnot0(p,  l = 1,cost='h'): ## probability vector and value of lambda\n",
    "    # The part where it is about prob of deciding at turn 0\n",
    "    p_real = np.exp(p)\n",
    "    p_real[0]=0  \n",
    "    p_real[5]=0\n",
    "    \n",
    "    # node A\n",
    "    H1 = p[1] - p[2] -  l*(payoff(p_real, cost)[0,1]- payoff(p_real, cost)[0,2] )\n",
    "    H2 = p[1] - p[3] -  l*(payoff(p_real, cost)[0,1]- np.max(payoff(p_real, cost)[0,3:]))\n",
    "    H3 = p[2] - p[3] -  l*(payoff(p_real, cost)[0,2]- np.max(payoff(p_real, cost)[0,3:]))\n",
    "    # node B\n",
    "    H4 = p[6] - p[7] - l*(payoff(p_real, cost)[1,1]- payoff(p_real, cost)[1,2] )\n",
    "    H41 = p[6] - p[8] - l*(payoff(p_real, cost)[1,1]- np.max(payoff(p_real, cost)[1,3:] ))\n",
    "    H42 = p[7] - p[8] - l*(payoff(p_real, cost)[1,2]- np.max(payoff(p_real, cost)[1,3:] ))\n",
    "    # node C\n",
    "    H5 = p[11] - p[12] - l*(payoff(p_real, cost)[2,1]- payoff(p_real, cost)[2,2] )\n",
    "    H51 = p[11] -p[13] - l*(payoff(p_real, cost)[2,1]- np.max(payoff(p_real, cost)[2,3:] ))\n",
    "    H52 = p[12] - p[13] - l*(payoff(p_real, cost)[2,2]- np.max(payoff(p_real, cost)[2,3:] ))\n",
    "    # node D\n",
    "    H6 = p[16] - p[17] - l*(payoff(p_real, cost)[3,1]-payoff(p_real, cost)[3,2] )\n",
    "    H61 =  p[16] - p[18] - l*(payoff(p_real, cost)[3,1]- np.max(payoff(p_real, cost)[3,3:] ))\n",
    "    H62 =  p[17] - p[18] - l*(payoff(p_real, cost)[3,2]- np.max(payoff(p_real, cost)[3,3:] ))\n",
    "    # node E\n",
    "    H7 = p[21] - p[22]  - l*(payoff(p_real, cost)[4,1]- payoff(p_real, cost)[4,2] )\n",
    "    H71 = p[21] - p[23] - l*(payoff(p_real, cost)[4,1]- np.max(payoff(p_real, cost)[4,3:] ))\n",
    "    H72 = p[22] - p[23] - l*(payoff(p_real, cost)[4,2]- np.max(payoff(p_real, cost)[4,3:] ))\n",
    "    \n",
    "    H = np.array([H1, H2, H3, H4, H41, H42,H5, H51, H52, H6, H61, H62, H7, H71, H72])\n",
    "    res =  np.dot(np.transpose(H),H) \n",
    "    return res\n",
    "\n",
    "\n",
    "cons = ({'type': 'eq', 'fun' : lambda p: 1- np.exp(p[3])-np.exp(p[1]) -np.exp(p[2])  } ,\n",
    "    {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[8]) - np.exp(p[6])  -np.exp(p[7])},\n",
    "            {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[13]) -np.exp(p[11])  -np.exp(p[12]) },\n",
    "    {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[18]) -np.exp(p[16]) -np.exp(p[17]) },\n",
    "    {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[23]) -  np.exp(p[21]) -np.exp(p[22]) },\n",
    "   \n",
    "   )\n",
    "\n",
    "cost='h'\n",
    "lSeq = np.arange(0,10,.01)\n",
    "QRE_turn1_Anot0Bnot0 = np.zeros((len(lSeq), 25))\n",
    "p0 = np.log([0.2,0.2,0.2,0.2,0.1, 0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1])\n",
    "for (i,l) in enumerate(lSeq):\n",
    "    res = minimize(F_Anot0Bnot0, p0, args=(l,cost,), method='SLSQP',constraints=cons)\n",
    "    p0 = res.x # use the new value as the new guess for next lambda\n",
    "    QRE_turn1_Anot0Bnot0[i] =  np.exp(res.x)\n",
    "np.savetxt(datafolder+'QRE_turn1_Anot0Bnot0_bH.csv', QRE_turn1_Anot0Bnot0, delimiter=',')\n",
    "\n",
    "cost='l'\n",
    "lSeq = np.arange(0,10,.01)\n",
    "QRE_turn1_Anot0Bnot0 = np.zeros((len(lSeq), 25))\n",
    "p0 = np.log([0.2,0.2,0.2,0.2,0.1, 0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1])\n",
    "for (i,l) in enumerate(lSeq):\n",
    "    res = minimize(F_Anot0Bnot0, p0, args=(l,cost,), method='SLSQP',constraints=cons)\n",
    "    p0 = res.x # use the new value as the new guess for next lambda\n",
    "    QRE_turn1_Anot0Bnot0[i] =  np.exp(res.x)\n",
    "np.savetxt(datafolder+'QRE_turn1_Anot0Bnot0_bL.csv', QRE_turn1_Anot0Bnot0, delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Try something new, use the second position to denote 1-p[1]-p[2]\n",
    "## This is the eq at turn 1\n",
    "## can update the prob matrix in function F\n",
    "#Define the function whose 0 we want to find  (Turocy)\n",
    "def F_Anot0B0(p,  l = 1,cost='h'): ## probability vector and value of lambda\n",
    "    # The part where it is about prob of deciding at turn 0\n",
    "    p_real = np.exp(p)\n",
    "    p_real[0]=0\n",
    "    p_real[6:9]=0    \n",
    "    p_real[5]=1\n",
    "    \n",
    "    # node A\n",
    "    H1 = p[1] - p[2] -  l*(payoff(p_real, cost)[0,1]- payoff(p_real, cost)[0,2] )\n",
    "    H2 = p[1] - p[3] -  l*(payoff(p_real, cost)[0,1]- np.max(payoff(p_real, cost)[0,3:]))\n",
    "    H3 = p[2] - p[3] -  l*(payoff(p_real, cost)[0,2]- np.max(payoff(p_real, cost)[0,3:]))\n",
    "    # node C\n",
    "    H5 = p[11] - p[12] - l*(payoff(p_real, cost)[2,1]- payoff(p_real, cost)[2,2] )\n",
    "    H51 = p[11] -p[13] - l*(payoff(p_real, cost)[2,1]- np.max(payoff(p_real, cost)[2,3:] ))\n",
    "    H52 = p[12] - p[13] - l*(payoff(p_real, cost)[2,2]- np.max(payoff(p_real, cost)[2,3:] ))\n",
    "    # node D\n",
    "    H6 = p[16] - p[17] - l*(payoff(p_real, cost)[3,1]-payoff(p_real, cost)[3,2] )\n",
    "    H61 =  p[16] - p[18] - l*(payoff(p_real, cost)[3,1]- np.max(payoff(p_real, cost)[3,3:] ))\n",
    "    H62 =  p[17] - p[18] - l*(payoff(p_real, cost)[3,2]- np.max(payoff(p_real, cost)[3,3:] ))\n",
    "    # node E\n",
    "    H7 = p[21] - p[22]  - l*(payoff(p_real, cost)[4,1]- payoff(p_real, cost)[4,2] )\n",
    "    H71 = p[21] - p[23] - l*(payoff(p_real, cost)[4,1]- np.max(payoff(p_real, cost)[4,3:] ))\n",
    "    H72 = p[22] - p[23] - l*(payoff(p_real, cost)[4,2]- np.max(payoff(p_real, cost)[4,3:] ))\n",
    "    \n",
    "    H = np.array([H1, H2, H3,H5, H51, H52, H6, H61, H62, H7, H71, H72])\n",
    "    res =  np.dot(np.transpose(H),H) \n",
    "    return res\n",
    "\n",
    "\n",
    "cons = ({'type': 'eq', 'fun' : lambda p: 1- np.exp(p[3])-np.exp(p[1]) -np.exp(p[2])  } ,\n",
    "            {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[13]) -np.exp(p[11])  -np.exp(p[12]) },\n",
    "    {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[18]) -np.exp(p[16]) -np.exp(p[17]) },\n",
    "    {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[23]) -  np.exp(p[21]) -np.exp(p[22]) },\n",
    "   \n",
    "   )\n",
    "\n",
    "cost='h'\n",
    "lSeq = np.arange(0,10,.01)\n",
    "QRE_turn1_Anot0B0 = np.zeros((len(lSeq), 25))\n",
    "p0 = np.log([0.2,0.2,0.2,0.2,0.1, 0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1])\n",
    "for (i,l) in enumerate(lSeq):\n",
    "    res = minimize(F_Anot0B0, p0, args=(l,cost,), method='SLSQP',constraints=cons)\n",
    "    p0 = res.x # use the new value as the new guess for next lambda\n",
    "    QRE_turn1_Anot0B0[i] =  np.exp(res.x)\n",
    "np.savetxt(datafolder+'QRE_turn1_Anot0B0_bH.csv', QRE_turn1_Anot0B0, delimiter=',')\n",
    "\n",
    "cost='l'\n",
    "lSeq = np.arange(0,10,.01)\n",
    "QRE_turn1_Anot0B0 = np.zeros((len(lSeq), 25))\n",
    "p0 = np.log([0.2,0.2,0.2,0.2,0.1, 0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1])\n",
    "for (i,l) in enumerate(lSeq):\n",
    "    res = minimize(F_Anot0B0, p0, args=(l,cost,), method='SLSQP',constraints=cons)\n",
    "    p0 = res.x # use the new value as the new guess for next lambda\n",
    "    QRE_turn1_Anot0B0[i] =  np.exp(res.x)\n",
    "np.savetxt(datafolder+'QRE_turn1_Anot0B0_bL.csv', QRE_turn1_Anot0B0, delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-39-4f2f953d7264>:7: UserWarning: You have mixed positional and keyword arguments, some input may be discarded.\n",
      "  lgd = ax.legend(handles, labels = ['1','2','>= 3'], loc = 0)\n"
     ]
    },
    {
     "data": {
      "image/png": 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n6ElRlyIiMqRyPtB/v3wbAGfO0ZehIpLbcj7Q/7DiTeZPqWBSpbpbRCS35XSg72rZz1827OLMOROiLkVEZMjldKA/v2YH7nDKzPFRlyIiMuRyOtCfW7OD0hGFHFMzJupSRESGXG4H+hs7qKutorgwpzdTRATI4UBv2NPG69uaOVkn4hKRPJGzgb543U4ATpxRFXElIiLZkbOB/vLG3YwoLGDe5IqoSxERyYqcDfSXNu5mzuQKRhbpP0NFJD/kZKB3dHaxtL6Rt03V0S0ikj9yMtBf39bMvvZOFkytjLoUEZGsyclAf3njbgCOnTo24kpERLInJwP91c2NlI8sonZcadSliIhkTU4G+qqte5g9qRwz/TuRiOSPnAt0d2fllj3MnqjDFUUkv+RcoG/avY89bR0cNbE86lJERLIq5wJ95ZY9AMyZpEAXkfySVqCb2dlmtsrMVpvZDSmmV5rZL83sZTNbZmZXZr7U9Kx6Mwj0WRMU6CKSXwYMdDMrBL4PnAPMBS4xs7lJs10HLHf3BcDpwC1mNiLDtaZlxZYmplaNorykOIrVi4hEJp0W+gnAandf4+77gQeAC5LmcaDcgsNKRgM7gY6MVpqm1duaObJ6dBSrFhGJVDqBPgXYmDBcH45L9D1gDrAZWAp8yt27khdkZteY2RIzW9LQ0HCQJfetq8tZt6OFGQp0EclD6QR6qoO5PWn4vcBfgcnAscD3zKzXcYPufqe717l7XXV19aCLHcjWplZa27uYUV2W8WWLiAx36QR6PTA1YbiGoCWe6ErgEQ+sBtYCszNTYvrWNLQAMH28Al1E8k86gb4YmGlm08MvOi8GHk2aZwNwBoCZTQCOAtZkstB0rN3eDMAR6nIRkTxUNNAM7t5hZh8HHgMKgXvcfZmZXRtOvwP4KnCvmS0l6KL5rLtvH8K6U3qjoYWyEYUcVj4y26sWEYncgIEO4O6LgEVJ4+5IuL0Z+JvMljZ4a7e3ML26TOdwEZG8lFO/FF27vYXp49XdIiL5KWcCvaOzi02793F4lU6ZKyL5KWcCfUtjK51dztSqUVGXIiISiZwJ9Ppd+wCoGasWuojkpxwK9L0A1IxVC11E8lMOBfo+zGBSpQJdRPJTTgX6xIoSRhTlzCaJiAxKzqRf/a696m4RkbyWQ4G+T1+Iikhey4lA7+jsYmtTq1roIpLXciLQu49BnzJGgS4i+SsnAn1rUysAkxToIpLHciLQ3wwDfUKFzrIoIvkrRwK9DYCJFSURVyIiEp2cCPRtTa2MKCqgclRx1KWIiEQmJwL9zaZWJlSM1HnQRSSv5UigtzGhXN0tIpLfciPQ97QyQf3nIpLnciPQGxXoIiKxD/Tmtg5a9nfqkEURyXuxD/S3jkFXC11E8lvOBPphaqGLSJ6LfaBvC39UdJiOchGRPBf7QN/eHAR69Wi10EUkv8U+0He27KeowKgYVRR1KSIikcqJQB9bNkK/EhWRvJcTgT6ubETUZYiIRC4nAn1sqQJdRCQnAr1qtAJdRCT23yTuUJeLSM5rb2+nvr6e1tbWqEvJmpKSEmpqaiguTv+04GkFupmdDdwGFAJ3ufvNKeY5HbgVKAa2u/tpaVdxkDo6u2jc106VAl0kp9XX11NeXk5tbW1eHADh7uzYsYP6+nqmT5+e9v0G7HIxs0Lg+8A5wFzgEjObmzTPGOB24Hx3nwdcNJjiD9auve0ACnSRHNfa2sq4cePyIswBzIxx48YN+hNJOn3oJwCr3X2Nu+8HHgAuSJrnUuARd98A4O7bBlXFQdrZsh9QoIvkg3wJ824Hs73pBPoUYGPCcH04LtEsYKyZPWlmL5rZh/so8BozW2JmSxoaGgZdbLIdLcGvRBXoIiLpBXqqtwlPGi4Cjgf+Fngv8AUzm9XrTu53unudu9dVV1cPuthk3S30cWX62b+IDK2rrrqKww47jPnz50ddSp/SCfR6YGrCcA2wOcU8v3X3FnffDvwJWJCZEvu2Kwz0sWX6c2gRGVpXXHEFv/3tb6Muo1/pBPpiYKaZTTezEcDFwKNJ8/wCOMXMisysFDgRWJHZUnvb0R3o+mGRiAyxU089laqqqqjL6NeAhy26e4eZfRx4jOCwxXvcfZmZXRtOv8PdV5jZb4FXgC6CQxtfHcrCIWihV44qprgw9r+PEpE0ffmXy1i+uSmjy5w7uYIvvW9eRpcZhbSOQ3f3RcCipHF3JA3/G/BvmSttYLv3tTOmVN0tIiIQ81+KNu1rp6JEgS6ST3KhJT1UYt1X0bivXedBFxEJxTrQm1o7qBylFrqIDL1LLrmEk08+mVWrVlFTU8Pdd98ddUm9xLp5qy4XEcmW+++/P+oSBhTrFnrQ5aJAFxGBGAd6a3snbR1d6nIREQnFNtCbWoMzLVaUxLrXSEQkY+Ib6Ps6ANTlIiISim+gd7fQFegiIkCMA71xX3eXiwJdRARiHOhNYaDrS1ERyYaNGzfy7ne/mzlz5jBv3jxuu+22qEvqJbbfKHYHun4pKiLZUFRUxC233MJxxx3Hnj17OP744znrrLOYO3fuwHfOkvi20FvDL0XV5SIiWTBp0iSOO+44AMrLy5kzZw6bNm2KuKqeYtu8bdzXzsiiAkqKC6MuRUSy6Tc3wNalmV3mxKPhnJvTnn3dunW89NJLnHjiiZmt4xDFt4WuX4mKSASam5u58MILufXWW6moqIi6nB5i20Jvam3XF6Ii+WgQLelMa29v58ILL+Syyy7jgx/8YGR19CW2LfTGfe36laiIZI27c/XVVzNnzhyuv/76qMtJKbaB3rSvQ10uIpI1zzzzDD/+8Y95/PHHOfbYYzn22GNZtGjRwHfMotg2cZvbOjh8XGnUZYhInnjXu96Fu0ddRr9i20Lf09pBubpcREQOiG2gt7R1UDZCgS4i0i2Wgd7Z5exr76RspAJdRKRbLAO9uS34lai6XERE3hLLQG8JA10tdBGRtyjQRURyRCwDfU93l4sCXURi6IUXXjhwLPuCBQv4+c9/npHlxjIR1UIXkWzbtWsXY8eOzciy5s+fz5IlSygqKmLLli0sWLCA973vfRQVHVqmxbKF/lag60yLIpIddXV1XHrppTz++OOH/AOj0tLSA+Hd2tqKmWWixHi20Pe0dne56Kf/IvnmGy98g5U7V2Z0mbOrZvPZEz7b7zyvvfYav/nNb/je977Hddddx8KFC7niiiuYPHkyAJ/+9Kd54oknet3v4osv5oYbbug1/s9//jNXXXUV69ev58c//vEht84hpoGuFrqIZFthYSHnnXce5513Hg0NDdx4441MmzaNZ599lhNOOIHvfOc7g1reiSeeyLJly1ixYgUf+chHOOeccygpKTmkGuMZ6Ps7AfWhi+SjgVrSQ6mxsZEHH3yQH/7whxQXF3P33XdzzDHHAINvoXebM2cOZWVlvPrqq9TV1R1SfWklopmdDdwGFAJ3uXvKExKb2duB54G/d/eHD6myfuxp7aC40BhZFMuvAEQkhi6//HKee+45LrroIu677z5mzpzZY/pgWuhr165l6tSpFBUVsX79elatWkVtbe0h1zhgoJtZIfB94CygHlhsZo+6+/IU830DeOyQqxpAS1sHZSOLMvZFgojIQD70oQ9x7733ZqSv++mnn+bmm2+muLiYgoICbr/9dsaPH3/Iy02nshOA1e6+BsDMHgAuAJYnzfcJ4GfA2w+5qgHoxFwikm3nn39+xpa1cOFCFi5cmLHldUunz2IKsDFhuD4cd4CZTQE+ANzR34LM7BozW2JmSxoaGgZb6wHNbTp1rohIsnQCPVW/RvJBmLcCn3X3zv4W5O53unudu9dVV1enW2MvzWGXi4iIvCWdVKwHpiYM1wCbk+apAx4I+7THA+eaWYe7/3dGqkzS0tZBZemIoVi0iAxT7p5X35sdzI+X0mmhLwZmmtl0MxsBXAw8mrTi6e5e6+61wMPAPw5VmEPY5aIWukjeKCkpYceOHcP+L+Ayxd3ZsWPHoI9LHzAV3b3DzD5OcPRKIXCPuy8zs2vD6f32mw+FoMtFPyoSyRc1NTXU19dzKN+9xU1JSQk1NTWDuk9azVx3XwQsShqXMsjd/YpBVXAQWtr0b0Ui+aS4uJjp06dHXcawF7tf5nR1OS37O9hfsJFNzZuiLkdEZNiIXaDvbe/ERmzi0e3/zKW/vpS97XujLklEZFiIXaC3tHVQXPkSADtbd/LHDX+MuCIRkeEhdoHe3NZB4agNHF42j7Ejx/L8luejLklEZFiI3TeLe/a1UzDyTWrKjqW8dKoCXUQkFLsW+uY9b2KFbUwdXcvR449m295t7GzdGXVZIiKRi12gN2z4DQCzRlZyVNVRAKzauSrKkkREhoXYBfpI38uctv3MKx3LUWMV6CIi3WIX6BfPOomHNm9lbkUFY0rGMKF0Aqt2KdBFRGIX6BSXBtfh8edHVR2lQBcRIZaBPiq4bt8HwIzKGaxvXE9nV79n7hURyXkxDPSeLfTailr2d+1nS8uWCIsSEYleDAO9Zwu9trIWgHVN66KpR0RkmIhhoHe30MNAr6gFYF3jumjqEREZJmIY6N0t9BYAqkqqKB9Rrha6iOS9GAd60EI3M6ZXTFcLXUTyXvwC3Szodkk4bW5tZS1rm9ZGWJSISPTiF+gQtNLDFjoE/ejb9m6jJeyGERHJRzEN9NKega4jXURE4hroo2D/W61xHekiIhLnQE9ooU+rmIZhaqGLSF6LaaD3/FJ0ZOFIpoyewtpGfTEqIvkrxoG+r8eo6ZXTFegiktdiGuijUgb6+iadpEtE8ldMA71nlwsEZ11s62xjc8vmiIoSEYlWTAN9VO9AHzMDQN0uIpK3YhroKfrQK6YDCnQRyV8xDfTeLfQxJWOoKqlSoItI3oppoJdCVwd0tvcYXVtRy5rGNREVJSISrZgGevcZF3v3o6uFLiL5Kq1AN7OzzWyVma02sxtSTL/MzF4JL8+a2YLMl5pgRFlw3dbcY/SMyhnsbtvNztadQ7p6EZHhaMBAN7NC4PvAOcBc4BIzm5s021rgNHc/BvgqcGemC+1hZHlwvb9noE+v1BejIpK/0mmhnwCsdvc17r4feAC4IHEGd3/W3XeFg88DNZktM8nIiuC6bU+P0TMqg0MX1Y8uIvkonUCfAmxMGK4Px/XlauA3qSaY2TVmtsTMljQ0NKRfZbLuFnpbU4/RE8smUlpUyupdqw9+2SIiMZVOoFuKcZ5yRrN3EwT6Z1NNd/c73b3O3euqq6vTrzLZgUDv2UIvsAJmjZ3Fyp0rD37ZIiIxlU6g1wNTE4ZrgF6/rzezY4C7gAvcfUdmyutDH4EOcFTVUby+63XcU77niIjkrHQCfTEw08ymm9kI4GLg0cQZzGwa8Aiw0N1fy3yZSfoJ9FljZ7GnfY/O6SIieadooBncvcPMPg48BhQC97j7MjO7Npx+B/BFYBxwu5kBdLh73ZBV3U+gz66aDcDKnSuZMrq/rn4RkdwyYKADuPsiYFHSuDsSbn8U+GhmS+tHYTEUjer1pSjAkWOOxDBe2/kaZ0w7I2sliYhELZ6/FIWglZ6ihV5aXMrhFYezateqCIoSEYlOzgU6BF+M6kgXEck3ORnos6tms6l5E41tjVkuSkQkOjkZ6MeMPwaAVxpeyWZFIiKRinGgV/QZ6PPHz6fACni54eUsFyUiEp0YB3p5yqNcIPhidNbYWQp0EckrMQ/01C10gAXVC1i6fSmdXZ1ZLEpEJDrxDvTWJujjJ/4LqhfQ0t7CG41vZLkwEZFoxDfQR40B7+x1TvRux1QHX4yq20VE8kV8A710XHC9N/V5wKaVT2NcyThefPPFLBYlIhKdnA10M+PESSfy/ObndeZFEckLORDoff9/6MmTT2ZH6w5e2zX0J4AUEYlaDgR636deP3nSyQA8v+X5bFQkIhKpGAd6VXDdTwt9QtkEZlTO4JlNz2SpKBGR6MQ30EdWghX220IHOG3qaSzeupim/al/hCQikiviG+gFBUErfe/2fmc7c9qZdHgHT218KkuFiYhEI76BDjB6IuzZ2u8s88fP57DSw/jD+j9kqSgRkWjEO9ArJkNT//8dWmAFnDntTJ7Z/Iy6XUQkp8U80CfBni0Dznb+kefT1tnGotfcQ9wAAAgNSURBVDWLBpxXRCSuYh7oU6ClATra+p1tbtVcZlfN5pHXH8lSYSIi2RfvQC+fFFwP0I9uZnzgyA+wYucKljYszUJhIiLZF+9Ar5wSXDduHHDWC468gPIR5dz96t1DXJSISDTiHehVRwTXO1YPOGtZcRmXzr6UP274I2/s1il1RST3xDvQK6dC4UjY/npas1825zLKisv4zovfGeLCRESyL96BXlAA446AHem1uMeWjOVjx3yMp+qf4ulNTw9xcSIi2RXvQAcYPwu2LU979svnXE5tRS1ffu7LNLY1DmFhIiLZFf9An3Ic7F4PzQ1pzV5cWMzXT/k62/du56Znb6LLu4a4QBGR7Ih/oNe8PbiuX5z2XeaPn8+nj/80f9jwB25Zcov+AENEckJR1AUcsknHQlEJrHkSZp+b9t0Wzl1IfXM99y2/j7bONm484UYKCwqHrk4RkSEW/xb6iFI44gxY+SvoSr/7xMy44YQbuHLelTy46kE+9vuPsbm5//PCiIgMZ/EPdICjL4SmTbBqcOdqKbACrq+7nq+84yss3b6U9//i/Xz3L99lV+uuISpURGTopBXoZna2ma0ys9VmdkOK6WZm3w2nv2Jmx2W+1H7MuQCqZsDvPg+tgz9y5QMzP8AjFzzCqTWn8oOlP+A9//Uern/yen75xi9p2Jvel60iIlGzgb4QNLNC4DXgLKAeWAxc4u7LE+Y5F/gEcC5wInCbu5/Y33Lr6up8yZIlh1Z9ovXPwo/eFwT7uz8H00+DUWPBbFCLWb1rNT97/WcsWruIna3B39tNLJvIEWOOYEblDCaWTqS6tJrxo8ZTMaKC0uJSRhWNorQouLZBrk9EZDDM7EV3r0s5LY1APxm4yd3fGw7fCODuX0+Y5z+BJ939/nB4FXC6u/d5btuMBzrAG0/ALz8VHMYIwZelJWOgoAgKi4JrKwAGDt0unJUFzguFnawsdN4o6GJtgdM2wF2LHQpJuBwYNgrDNScuYrC3SWMe00E7IsPaByacxEf+9s6Dum9/gZ7OUS5TgMSzX9UTtMIHmmcK0CPQzewa4BqAadOmpbHqQTri3fCJF4NDGDf9BZq3Bl0wXZ3Q1RFeOtNaVAEwN7x0c3ea6GS7t9Pg7eyhk73exT662Oud7KWLDpxOnA4P3hQ6cTohvHYSv7Z1POE2KW8njulrnh63FeYiw964sglDstx0Aj1VAzE5NtKZB3e/E7gTghZ6GusevMJiOPwdwSXDDKgML0dkfOkiIocmnS9F64GpCcM1QPLxfenMIyIiQyidQF8MzDSz6WY2ArgYeDRpnkeBD4dHu5wENPbXfy4iIpk3YJeLu3eY2ceBxwi+37vH3ZeZ2bXh9DuARQRHuKwG9gJXDl3JIiKSSlo//Xf3RQShnTjujoTbDlyX2dJERGQwcuOXoiIiokAXEckVCnQRkRyhQBcRyRED/vR/yFZs1gCsP8i7jwe2Z7CcONA25wdtc344lG0+3N2rU02ILNAPhZkt6etcBrlK25wftM35Yai2WV0uIiI5QoEuIpIj4hroB3feyXjTNucHbXN+GJJtjmUfuoiI9BbXFrqIiCRRoIuI5IjYBfpAf1ida8xsqpk9YWYrzGyZmX0q6pqyxcwKzewlM/tV1LVkg5mNMbOHzWxl+HyfHHVNQ83MPh3u16+a2f1mVhJ1TZlmZveY2TYzezVhXJWZ/d7MXg+vx2ZiXbEK9PAPq78PnEPw73CXmNnc/u8Vex3AZ9x9DnAScF0ebHO3TwEroi4ii24Dfuvus4EF5Pi2m9kU4JNAnbvPJzg998XRVjUk7gXOThp3A/BHd58J/DEcPmSxCnTgBGC1u69x9/3AA8AFEdc0pNx9i7v/Jby9h+BFPiXaqoaemdUAfwvcFXUt2WBmFcCpwN0A7r7f3XdHW1VWFAGjzKwIKCUH/+nM3f8E7EwafQHwo/D2j4D3Z2JdcQv0vv6MOi+YWS3wNuDP0VaSFbcC/wI9/lc7l80AGoAfht1Md5lZWdRFDSV33wR8C9hA8Ifyje7+u2irypoJ3f/qFl4flomFxi3Q0/oz6lxkZqOBnwH/192boq5nKJnZecA2d38x6lqyqAg4DvgPd38b0EKGPoYPV2G/8QXAdGAyUGZml0dbVbzFLdDz8s+ozayYIMx/6u6PRF1PFrwTON/M1hF0q73HzH4SbUlDrh6od/fuT18PEwR8LjsTWOvuDe7eDjwCvCPimrLlTTObBBBeb8vEQuMW6On8YXVOMTMj6Fdd4e7fjrqebHD3G929xt1rCZ7jx909p1tu7r4V2GhmR4WjzgCWR1hSNmwATjKz0nA/P4Mc/yI4waPAR8LbHwF+kYmFpvWfosNFX39YHXFZQ+2dwEJgqZn9NRz3ufB/XiW3fAL4adhYWUOO/9m6u//ZzB4G/kJwNNdL5OBpAMzsfuB0YLyZ1QNfAm4GHjKzqwne2C7KyLr0038RkdwQty4XERHpgwJdRCRHKNBFRHKEAl1EJEco0EVEcoQCXUQkRyjQRURyhAJdJIGZHW1m683s/0Rdi8hgKdBFErj7UoLTDXw46lpEBkuBLtLbNmBe1EWIDJYCXaS3m4GRZnZ41IWIDIYCXSSBmZ0NlAG/Rq10iRkFukgo/IPibwL/CCwF5kdbkcjgKNBF3vJ54D53X4cCXWJIgS4ChH8scRbBf5mCAl1iSOdDFxHJEWqhi4jkCAW6iEiOUKCLiOQIBbqISI5QoIuI5AgFuohIjlCgi4jkiP8FHKQSc5YO+CgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "QRE_turn1_A0B0\n",
    "#Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(lSeq, QRE_turn1_A0B0[:,21],lSeq, QRE_turn1_A0B0[:,22],lSeq, QRE_turn1_A0B0[:,23])\n",
    "ax.set_xlabel('$\\lambda$')\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "lgd = ax.legend(handles, labels = ['1','2','>= 3'], loc = 0)\n",
    "ax.set_title(\"QRE when cost=\"+str(cost)+\" Prob of decision at node E for turn\")\n",
    "plt.show()    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Try something new, use the second position to denote 1-p[1]-p[2]\n",
    "## This is the eq at turn 1\n",
    "## can update the prob matrix in function F\n",
    "#Define the function whose 0 we want to find  (Turocy)\n",
    "def F_A0B0(p,  l = 1,cost='h'): ## probability vector and value of lambda\n",
    "    # The part where it is about prob of deciding at turn 0\n",
    "    p[0]=p[5]=1\n",
    "    p[1:4]=0\n",
    "    p[6:9]=0\n",
    "    p_real = np.exp(p)\n",
    "    # node A\n",
    "    H1 = p[0] - p[1] -  l*(payoff(p_real, cost)[0,0]- payoff(p_real, cost)[0,1] )\n",
    "    H2 = p[0] - p[2] -  l*(payoff(p_real, cost)[0,0]- np.max(payoff(p_real, cost)[0,2:]))\n",
    "    H3 = p[1] - p[2] -  l*(payoff(p_real, cost)[0,1]- np.max(payoff(p_real, cost)[0,2:]))\n",
    "    # node B\n",
    "    H4 = p[5] - p[6] - l*(payoff(p_real, cost)[1,0]- payoff(p_real, cost)[1,1] )\n",
    "    H41 = p[5] - p[7] - l*(payoff(p_real, cost)[1,0]- np.max(payoff(p_real, cost)[1,2:] ))\n",
    "    H42 = p[6] - p[7] - l*(payoff(p_real, cost)[1,1]- np.max(payoff(p_real, cost)[1,2:] ))\n",
    "    # node C\n",
    "    H5 = p[10] - p[11] - l*(payoff(p_real, cost)[2,0]- payoff(p_real, cost)[2,1] )\n",
    "    H51 = p[10] -p[12] - l*(payoff(p_real, cost)[2,0]- np.max(payoff(p_real, cost)[2,2:] ))\n",
    "    H52 = p[11] - p[12] - l*(payoff(p_real, cost)[2,1]- np.max(payoff(p_real, cost)[2,2:] ))\n",
    "    # node D\n",
    "    H6 = p[15] - p[16] - l*(payoff(p_real, cost)[3,0]-payoff(p_real, cost)[3,1] )\n",
    "    H61 =  p[15] - p[17] - l*(payoff(p_real, cost)[3,0]- np.max(payoff(p_real, cost)[3,2:] ))\n",
    "    H62 =  p[16] - p[17] - l*(payoff(p_real, cost)[3,1]- np.max(payoff(p_real, cost)[3,2:] ))\n",
    "    # node E\n",
    "    H7 = p[20] - p[21]  - l*(payoff(p_real, cost)[4,0]- payoff(p_real, cost)[4,1] )\n",
    "    H71 = p[20] - p[22] - l*(payoff(p_real, cost)[4,0]- np.max(payoff(p_real, cost)[4,2:] ))\n",
    "    H72 = p[21] - p[22] - l*(payoff(p_real, cost)[4,1]- np.max(payoff(p_real, cost)[4,2:] ))\n",
    "    \n",
    "    H = np.array([H1, H2, H3, H4, H41, H42, H5, H51, H52, H6, H61, H62, H7, H71, H72])\n",
    "    res =  np.dot(np.transpose(H),H) \n",
    "    return res\n",
    "\n",
    "\n",
    "cons = ({'type': 'eq', 'fun' : lambda p: 1- np.exp(p[0])-np.exp(p[1]) -np.exp(p[2])  } ,\n",
    "           {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[5]) - np.exp(p[6])  -np.exp(p[7])},\n",
    "            {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[10]) -np.exp(p[11])  -np.exp(p[12]) },\n",
    "    {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[15]) -np.exp(p[16]) -np.exp(p[17]) },\n",
    "    {'type': 'eq', 'fun' : lambda p: 1- np.exp(p[20]) -  np.exp(p[21]) -np.exp(p[22]) },\n",
    "   \n",
    "   )\n",
    "\n",
    "cost='h'\n",
    "lSeq = np.arange(0,10,.01)\n",
    "QRE_turn1_A0B0 = np.zeros((len(lSeq), 25))\n",
    "p0 = np.log([0.2,0.2,0.2,0.2,0.1, 0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1])\n",
    "for (i,l) in enumerate(lSeq):\n",
    "    res = minimize(F_A0B0, p0, args=(l,cost,), method='SLSQP',constraints=cons)\n",
    "    p0 = res.x # use the new value as the new guess for next lambda\n",
    "    QRE_turn1_A0B0[i] =  np.exp(res.x)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def payoff_turn1(A_decide_0, B_decide_0, cost):\n",
    "    '''This is for network (b)\n",
    "       group_behavior is a list of A,B,C,D,E 's decision turn for each round\n",
    "       p_B_1: prob of B deciding at turn 1 '''\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 group_behavior[1] == 0:\n",
    "        p_B_1 = 0\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",
    "#     pay_2 = pOther[5]*ProbCorrect_Bayesian(3,q)*diff_pay + (1- pOther[5])*ProbCorrect_Bayesian(5,q)*diff_pay - 2*c\n",
    "    # Depends on B's behavior\n",
    "    if group_behavior[1] == 0:\n",
    "        pay_2 = ProbCorrect_Bayesian(3,q)*diff_pay - 2*c\n",
    "    elif group_behavior[1] > 0:\n",
    "        pay_2 = ProbCorrect_Bayesian(5,q)*diff_pay - 2*c\n",
    "        \n",
    "    pay[0,1] = pay_1\n",
    "    pay[0,2] = pay_2\n",
    "    j = 2\n",
    "    i = 1\n",
    "    while j < 5:        \n",
    "        j = j+ 1\n",
    "        pay[0,j] = pay_2 - i*c\n",
    "        i += 1\n",
    "    \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",
    "    if group_behavior[0] == 0:\n",
    "        pay_2 = ProbCorrect_Bayesian(4,q)*diff_pay - 2*c\n",
    "    elif group_behavior[0] > 0:\n",
    "        pay_2 = ProbCorrect_Bayesian(5,q)*diff_pay - 2*c\n",
    "    \n",
    "    \n",
    "    pay[1,1] = pay_1\n",
    "    pay[1,2] = pay_2\n",
    "    j = 2\n",
    "    i = 1\n",
    "    while j < 5:        \n",
    "        j = j+ 1\n",
    "        pay[1,j] = pay_2 - i*c\n",
    "        i += 1\n",
    "    \n",
    "    \n",
    "    # indegree = 1, node C or D, (position 2,3)\n",
    "    pay_1 = ProbCorrect_Bayesian(2,q)*diff_pay - c\n",
    "#     pay_2 = pOther[0]*ProbCorrect_Bayesian(2,q)*diff_pay + (1-pOther[0])*ProbCorrect_Bayesian(4,q)*diff_pay - 2*c\n",
    "#     pay_3 = pOther[0]*ProbCorrect_Bayesian(2,q)*diff_pay + (pOther[1] + (1-pOther[0]-pOther[1])*pOther[5])*ProbCorrect_Bayesian(4,q)*diff_pay +(1-pOther[0]-pOther[1])*(1-pOther[5])*ProbCorrect_Bayesian(5,q)*diff_pay - 3*c\n",
    "\n",
    "    if group_behavior[0] == 0:\n",
    "        pay_2 = ProbCorrect_Bayesian(2,q)*diff_pay  - 2*c\n",
    "        pay_3 = ProbCorrect_Bayesian(2,q)*diff_pay  - 3*c\n",
    "    elif group_behavior[0] > 0:\n",
    "        pay_2 = ProbCorrect_Bayesian(4,q)*diff_pay - 2*c\n",
    "#         if group_behavior[0] == 1 or group_behavior[1] == 0 :\n",
    "        if group_behavior[0] == 1:\n",
    "            pay_3 = ProbCorrect_Bayesian(4,q)*diff_pay - 3*c\n",
    "        else  :\n",
    "            pay_3 = p_B_1 * ProbCorrect_Bayesian(4,q)*diff_pay  + (1-p_B_1) * ProbCorrect_Bayesian(5,q)*diff_pay - 3*c\n",
    "        \n",
    "    \n",
    "    \n",
    "    pay[2,1] = pay_1\n",
    "    pay[3,1] = pay_1\n",
    "    pay[2,2] = pay_2\n",
    "    pay[3,2] = pay_2\n",
    "    pay[2,3] = pay_3\n",
    "    pay[3,3] = pay_3\n",
    "    j = 3\n",
    "    i = 1\n",
    "    while j < 5:        \n",
    "        j = j+ 1\n",
    "        pay[2,j] = pay_3 - i*c\n",
    "        pay[3,j] = pay_3 - i*c\n",
    "        i += 1\n",
    "    \n",
    "    \n",
    "    # indegree = 1, node E, (position 4)\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 = pOther[0]*ProbCorrect_Bayesian(2,q)*diff_pay + (pOther[1] + (1-pOther[0]-pOther[1])*pOther[5])*ProbCorrect_Bayesian(3,q)*diff_pay + (1-pOther[0]-pOther[1])*(1-pOther[5])*ProbCorrect_Bayesian(5,q)*diff_pay - 3*c\n",
    "    if group_behavior[0] == 0:\n",
    "        pay_2 = ProbCorrect_Bayesian(2,q)*diff_pay - 2*c\n",
    "        pay_3 = ProbCorrect_Bayesian(2,q)*diff_pay - 3*c\n",
    "    elif group_behavior[0] > 0:\n",
    "        pay_2 = ProbCorrect_Bayesian(3,q)*diff_pay - 2*c\n",
    "        if group_behavior[0] == 1 :\n",
    "            pay_3 = ProbCorrect_Bayesian(3,q)*diff_pay - 3*c\n",
    "        else :\n",
    "            pay_3 = p_B_1*ProbCorrect_Bayesian(3,q)*diff_pay + (1-p_B_1)*ProbCorrect_Bayesian(5,q)*diff_pay - 3*c\n",
    "    \n",
    "    \n",
    "    \n",
    "    \n",
    "    pay[4,1] = pay_1\n",
    "    pay[4,2] = pay_2\n",
    "    pay[4,3] = pay_3\n",
    "    j = 3\n",
    "    i = 1\n",
    "    while j < 5:        \n",
    "        j = j+ 1\n",
    "        pay[4,j] = pay_3 - i*c\n",
    "        \n",
    "        i += 1\n",
    "\n",
    "    for i in range(5):\n",
    "        if group_behavior[i]==0 :\n",
    "            pay[i,1:] = pay[i,0]\n",
    "    return pay\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Define the function whose 0 we want to find  (Turocy)\n",
    "def F(p_B_1, l = 1,cost='h'): ## probability vector and value of lambda\n",
    "    # The part where it is about prob of deciding at turn 0\n",
    "    p_B_1_real = np.exp(p_B_1)\n",
    "    H = p_B_1 - (1-np.exp(p_B_1)) - l*(payoff_turn1(p_B_1_real, cost)[1,1]- np.max(payoff_turn1(p_B_1_real, cost)[1,2:] ))\n",
    "    p_real = np.exp(p)\n",
    "\n",
    "    # node A\n",
    "    H1 = p[0] - p[1] -  l*(payoff(p_real, cost)[0,0]- np.max(payoff(p_real, cost)[0,1:] ))\n",
    "    H2 = p[0] - (1- p_real[0] - p_real[1]) -  l*(payoff(p_real, cost)[0,0]- np.max(payoff(p_real, cost)[0,2:]))\n",
    "    H3 = p[1] - (1- p_real[0] - p_real[1]) -  l*(payoff(p_real, cost)[0,1]- np.max(payoff(p_real, cost)[0,2:]))\n",
    "    # node B\n",
    "    H4 = p[5] - (1-p_real[5]) - l*(payoff(p_real, cost)[1,0]- np.max(payoff(p_real, cost)[1,1:] ))\n",
    "#     # node C\n",
    "#     H5 = p[10] - (1-p_real[10]) - l*(payoff(p_real, cost)[2,0]- np.max(payoff(p_real, cost)[2,1:] ))\n",
    "#     # node D\n",
    "#     H6 = p[15] - (1-p_real[15]) - l*(payoff(p_real, cost)[3,0]- np.max(payoff(p_real, cost)[3,1:] ))\n",
    "#     # node E\n",
    "#     H5 = p[20] - (1-p_real[20]) - l*(payoff(p_real, cost)[4,0]- np.max(payoff(p_real, cost)[4,1:] ))\n",
    "    \n",
    "    H = np.array([H1, H2, H3, H4])\n",
    "    res =  np.dot(np.transpose(H),H) \n",
    "    return res\n",
    "\n",
    "\n",
    "cons = ({'type': 'ineq', 'fun' : lambda p: 1- np.exp(p[0])-np.exp(p[1]) } ,\n",
    "           {'type': 'ineq', 'fun' : lambda p: 1- np.exp(p[5])  },\n",
    "            {'type': 'ineq', 'fun' : lambda p: 1- np.exp(p[10])  },\n",
    "    {'type': 'ineq', 'fun' : lambda p: 1- np.exp(p[15])  },\n",
    "    {'type': 'ineq', 'fun' : lambda p: 1- np.exp(p[20])  },\n",
    "   \n",
    "   )\n",
    "\n",
    "\n",
    "cost='l'\n",
    "lSeq = np.arange(0,10,.25)\n",
    "QRE = np.zeros((len(lSeq),25))\n",
    "QRE_turn0 = np.zeros((len(lSeq), 5))\n",
    "p0 = np.log([0.2,0.2,0.2,0.2,0.1, 0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1,0.2,0.2,0.2,0.2,0.1])\n",
    "for (i,l) in enumerate(lSeq):\n",
    "    res = minimize(F, p0, args=(l,cost,), method='SLSQP',constraints=cons)\n",
    "    p0 = res.x # use the new value as the new guess for next lambda\n",
    "    QRE[i] =  np.exp(res.x)\n",
    "    A_turn0 = QRE[i, 0]\n",
    "    B_turn0 = QRE[i, 5]\n",
    "    C_turn0 = 1/np.exp(l * payoff(QRE[i], cost)[2,0]- np.max(payoff(QRE[i], cost)[2,1:]))\n",
    "    D_turn0 = 1/np.exp(l * payoff(QRE[i], cost)[3,0]- np.max(payoff(QRE[i], cost)[3,1:]))\n",
    "    E_turn0 = 1/np.exp(l * payoff(QRE[i], cost)[4,0]- np.max(payoff(QRE[i], cost)[4,1:]))\n",
    "    QRE_turn0[i] = [A_turn0, B_turn0, C_turn0, D_turn0, E_turn0]\n"
   ]
  }
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