CalculateNE_07212021_Networks.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "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\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "seqs7 = [[4, 2, 1, 5, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 9, 5, 3, 1, 2, 2, 2, 2, 7, 1, 4, 1, 1, 1, 3, 1, 1, 2, 1, 1, 2, 4, 1, 2, 2, 6, 3, 1, 6, 12, 2, 2, 2, 2, 1, 1, 1, 2, 3, 7, 1, 1, 3, 1, 1, 1, 1, 5, 2, 2, 2, 1, 1, 4, 2, 1, 2, 1, 2, 6, 1, 1, 1, 1, 2],\n",
    "             [2, 2, 1, 4, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 4, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 1, 7, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 5, 3, 3, 5, 5, 1, 1, 4, 2, 13, 2, 1, 1, 1, 2, 1, 2, 3, 2, 1, 3, 1, 1, 2, 1, 2, 2, 2, 4, 1, 1, 1, 1, 3, 1],\n",
    "             [1, 1, 2, 2, 2, 2, 2, 1, 4, 2, 2, 1, 3, 2, 2, 1, 1, 3, 3, 6, 1, 1, 2, 2, 1, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 3, 2, 1, 4, 1, 1, 4, 1, 1, 4, 2, 1, 1, 1, 2, 1, 3, 7, 7, 1, 1, 1, 2, 1, 1, 5, 3, 3, 4, 1, 1, 4, 3, 1, 3],\n",
    "             [2, 2, 4, 1, 1, 2, 3, 2, 2, 4, 1, 1, 2, 3, 1, 2, 2, 1, 1, 3, 1, 3, 3, 2, 1, 2, 2, 1, 5, 1, 2, 4, 3, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 4, 1, 6, 3, 2, 2, 1, 1, 1, 4, 4, 2, 1, 2, 2, 2, 2, 2, 2, 2, 4, 1, 1, 3, 2, 1, 4, 1, 1]]\n",
    "cumul7 = [np.roll(np.cumsum(s, dtype=int), 1) for s in seqs7]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "    seqs9 = [[4, 3, 7, 1, 1, 5, 3, 1, 1, 9, 8, 1, 2, 4, 10, 4, 1, 1, 1, 4, 1, 4, 2, 4, 1, 2, 8, 3, 7, 12, 4, 2, 2, 1, 2, 2, 3, 7, 1, 1, 3, 2, 1, 1, 9, 2, 1, 1, 4, 2],\n",
    "             [1, 2, 1, 2, 6, 2, 1, 1, 2, 2, 2, 5, 3, 1, 1, 4, 1, 1, 2, 2, 2, 3, 1, 4, 6, 2, 1, 2, 2, 2, 2, 2, 9, 1, 1, 3, 3, 1, 1, 7, 3, 3, 5, 5, 1, 1, 4, 15, 4, 6],\n",
    "             [3, 2, 1, 3, 1, 1, 2, 1, 4, 2, 4, 1, 1, 1, 4, 3, 2, 4, 2, 2, 7, 3, 3, 2, 3, 1, 3, 3, 6, 1, 6, 3, 2, 2, 2, 1, 1, 4, 1, 3, 2, 1, 1, 6, 3, 3, 6, 4, 2, 9],\n",
    "             [2, 4, 7, 7, 1, 1, 1, 3, 1, 5, 3, 3, 5, 1, 7, 1, 3, 2, 2, 5, 6, 8, 1, 1, 5, 1, 2, 3, 1, 3, 4, 5, 1, 2, 2, 1, 5, 3, 7, 1, 2, 4, 4, 1, 2, 1, 4, 3, 4, 4]]\n",
    "    cumul9 = [np.roll(np.cumsum(s, dtype=int), 1) for s in seqs9]\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "184"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max([np.max(cumul7), np.max(cumul9)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Help with the Group arrangements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 1. Simulation Setting and Network Graphs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prepare for the graphs in the final project"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# All connected graph\n",
    "K_5 = nx.complete_graph(5)\n",
    "nx.draw(K_5)\n",
    "#plt.savefig(outputfolder+\"complete_20.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# ------- DIRECTED\n",
    " \n",
    "# Build a dataframe with your connections\n",
    "# This time a pair can appear 2 times, in one side or in the other!\n",
    "df = pd.DataFrame({ 'from':['D', 'A', 'B', 'C','A'], 'to':['A', 'D', 'A', 'E','C']})\n",
    "df\n",
    " \n",
    "# Build your graph. Note that we use the DiGraph function to create the graph!\n",
    "G=nx.from_pandas_edgelist(df, 'from', 'to', create_using=nx.DiGraph() )\n",
    " \n",
    "# Make the graph\n",
    "plt.title(\"Directed\")\n",
    "nx.draw(G, with_labels=True, node_size=1500, alpha=0.3, arrows=True) \n",
    " \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ------- UNDIRECTED\n",
    " \n",
    "# Build a dataframe with your connections\n",
    "# This time a pair can appear 2 times, in one side or in the other!\n",
    "df = pd.DataFrame({ 'from':['D', 'A', 'B', 'C','A'], 'to':['A', 'D', 'A', 'E','C']})\n",
    "df\n",
    " \n",
    "# Build your graph. Note that we use the Graph function to create the graph!\n",
    "G=nx.from_pandas_edgelist(df, 'from', 'to', create_using=nx.Graph() )\n",
    " \n",
    "# Make the graphnx.draw(G, with_labels=True, node_size=1500, alpha=0.3, arrows=True)\n",
    "plt.title(\"UN-Directed\")\n",
    "nx.draw(G, with_labels=True, node_size=1500, alpha=0.3, arrows=True) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reversing a tuple using slicing technique \n",
    "# New tuple is created \n",
    "def Reverse(tuples): \n",
    "    new_tup = tuples[::-1] \n",
    "    return new_tup "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "C = combinations(list(range(10)), 0)\n",
    "CC = list(C)\n",
    "for ccc in range(len(CC)):\n",
    "    for chosen_links in CC[ccc]:\n",
    "        print(chosen_links)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "combo = combinations([5,4,3,2,1], 2)\n",
    "Network_original = list(combo)\n",
    "print(Network_original)\n",
    "Network_original[0] = Reverse(Network_original[0])\n",
    "print(Network_original)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'tuple'>\n"
     ]
    }
   ],
   "source": [
    "combo = combinations([5,4,3,2,1], 2)\n",
    "Name = list(combo)\n",
    "a= Name[0]\n",
    "print(type(a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 2. Simulation Starts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nCr(n,r):\n",
    "    f = math.factorial\n",
    "    return f(n) / f(r) / f(n-r)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ProbCorrect_Bayesian(n, q):\n",
    "    '''Based on Bayesian rule, the prob of making a correct guess by observing n signals '''\n",
    "    nn = 0\n",
    "    prob = 0\n",
    "    \n",
    "    while nn <=  (n/2):\n",
    "        \n",
    "        #print(nn)\n",
    "        #if ((n-nn) % 2 ) == 0 & (nn!=0) :\n",
    "        if nn ==  (n/2) :\n",
    "            prob += nCr(n,(n-nn))*(q**(n-nn))*((1-q)**(nn))*(1/2)\n",
    "            #print(prob)\n",
    "        else :\n",
    "            prob += nCr(n,(n-nn))*(q**(n-nn))*((1-q)**(nn))\n",
    "            #print(prob)\n",
    "        nn += 1\n",
    "        \n",
    "    \n",
    "    return prob\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.68131"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ProbCorrect_Bayesian(3,0.7) - (ProbCorrect_Bayesian(5,0.7)-ProbCorrect_Bayesian(1,0.7))/4*3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ProbLinear(n,q):\n",
    "    # 1. the difference remain the same, ProbCorrect_Bayesian(5,q)-ProbCorrect_Bayesian(1,q) \n",
    "    # When q = 0.7, the difference is (ProbCorrect_Bayesian(5,0.7)-ProbCorrect_Bayesian(1,0.7))/4 = 0.3423\n",
    "    # 2. Ensure that the middle point is the correct probability\n",
    "    # ProbCorrect_Bayesian(3,0.7) = a + 0.3423*3\n",
    "    # a = 0.68131\n",
    "    \n",
    "    b = ProbCorrect_Bayesian(5,q)-ProbCorrect_Bayesian(1,q))/4\n",
    "    a = ProbCorrect_Bayesian(3,q) - b*3\n",
    "    \n",
    "    return a+b*n\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.71554"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ProbLinear(1,0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the agent\n",
    "class Agent: \n",
    "    ''' Class definition of the Agent in network model'''\n",
    "    \n",
    "    def __init__(self, location, InforSet, waiting_cost, payoff_correct, payoff_wrong, q, period, network,  action=-1,):\n",
    "        '''Initialize agent.\n",
    "            location -- location of the agent, index of agent in the environment\n",
    "            \n",
    "            InforSet -- the information set this agent observes, includes the index number of the observed signals,\n",
    "                        {1,2,3,...}, takes the form of []\n",
    "            \n",
    "            waiting_cost -- waiting cost for waiting for one more period\n",
    "            payoff_correct -- the payoff amount for a correct guess\n",
    "            payoff_wrong -- the payoff amount for a wrong guess\n",
    "            q: informativeness\n",
    "            \n",
    "            period: the period played in the network\n",
    "            network -- the network this agent is in\n",
    "            \n",
    "            action -- action of the agent, the time that agent decides to guess, t is in {0,1,2,3...},\n",
    "                        when action is -1, not decided yet\n",
    "            \n",
    "            '''\n",
    "        \n",
    "        \n",
    "        #infor_set -- the number of unique signals that the agent can observe at time t\n",
    "        \n",
    "        self.location = location\n",
    "        self.InforSet = InforSet\n",
    "        \n",
    "        self.waiting_cost = waiting_cost\n",
    "        self.payoff_correct = payoff_correct\n",
    "        self.payoff_wrong = payoff_wrong\n",
    "        self.q = q\n",
    "        \n",
    "        self.period = period\n",
    "        self.network = network\n",
    "        \n",
    "        self.action = action   \n",
    "     \n",
    "    def StopWhenInDegree1(self):\n",
    "        if self.network.in_degree(self.location) == 1 : \n",
    "            self.action = self.period\n",
    "        \n",
    "        return self.action\n",
    "    \n",
    "    def MaxWaitingPeriod(self):\n",
    "            # The max waiting period is jointly determined by the waiting cost and the expected number of additional private signals that can be observed in each period \n",
    "            # Compare 2 numbers:\n",
    "            # Based on the cost, the max number of peirods can afford\n",
    "            # Based on the connectiveness, the longest path \n",
    "        \n",
    "        # Firstly, based on the wating cost and the payoff schemes to decide the max waiting period\n",
    "        if self.waiting_cost == 0 :\n",
    "            EconMaxWaiting =  math.inf\n",
    "        else :\n",
    "            EconMaxWaiting = int((self.payoff_correct- self.payoff_wrong) / self.waiting_cost)\n",
    "            \n",
    "        self.MaxPeriod = np.zeros(nx.number_of_nodes(self.network))\n",
    "        for i in range(nx.number_of_nodes(self.network)):    \n",
    "            #print(i)\n",
    "            try:\n",
    "                paths = list(nx.shortest_simple_paths(self.network,  i+1, self.location))\n",
    "            #print(paths)\n",
    "                length = [len(x) for x in paths]\n",
    "                self.MaxPeriod[i]=min(max(length)-1, EconMaxWaiting)\n",
    "            except nx.NetworkXNoPath:\n",
    "                self.MaxPeriod[i]=EconMaxWaiting\n",
    "            \n",
    "            \n",
    "                \n",
    "        return self.MaxPeriod\n",
    "    \n",
    "    def MinWaitingPeriod(self):\n",
    "            # The shortest path that this agent can observe the other agent's private signal \n",
    "            \n",
    "        self.MinPeriod = np.zeros(nx.number_of_nodes(self.network))\n",
    "        for i in range(nx.number_of_nodes(self.network)):    \n",
    "            #print(i)\n",
    "            try:\n",
    "                paths = list(nx.shortest_simple_paths(self.network,  i+1, self.location))\n",
    "            #print(paths)\n",
    "                length = [len(x) for x in paths]\n",
    "                self.MinPeriod[i]=min(length)-1\n",
    "            except nx.NetworkXNoPath:\n",
    "                self.MinPeriod[i]=math.inf\n",
    "                \n",
    "        return self.MinPeriod\n",
    "        \n",
    "    def OptimalStoppingRule(self):\n",
    "        # Optimal rule depends only on the MinPeriod, the best case scenario\n",
    "        # Step 1: Use the self.MinPeriod to decide how many additional private signals can be observed \n",
    "        # Step 2: Compare for each period, the added expected payoff vs the incurred additional cost\n",
    "        ExpectedPayoffs = []\n",
    "        \n",
    "        \n",
    "#         MaxPeriod = 0\n",
    "#         MaxExpectedPayoff = 0\n",
    "#         AddedPayoff = 0 \n",
    "#         IncurredCost = 0\n",
    "        \n",
    "#         if IncurredCost<= AddedPayoff:\n",
    "#             Period += 1\n",
    "#             NumSignals = sum(self.MinPeriod<= Period)\n",
    "#             NewExpectedPayoff = self.payoff_wrong +  (self.payoff_correct  - self.payoff_wrong) * ProbCorrect_Bayesian(NumSignals, self.q)\n",
    "#             AddedPayoff = NewExpectedPayoff - ExpectedPayoff\n",
    "#             IncurredCost = self.waiting_cost\n",
    "            \n",
    "#       for Period in range(self.period, 11) :\n",
    "        inforset = copy.deepcopy(self.InforSet)\n",
    "        for Period in range(self.period, 11) :\n",
    "            for j in range(nx.number_of_nodes(self.network)) :\n",
    "                #if (( self.MinPeriod[j] + self.period ) <= Period)  and (j+1 not in self.InforSet) :\n",
    "                if ( self.MinPeriod[j]  <= Period)  and (j+1 not in inforset) :\n",
    "                    inforset.append(j+1)\n",
    "\n",
    "                    \n",
    "            NumSignals = len(inforset)\n",
    "            ExpectedPayoff = self.payoff_wrong +  (self.payoff_correct  - self.payoff_wrong) * ProbCorrect_Bayesian(NumSignals, self.q) -  (self.waiting_cost*Period)\n",
    "            ExpectedPayoffs.append((Period,NumSignals, ExpectedPayoff,inforset ))\n",
    "            \n",
    "            \n",
    "        self.ExpectedPayoffs_data = pd.DataFrame(columns = ['Period', 'NumSignals' ,'ExpectedPayoff', \"InforSet\"], data = ExpectedPayoffs)\n",
    "        \n",
    "         \n",
    "        optimal = self.ExpectedPayoffs_data['ExpectedPayoff'].idxmax()\n",
    "        \n",
    "        # Before, tried to use the period, not working\n",
    "        # Instead, use the number of signals as the stopping rule \n",
    "        return self.ExpectedPayoffs_data.loc[optimal, :]\n",
    "\n",
    "        \n",
    "#         return \"Period: \"+str(Period)+\" ; Number of Signals:\"+str(NumSignals)\n",
    "            \n",
    "\n",
    "        \n",
    "        \n",
    "     #   def MaxExpectedPayoff(self):\n",
    "            # Based on the network position, an agent should be able to calculate her max expected payoff\n",
    "            # which is jointly decided by the agent's own position in the network, the knowledge of the network, and other participants' decisions\n",
    "            # It can be reached when the number of one signal reaches a certain amount/ the period has reached a certain time \n",
    "            # The first case means that signal draws might be better than expected, so the decision will happen earlier\n",
    "            # The second case means that one the agent reaches this period, there won't be more information coming in, should make a decision (last resort)\n",
    "            # If they use the bayesian updating probability to calculate their expected payoff, then the optimal stopping rule will be a threshold of number of private signals this agent can observe \n",
    "            # Here it is either the number of private signals or the number of periods\n",
    "            \n",
    "    def __str__(self):\n",
    "        return \"Agent!\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the agent with linear prob\n",
    "class Agent_linear: \n",
    "    ''' Class definition of the Agent in network model'''\n",
    "    \n",
    "    def __init__(self, location, InforSet, waiting_cost, payoff_correct, payoff_wrong, q, period, network,  action=-1,):\n",
    "        '''Initialize agent.\n",
    "            location -- location of the agent, index of agent in the environment\n",
    "            \n",
    "            InforSet -- the information set this agent observes, includes the index number of the observed signals,\n",
    "                        {1,2,3,...}, takes the form of []\n",
    "            \n",
    "            waiting_cost -- waiting cost for waiting for one more period\n",
    "            payoff_correct -- the payoff amount for a correct guess\n",
    "            payoff_wrong -- the payoff amount for a wrong guess\n",
    "            q: informativeness\n",
    "            \n",
    "            period: the period played in the network\n",
    "            network -- the network this agent is in\n",
    "            \n",
    "            action -- action of the agent, the time that agent decides to guess, t is in {0,1,2,3...},\n",
    "                        when action is -1, not decided yet\n",
    "            \n",
    "            '''\n",
    "        \n",
    "        \n",
    "        #infor_set -- the number of unique signals that the agent can observe at time t\n",
    "        \n",
    "        self.location = location\n",
    "        self.InforSet = InforSet\n",
    "        \n",
    "        self.waiting_cost = waiting_cost\n",
    "        self.payoff_correct = payoff_correct\n",
    "        self.payoff_wrong = payoff_wrong\n",
    "        self.q = q\n",
    "        \n",
    "        self.period = period\n",
    "        self.network = network\n",
    "        \n",
    "        self.action = action   \n",
    "     \n",
    "    def StopWhenInDegree1(self):\n",
    "        if self.network.in_degree(self.location) == 1 : \n",
    "            self.action = self.period\n",
    "        \n",
    "        return self.action\n",
    "    \n",
    "    def MaxWaitingPeriod(self):\n",
    "            # The max waiting period is jointly determined by the waiting cost and the expected number of additional private signals that can be observed in each period \n",
    "            # Compare 2 numbers:\n",
    "            # Based on the cost, the max number of peirods can afford\n",
    "            # Based on the connectiveness, the longest path \n",
    "        \n",
    "        # Firstly, based on the wating cost and the payoff schemes to decide the max waiting period\n",
    "        if self.waiting_cost == 0 :\n",
    "            EconMaxWaiting =  math.inf\n",
    "        else :\n",
    "            EconMaxWaiting = int((self.payoff_correct- self.payoff_wrong) / self.waiting_cost)\n",
    "            \n",
    "        self.MaxPeriod = np.zeros(nx.number_of_nodes(self.network))\n",
    "        for i in range(nx.number_of_nodes(self.network)):    \n",
    "            #print(i)\n",
    "            try:\n",
    "                paths = list(nx.shortest_simple_paths(self.network,  i+1, self.location))\n",
    "            #print(paths)\n",
    "                length = [len(x) for x in paths]\n",
    "                self.MaxPeriod[i]=min(max(length)-1, EconMaxWaiting)\n",
    "            except nx.NetworkXNoPath:\n",
    "                self.MaxPeriod[i]=EconMaxWaiting\n",
    "            \n",
    "            \n",
    "                \n",
    "        return self.MaxPeriod\n",
    "    \n",
    "    def MinWaitingPeriod(self):\n",
    "            # The shortest path that this agent can observe the other agent's private signal \n",
    "            \n",
    "        self.MinPeriod = np.zeros(nx.number_of_nodes(self.network))\n",
    "        for i in range(nx.number_of_nodes(self.network)):    \n",
    "            #print(i)\n",
    "            try:\n",
    "                paths = list(nx.shortest_simple_paths(self.network,  i+1, self.location))\n",
    "            #print(paths)\n",
    "                length = [len(x) for x in paths]\n",
    "                self.MinPeriod[i]=min(length)-1\n",
    "            except nx.NetworkXNoPath:\n",
    "                self.MinPeriod[i]=math.inf\n",
    "                \n",
    "        return self.MinPeriod\n",
    "        \n",
    "    def OptimalStoppingRule(self):\n",
    "        # Optimal rule depends only on the MinPeriod, the best case scenario\n",
    "        # Step 1: Use the self.MinPeriod to decide how many additional private signals can be observed \n",
    "        # Step 2: Compare for each period, the added expected payoff vs the incurred additional cost\n",
    "        ExpectedPayoffs = []\n",
    "        \n",
    "\n",
    "        inforset = copy.deepcopy(self.InforSet)\n",
    "        for Period in range(self.period, 11) :\n",
    "            for j in range(nx.number_of_nodes(self.network)) :\n",
    "                #if (( self.MinPeriod[j] + self.period ) <= Period)  and (j+1 not in self.InforSet) :\n",
    "                if ( self.MinPeriod[j]  <= Period)  and (j+1 not in inforset) :\n",
    "                    inforset.append(j+1)\n",
    "\n",
    "                    \n",
    "            NumSignals = len(inforset)\n",
    "            ExpectedPayoff = self.payoff_wrong +  (self.payoff_correct  - self.payoff_wrong) * ProbLinear(NumSignals, self.q) -  (self.waiting_cost*Period)\n",
    "            ExpectedPayoffs.append((Period,NumSignals, ExpectedPayoff,inforset ))\n",
    "            \n",
    "            \n",
    "        self.ExpectedPayoffs_data = pd.DataFrame(columns = ['Period', 'NumSignals' ,'ExpectedPayoff', \"InforSet\"], data = ExpectedPayoffs)\n",
    "        \n",
    "         \n",
    "        optimal = self.ExpectedPayoffs_data['ExpectedPayoff'].idxmax()\n",
    "        \n",
    "        # Before, tried to use the period, not working\n",
    "        # Instead, use the number of signals as the stopping rule \n",
    "        return self.ExpectedPayoffs_data.loc[optimal, :]\n",
    "\n",
    "        \n",
    "#         return \"Period: \"+str(Period)+\" ; Number of Signals:\"+str(NumSignals)\n",
    "            \n",
    "\n",
    "        \n",
    "        \n",
    "     #   def MaxExpectedPayoff(self):\n",
    "            # Based on the network position, an agent should be able to calculate her max expected payoff\n",
    "            # which is jointly decided by the agent's own position in the network, the knowledge of the network, and other participants' decisions\n",
    "            # It can be reached when the number of one signal reaches a certain amount/ the period has reached a certain time \n",
    "            # The first case means that signal draws might be better than expected, so the decision will happen earlier\n",
    "            # The second case means that one the agent reaches this period, there won't be more information coming in, should make a decision (last resort)\n",
    "            # If they use the bayesian updating probability to calculate their expected payoff, then the optimal stopping rule will be a threshold of number of private signals this agent can observe \n",
    "            # Here it is either the number of private signals or the number of periods\n",
    "            \n",
    "    def __str__(self):\n",
    "        return \"Agent!\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Agent!\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0., 1., 2., 2., 1.])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# To calculate the N.E. (loop is needed)\n",
    "#    def __init__(self, location, InforSet, waiting_cost, payoff_correct, \n",
    "#                 payoff_wrong, q, P, network,  action=-1,):\n",
    "\n",
    "A = Agent_linear(1,[1],0,110,10,0.6,0,G)\n",
    "print(A)\n",
    "#A.waiting_cost\n",
    "A.MinWaitingPeriod()\n",
    "#A.OptimalStoppingRule()\n",
    "#A.StopWhenInDegree1()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the environment\n",
    "class DirectedNetwork: \n",
    "    ''' Class definition of the Environment'''\n",
    "        \n",
    "    def __init__(self, Network, TrueNature, Sig_Acc,  Waiting_Cost, Payoff_Correct, Payoff_Wrong, Period = 0, Decisions=[], InforSets=[]):\n",
    "        \n",
    "        \n",
    "        '''Initialize environment.\n",
    "            Network -- network representation\n",
    "            TrueNature -- the true nature status, 1 or -1\n",
    "            Sig_Acc -- signal informativeness\n",
    "            Period -- timing of the game\n",
    "            Decisions -- [0,1,...] the decisions of all participants, the Period that this agent makes a guess \n",
    "            InforSets -- the inforset each participant has at the begining of each Period \n",
    "        '''\n",
    "        self.Network = Network\n",
    "        self.TrueNature = TrueNature\n",
    "        self.Sig_Acc = Sig_Acc\n",
    "        self.Waiting_Cost = Waiting_Cost\n",
    "        self.Payoff_Correct = Payoff_Correct\n",
    "        self.Payoff_Wrong = Payoff_Wrong\n",
    "        \n",
    "        self.Period = Period\n",
    "        if Decisions == [] :\n",
    "            self.Decisions = -1 * np.ones(self.Network.number_of_nodes())\n",
    "        else :\n",
    "            self.Decisions = Decisions\n",
    "        \n",
    "        if InforSets == [] and (self.Period == 0) :\n",
    "            self.InforSets = [ [x] for x in range(1, 1+self.Network.number_of_nodes())]\n",
    "        else :\n",
    "            self.InforSets = InforSets\n",
    "            \n",
    "            \n",
    "        self.InforFlow = nx.adjacency_matrix(self.Network)\n",
    "        \n",
    "    def AssignSignals(self):\n",
    "        self.SignalDraw = np.random.rand(self.Network.number_of_nodes())\n",
    "        self.Signals = np.zeros(self.Network.number_of_nodes())\n",
    "        for i in range(self.Network.number_of_nodes()):\n",
    "            if (self.SignalDraw[i] <= self.Sig_Acc):\n",
    "                self.Signals[i] = self.TrueNature\n",
    "            else :\n",
    "                self.Signals[i] = -1 *self.TrueNature\n",
    "        \n",
    "        return self.Signals\n",
    "        \n",
    "    \n",
    "    def SimultaneousMove(self) :\n",
    "        print('this is Period '+str(self.Period))\n",
    "        # Obtain the decision for each agent given the current Period inforset\n",
    "        for j in range(self.Network.number_of_nodes()):\n",
    "            if self.Decisions[j] == -1 :\n",
    "                agent = Agent( j+1 , self.InforSets[j], self.Waiting_Cost, self.Payoff_Correct, self.Payoff_Wrong, self.Sig_Acc, self.Period, self.Network)\n",
    "    #             print(str(j+1)+str([self.InforSets[j]]))\n",
    "                agent.MinWaitingPeriod()\n",
    "                agent.OptimalStoppingRule()\n",
    "               # print(agent.InforSet)\n",
    "                print('Agent '+str(j))\n",
    "                print(agent.ExpectedPayoffs_data)\n",
    "                print('Highest Payoff'+str(agent.ExpectedPayoffs_data['ExpectedPayoff'].idxmax()))\n",
    "                print(agent.OptimalStoppingRule())\n",
    "\n",
    "                optimal = agent.ExpectedPayoffs_data['ExpectedPayoff'].idxmax()\n",
    "                self.OptimalNumSig = agent.ExpectedPayoffs_data['NumSignals'].loc[optimal] \n",
    "            \n",
    "               # print('Agent '+str(j+1)+'s Optimal Number of Signals'+str(self.OptimalNumSig ))\n",
    "                \n",
    "                \n",
    "                \n",
    "                # Note: here if the agent makes the decision, then the network reduces!\n",
    "                #if self.Period in self.OptimalPeriod :\n",
    "               # print('Inforset'+str(self.InforSets))\n",
    "                if  self.OptimalNumSig == len(self.InforSets[j]) :\n",
    "                    self.Decisions[j] =self.Period\n",
    "    \n",
    "    def SimultaneousMove_linear(self) :\n",
    "        print('this is Period '+str(self.Period))\n",
    "        # Obtain the decision for each agent given the current Period inforset\n",
    "        for j in range(self.Network.number_of_nodes()):\n",
    "            if self.Decisions[j] == -1 :\n",
    "                agent = Agent_linear( j+1 , self.InforSets[j], self.Waiting_Cost, self.Payoff_Correct, self.Payoff_Wrong, self.Sig_Acc, self.Period, self.Network)\n",
    "    #             print(str(j+1)+str([self.InforSets[j]]))\n",
    "                agent.MinWaitingPeriod()\n",
    "                agent.OptimalStoppingRule()\n",
    "               # print(agent.InforSet)\n",
    "                print('Agent '+str(j))\n",
    "                print(agent.ExpectedPayoffs_data)\n",
    "                print('Highest Payoff'+str(agent.ExpectedPayoffs_data['ExpectedPayoff'].idxmax()))\n",
    "                print(agent.OptimalStoppingRule())\n",
    "\n",
    "                optimal = agent.ExpectedPayoffs_data['ExpectedPayoff'].idxmax()\n",
    "                self.OptimalNumSig = agent.ExpectedPayoffs_data['NumSignals'].loc[optimal] \n",
    "            \n",
    "               # print('Agent '+str(j+1)+'s Optimal Number of Signals'+str(self.OptimalNumSig ))\n",
    "                \n",
    "                \n",
    "                \n",
    "                # Note: here if the agent makes the decision, then the network reduces!\n",
    "                #if self.Period in self.OptimalPeriod :\n",
    "               # print('Inforset'+str(self.InforSets))\n",
    "                if  self.OptimalNumSig == len(self.InforSets[j]) :\n",
    "                    self.Decisions[j] =self.Period\n",
    "\n",
    "        \n",
    "    def NextPeriod(self):\n",
    "        #Two steps: 1. update the inforset, regardless of each agent's decision, the infor will be transimitted using the previous network stucture\n",
    "        # 2. based on the decisions, the network is \"down-graded\"\n",
    "        \n",
    "        # Firstly, define the inforset \n",
    "        # Here the NextInforSets is updated using current network structure\n",
    "        self.NextInforsets = copy.deepcopy(self.InforSets)\n",
    "        #self.NextInforsets = []\n",
    "        for j in range(self.Network.number_of_nodes()) :\n",
    "            #self.NextInforsets[j] = copy.deepcopy(self.InforSets[j])\n",
    "            self.temp = copy.deepcopy(self.InforSets[j])\n",
    "            for i in range(self.Network.number_of_nodes()):\n",
    "                #if (i != j) and self.Network.has_edge(i+1,j+1) and (i+1 not in self.temp):\n",
    "                if (i != j) and self.Network.has_edge(i+1,j+1) :\n",
    "                    for x in self.InforSets[i] :\n",
    "                        if x not in self.temp:\n",
    "                            self.temp.append(x)         \n",
    "            self.NextInforsets[j]=self.temp\n",
    "            #print(\"InforSets: \"+str(self.InforSets))\n",
    "            #print('Next Inforsets: '+str(self.NextInforsets))\n",
    "      \n",
    "        #return self.NextInforsets\n",
    "        \n",
    "        # Secondly, based on decisions, \"down-grade\" the network structure\n",
    "        self.NextNetwork = copy.deepcopy(self.Network)\n",
    "        for j in range(self.Network.number_of_nodes()) :\n",
    "            if  self.Decisions[j] == self.Period :\n",
    "                self.NextNetwork.remove_edges_from(list(self.NextNetwork.in_edges(j+1)))\n",
    "        \n",
    "        #return self.NextNetwork            \n",
    "        \n",
    "        # Thirdly, update the next Period number\n",
    "        self.NextPeriod = self.Period + 1\n",
    "              \n",
    "        \n",
    "    \n",
    "                \n",
    "\n",
    "     \n",
    "            \n",
    "\n",
    "        \n",
    "    def __str__(self):\n",
    "        plt.title(\"True Nature is: \"+str(self.TrueNature)+\"; Signal Informativeness: \"+str(self.Sig_Acc))\n",
    "        nx.draw(self.Network, pos=nx.circular_layout(self.Network), with_labels=True, node_size=1500, alpha=1, arrows=True) \n",
    "       # plt.show()\n",
    "        return \"True Nature is: \"+str(self.TrueNature)+\"; Signal Informativeness: \"+str(self.Sig_Acc)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define an environment to calculate Behavioral Prediction, additional input as the realized signals \n",
    "class DirectedNetworkAndRealizedSignals:\n",
    "\n",
    "    ''' Class definition of the Environment that helps calculate the behavioral prediction:\n",
    "            this is for a naive agent who has the following decision rule:\n",
    "            1. decide whether he should wait or not at p=0, based on whether he can observe additional signal or not\n",
    "            2. if he can observe additional signals, always wait to period 1\n",
    "            3. if the signals are not informative, then wait for another signal\n",
    "            4. Stop until the agent can make a decision or the information set does not increase in the next period\n",
    "    '''\n",
    "\n",
    "    def __init__(self, DirectedNetwork, Signals, Half_Guess=[], Self_Guess=[] ):\n",
    "        \n",
    "        \n",
    "        '''Initialize environment.\n",
    "            Network -- the orignals directed network environment\n",
    "            Signals -- the realized signals\n",
    "        '''\n",
    "        self.DirectedNetwork = copy.deepcopy(DirectedNetwork)\n",
    "        self.Signals = copy.deepcopy(Signals)\n",
    "        \n",
    "        self.Period = self.DirectedNetwork.Period\n",
    "        \n",
    "        if (Half_Guess==[]) and (self.Period == 0) :\n",
    "            self.Half_Guess = np.zeros(nx.number_of_nodes(self.DirectedNetwork.Network))\n",
    "        else :\n",
    "            self.Half_Guess = Half_Guess\n",
    "        \n",
    "        if (Self_Guess ==[]) and (self.Period == 0) :\n",
    "            self.Self_Guess = np.zeros(nx.number_of_nodes(self.DirectedNetwork.Network))\n",
    "        else :\n",
    "            self.Self_Guess = Self_Guess\n",
    "        \n",
    "#         if InforSets == [] and (self.Period == 0) :\n",
    "#             self.InforSets = [ [x] for x in range(1, 1+self.DirectedNetwork.Network.number_of_nodes())]\n",
    "#         else :\n",
    "#             self.InforSets = InforSets\n",
    "            \n",
    "        self.Decisions = self.DirectedNetwork.Decisions\n",
    "        self.InforSets = self.DirectedNetwork.InforSets\n",
    "        \n",
    "        \n",
    "    def SimultaneousMove(self) :\n",
    "        print('This is Period '+str(self.Period))\n",
    "        self.NewInforsets = copy.deepcopy(self.InforSets)\n",
    "        # Obtain the decision for each agent given the current Period inforset\n",
    "        for j in range(nx.number_of_nodes(self.DirectedNetwork.Network)):\n",
    "           \n",
    "            if self.Decisions[j] == -1 :\n",
    "                agent = Agent( j+1 , self.InforSets[j], self.DirectedNetwork.Waiting_Cost, \n",
    "                              self.DirectedNetwork.Payoff_Correct, self.DirectedNetwork.Payoff_Wrong, \n",
    "                              self.DirectedNetwork.Sig_Acc, self.Period, self.DirectedNetwork.Network)\n",
    "            # Whenever there is no incoming links, stop\n",
    "                if agent.StopWhenInDegree1() != -1 :\n",
    "                    self.Decisions[j] = agent.StopWhenInDegree1()\n",
    "                    self.Half_Guess[j] = self.Signals[j]\n",
    "                    self.Self_Guess[j] = self.Signals[j]\n",
    "            \n",
    "#             # Obtain the \"Expected\" new (next) period inforsets\n",
    "#             if self.Decisions[j] == -1 :\n",
    "#                 temp = self.InforSets[j]\n",
    "#                 for i in range(nx.number_of_nodes(self.DirectedNetwork.Network)):\n",
    "#                     if (i != j) and self.DirectedNetwork.Network.has_edge(i+1,j+1) :\n",
    "#                         for x in self.InforSets[i] :\n",
    "#                             if x not in temp:\n",
    "#                                 temp.append(x)         \n",
    "#                 self.NewInforsets[j]=temp\n",
    "   \n",
    "            if self.Decisions[j] == -1 and self.Period >0 :\n",
    "#                 print(\"Run to Here\")\n",
    "                # Based on the signals' realization, makes a decision        \n",
    "                Decide = 0\n",
    "                for x in  self.InforSets[j] :\n",
    "                    Decide += self.Signals[x-1]\n",
    "                \n",
    "#                 print('Decide')\n",
    "#                 print(Decide)\n",
    "                    \n",
    "                if Decide > 0 :\n",
    "                        self.Decisions[j] = self.Period\n",
    "                        self.Half_Guess[j] = 1\n",
    "                        self.Self_Guess[j] = 1\n",
    "                elif  Decide < 0 :\n",
    "                        self.Decisions[j] = self.Period\n",
    "                        self.Half_Guess[j] = -1\n",
    "                        self.Self_Guess[j] = -1\n",
    "#                 elif Decide == 0 and self.NewInforsets[j]==self.DirectedNetwork.Inforsets[j] :\n",
    "                elif Decide == 0 :\n",
    "        # Note here the next period signal sets is the \"expected\" infor sets based on current network, \n",
    "        # may not be the real next period network \n",
    "        # For any signal that is not in the inforset, if the min_period to obtain is to wait for infinite time (no way to pass through), then decide\n",
    "                    agent.MinWaitingPeriod()\n",
    "                    for i in range(nx.number_of_nodes(self.DirectedNetwork.Network)):    \n",
    "                        if (i not in self.InforSets[j] ) and agent.MinPeriod[i]==math.inf:\n",
    "                            self.Decisions[j] = self.Period \n",
    "                            self.Half_Guess[j] = 2*np.random.randint(2)-1\n",
    "                            self.Self_Guess[j] = self.Signals[j]\n",
    "\n",
    "        return print(self.Self_Guess)\n",
    "\n",
    "        \n",
    "    def NextPeriod(self):\n",
    "        #Two steps: 1. update the inforset, regardless of each agent's decision, the infor will be transimitted using the previous network stucture\n",
    "        # 2. based on the decisions, the network is \"down-graded\"\n",
    "        \n",
    "        # Firstly, define the inforset \n",
    "        # Here the NextInforSets is updated using current network structure\n",
    "        self.NextInforsets = copy.deepcopy(self.InforSets)\n",
    "        #self.NextInforsets = []\n",
    "        for j in range(nx.number_of_nodes(self.DirectedNetwork.Network)) :\n",
    "            #self.NextInforsets[j] = copy.deepcopy(self.InforSets[j])\n",
    "            self.temp = copy.deepcopy(self.InforSets[j])\n",
    "            for i in range(nx.number_of_nodes(self.DirectedNetwork.Network)):\n",
    "                #if (i != j) and self.DirectedNetwork.Network.has_edge(i+1,j+1) and (i+1 not in self.temp):\n",
    "                if (i != j) and self.DirectedNetwork.Network.has_edge(i+1,j+1) :\n",
    "                    for x in self.InforSets[i] :\n",
    "                        if x not in self.temp:\n",
    "                            self.temp.append(x)         \n",
    "            self.NextInforsets[j]=self.temp\n",
    "            #print(\"InforSets: \"+str(self.InforSets))\n",
    "            #print('Next Inforsets: '+str(self.NextInforsets))\n",
    "      \n",
    "        #return self.NextInforsets\n",
    "        \n",
    "        # Secondly, based on decisions, \"down-grade\" the network structure\n",
    "        self.NextNetwork = copy.deepcopy(self.DirectedNetwork.Network)\n",
    "        for j in range(nx.number_of_nodes(self.DirectedNetwork.Network)) :\n",
    "            if  self.Decisions[j] == self.Period :\n",
    "                self.NextNetwork.remove_edges_from(list(self.NextNetwork.in_edges(j+1)))\n",
    "        \n",
    "        #return self.NextNetwork            \n",
    "        \n",
    "        # Thirdly, update the next Period number\n",
    "        self.NextPeriod = self.Period + 1\n",
    "              \n",
    "        \n",
    "    def __str__(self):\n",
    "\n",
    "        return \"The directed network environment is : \"+str(self.DirectedNetwork)+\"; Realized Signals are : \"+str(self.Signals)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Starting Calculating the Predictions and Simulations (Data Generation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Draw the networks & Obtain certain Characteristics of the networks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "#outputfolder = \"C:\\\\Users\\\\lyu75\\\\ECON690Agent_Based\\\\FieldExam\\\\\"\n",
    "#outputfolder = \"U:\\\\ECON690Agent_Based\\\\FieldExam\\\\\"\n",
    "outputfolder = \"C:\\\\Users\\\\xinxi\\\\Anaconda3\\\\Xinxin's Files\\\\Networks\\\\4O3I_Distance\\\\\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "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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9+/a164AFAJVKhbNnz+LEiRPYu3cvCgoK8M6uM/gxv8amwesqFqL2/AHUJG/H+PHjMX78eIwYMcLu/5Ei3KDQJUZVVVVmqwgaGhoQHR1tErCBgYEOFw41NTXw8/ODRCJBc3Mz9Ho9evfujd9//x1L9ufhQM51mwSvm0SE8fKeGMR+w9NPTwIAuLu7Q6PRYMGCBfjss8+sXgPhl12ErrJeBUV5PRo1emh1BkjEQnhIRQjr4UVbI62kurraLGBv3ryJ6Ohok3nYoKAghwvYe1mwYAG+/PJLaLVauLu748svv8S0adPAGMPqJAV2ni2xavC6SUSYHtcLy0bLAAB9+vRBSUnJ7Z9zc0NOTg769+9vtesT+8BL6NY2apCYUYpkhRKKigZodAZIxUIwxsDY7TZ3AoHA+HVZd0/Ey3wxOSaAFpC3QU1NjVnA1tbWthqwQmH77IGkVqsxZ84cHDhwACqVCh4eHqisrIRE8t+HWMcuKrE4MRsqrYHTVQ1SkRBuUiHWT5ab7DzbsmUL3nzzTWi1WhgMBnz66ad47bXXOLsusU82Dd3s0jpsP1WIZIUSAgEeaiumq0QIxm5v45w7LBByWtfYqhs3bpgF7I0bNxAVFWUSsP369Wu3AXu36upqTJw4EV27dsWWLVswYsQIPPvss3j//ffNfm1dkwZL9+chpaAKap3eog0UQgHgIhZhZIgP1iREwNvd9IahsbER/v7+WL9+Paqrq7FkyRK88MIL+PLLL9t+UWL3bBK6VvlGDvbBmonm38jOpLa21mwdbHV1tUnAxsbGOlXA3u3y5csYM2YMnn76afztb3+DUCiEVquFSCS67+9Jzh83CMcsuEEY9ccNwv02Pmg0Gkilt7+HDx06hISEBAwaNAipqakQi6k1Sntk9dC15kc2V4kQG6bInaJZSG1tLTIzM00CtqqqCnK53CRg+/fv77QBe7eTJ09i6tSpWLNmDV544YU2jVHbqMG+zGu3p8LK66HSGeDSylSYWmeAq1gIWQ8vxMt88XS0f5umwhQKBeLi4uDl5YXc3Fx07ty5TXUT+2W10OXj4UR7eeBTV1dnErDp6emorKxEVFSUyVKt4OBgCth7+Prrr7F06VLs3r0bjz/e9j63d6usV0FR0YBGtc74zMHDRQxZd0/OHvrW1dVBLpejuroap0+fxsCBAzkZl9gHq4QuY8z2y3Aie2LtxAiHC96WgL1zHlapVEIul5sFrEgk4rtcu2cwGPDee+9h3759OHz4MEJCQvguqU0MBgPi4+ORlpaGPXv2YNKkSXyXRDhildBddfgivrfyHe7dWu54l48Js9k1H9bNmzfNAraiogKRkZEm62BDQkIoYNugqakJM2bMQFVVFfbv34+uXbvyXZLFXnnlFWzZsgUffvghVqxYwXc5hAOchy6fWyvdJCJsnBZlF3O89fX1xoBtmSa4fv26WcCGhoZSwHKgvLwc48ePh0wmw/bt2+Hiws3ZZfZgy5YtWLhwISZNmoS9e/fyXQ6xEKehay9NRFLfetymqxrq6+uRlZVlErBlZWUYOHCgyTKt0NBQeiJtBTk5ORg3bhzmzZuHZcuWOdwU04NISUnBk08+idDQUJw9exaurrRpyFFxGrrO0C6voaHBLGBLS0vNAlYmk1HA2sDhw4cxa9YsbNq0Cc888wzf5VhVcXExoqOjIRKJkJ2djZ49e/JdEmkDzkK3PTaGvnXrFrKyskyWaZWUlCAiIsIkYMPCwihgbYwxho0bN2Lt2rXYv3+/8Qy09q6pqQmxsbH4/fffceLECQwZMoTvkshD4ix0Hf0IlFu3biE7O9skYIuLixEREWGyikAmk5lsHSW2p9Pp8NprryE1NRWHDh1Cnz59+C7JpgwGAxISEnDo0CF8/fXXmDlzJt8lkYfAye1ZbaMGyQqlXQQuABgYcEyhRG2jptUF6o2NjWYBW1RUhAEDBiAmJgYjR47EW2+9hbCwMApYO1NfX49nnnkGBoMBv/76Kzp27Mh3STYnFArx008/YdmyZZg9ezby8/PxySef8F0WeUCc3OluS7uKDckFdnes9eJRIZge090kYNPT0/H7778bA7blDjY8PJwC1s4VFxdj7NixGDZsGD7//HOa0gGwc+dOzJw5E/Hx8UhKSqLNMg6Ak9Cd8o/TOFdUa9EY1Qf/H1RFOTBoVRB5dILX4EnwjHzSojGF1VdRsXMJwsPDTZZphYeHG/e7E8dw5swZTJw4Ee+++y4WLVrULlcotFV6ejqGDx8Of39/ZGZmokOHDnyXRO6Dk1sFRUWDxWN4DZ6MLv/3NQjEEmhrSlHx/VJIfYPg0r1fm8d069EPdXV1FLAObs+ePVi4cCG+/vprjBs3ju9y7E5sbCwKCwsRFRUFf39/ZGRkICgoiO+yyD1Y/FlEWa+CRmf5tILUpzcE4paP9wIIIICuttyiMbVMgDqV/Ux5kIfDGMPq1avx9ttv49ixYxS499G9e3cUFxejX79+kMlkOHbsGN8lkXuw+E5XUV4PqVgINQfBW3N0MxrzjoPp1JD6BsEtKNai8VzEQigqGuj0CQekVqsxb948XLhwAWfOnKE1qQ9AKpUiPT0dzz33HJ566ils2LCBmqLbIYtDt1GjB1f7K7o8uQCdR70EddklqEryIBBZ9mCLMYZGNX+740jb1NTUICEhAV27dkVqaio8PDz4Lsmh7NixAxEREXjjjTeQn5+P7du3810SuYPF0wtanQFcdm8QCEVwDQiHvqEaDVlJFo3FGDiZ+iC2c/nyZQwePBhDhgzBvn37KHDb6N1338VPP/2Eb7/9Fo899hh0Orr5sBcWh65ELIRVHiQbDBbP6QoEgFRs+hbVarVFYxLrSUlJwfDhw7FkyRKsW7eOlj9ZaNy4ccjNzUVubi769u2LGzdu8F0SAQeh6yEVWbx8R99Yh8aLqTBomsEMejQXZqBRkQrX3pEWjSsQCCAVMpw4cQKLFy9Gv3794ObmhurqaovGJdz75ptv8Mwzz2DXrl2YM2cO3+W0GzKZDCUlJRCJROjVqxfy8vL4LsnpWTynK+vhZflHeIEADVlHUHN0M8AMEHfshk5PzIV7sGX76dVaPZ4aHAHWVPfH8SoMrq6u6NKli2X1Es7c2XQ8NTUVoaGhfJfU7nh7e6OwsBBPPPEEoqKisHfvXkycOJHvspwWJ5sjIj48igYe2znei5erGC92uox33nnHOK0gEong6+trshstJiYG3bt357la59PSdLyyshL/+te/2kXTcXu3YMECbN26FR999BGWL1/OdzlOiZNJM1l3Ty6G4ZyshxcWLVqEjIwM+Pn5QSgUYuHChfj111/x/PPPQ6VS4bPPPkNYWBj8/PwwYcIEfPTRR0hKSoJSqeS7/HatvLwcI0aMgLu7O5KTkylwbWTz5s344osvsHLlSkyZMoXvcpxSu++9MHdYIIDbjVLmz5+P+fPnY/jw4Sa/ljGGoqIis+PM3d3dTU7ajYmJQbdu3fh4O+1KTk4Oxo8fj7lz57bbpuP2rqUpukwmw7lz52jXpg1xErq1jRoMXnuckw0SXHERC3FmyRNtOgYbuB3Ev//+u1kQd+jQwaSXLgXxwzl8+DBmz56NjRs3tvum4/aupSm6WCxGVlYWbUCxEeqn+xAYYygsLDQJ4szMTHh6epoFsY+PD6fXbg82btyINWvW4IcffqDm23aiqakJMTExKCoqoqboNkInR1iIMYarV6+aBXHHjh1NpiViYmKcdt5Sp9Ph9ddfx8mTJ3Ho0CH07duX75LIHagpum3RGWlWYDAYjEHcEsaZmZno1KmTWRC39+VrdzYd37t3r1M2HXcU7733HtauXYvFixdTU3QrapenAae9/Rd0dLOvhuQGgwG//fabSRBnZWWhc+fOZkHcuXNnvsvlREvT8cceewwbN26kpuMOoKUp+qhRo3D48GHaFWgFnIYuABy7qMSi3Vm8TDO4SUTYOC0K8TJfm1+7LQwGA65cuWIWxF27djVZRxwdHe1wQXz27FkkJCTgnXfewWuvvUYrFBwINUW3Ls5DFwD+evgidp4tsWnwuklEmB7XC8vHhNnsmtbQEsR3Hi+UlZWFbt26mQVxp06d+C63VXv37sUrr7xCTccdWEVFBaKioqBSqZCenk5N0TlkldBljGHJ/jwcyLluk+B1k4gwXt4TaxMi2uUdlV6vNwnijIwMYxDfuY44Ojoa3t7Wf3h4L4wxrFmzBlu3bsWBAwcgl8t5q4VYTqPRYOjQocjNzcXhw4cxatQovktqF6wSusAfXf+TFFa/4225w102WtYuA/de9Ho9CgoKTII4Ozsbvr6+ZkFsi4dXarUaL730EvLz83HgwAFa89mOPPfcc9i1axf+/ve/49VXX+W7HIdntdBtceyiEosTs6HSGjhd1SAVCeEmFWL9ZLnDzOFam16vx+XLl02Wr2VnZ6NHjx4mD+q4DuKamhpMnDgRnTt3xo4dO6gHbju0du1avPfee3jxxRexbds2vstxaFYPXeD2qoal+/OQUlAFtU5v0QYKoQBwEYswMsQHaxIi4O1O2xfvR6/X49KlSyZBnJOTg549e5oFsZeX10OPX1BQgDFjxmDixIlYs2YNPe1uxw4cOIBJkyYhLi4OKSkptBqljWwSui1ySuuw/VQhjimUEAjwUL0aXCVCMAaMkvli7rBAm2x8aK90Op1ZEOfm5sLPz89k+VpUVNR9gzglJQXPPPMMVq9ejRdffNGG74Dw5cKFCxg8eDA6deqE7Oxsh1tVYw9sGrotahs12Jd5DckKJRTl9VDpDHARC//oeXv7xAeBQAC1zgBXsRCyHl6Il/ni6Wj/NvdSIPen0+mgUChMlq/l5uYiICDALIg9PT3xzTff4N1338WuXbvwxBNP8F0+saG6ujrI5XJUV1fjzJkzGDBgAN8lORReQvdulfUqKCoa0KjWQaMzQCoWwsNFDFl3TzrJl0c6nQ4XL140C2I3NzdoNBosXLgQo0ePRlRUFK3ldDIGgwF/+ctf8O9//xuJiYlISEjguySHYRehSxxDU1MTnnvuORQVFWHmzJnG1RP5+fno3bu3yTpiuVxOQewEqCn6w6OZcPJAysvLMWHCBISEhOA///kPXFxcjD+n1Wpx8eJF4/zwrl27kJ+fjz59+pgFMa1saF82b96MAQMG4NVXX0V+fj52797Nd0l2j+50yZ/Kzc3FuHHj8OKLL2L58uUPtB5aq9XiwoULJuuI8/PzERgYaBbE7u7uNngXxJpOnjyJp556CmFhYTh79iw1Rb8PCl1yX0lJSZg1axY+//xzTJ061aKxNBqNWRBfuHABgYGBJhs6IiMjKYgdUHFxMaKioiCRSKgp+n1Q6JJ72rhxI/72t79h//79VmturdFokJ+fb7J87eLFiwgKCjJZR0xB7BjubIqekpKCuLg4vkuyOxS6xAzfTcfVarVZECsUCvTr188siN3c3GxaG/lzBoMBEyZMQFJSEr755hs8//zzfJdkVyh0iYmWpuN6vR6JiYl203RcrVYjLy/PJIgvXbqE/v37m6wjjoyMhKsrLTO0B0uXLsW6devw1ltv4eOPP+a7HLtBoUuM7mw6/vnnn0Misa9G8HdTqVRmQXz58mUEBwebBPHAgQMpiHlCTdHNUegSAO2n6bhKpUJubq7Jho6CggKEhISYBfGdy96I9Zw/fx4jRoygpuh/oNAlSExMxIIFC9pt0/Hm5mazIL5y5QpCQ0NNlq9FRERQEFtJRUUF5HI51Go1MjMznfpwUgpdJ8YYw9q1a7FlyxanazreEsR3Ll+7cuUKZDKZSRAPGDCAgpgjGo0GQ4YMQV5eHo4cOeK0PTsodJ2URqPBvHnzkJeXh4MHD9KaStwO4pycHJMg/u233xAWFmYWxLT4v+2mT5+O3bt347PPPsPChQv5LsfmKHSdEDUdf3BNTU1mQXz16lWEhYWZLF+jIH44LU3R582bh61bt/Jdjk1R6DqZlqbjCQkJWLt2LT1NboPGxkbk5OSYrJooLCxEeHi4WRDb+woQPrU0RR88eDBOnjzpNE3RKXSdSEvT8b/+9a+YO3cu3+W0K42NjcjOzjYJ4qKiIrMgDg8PpyC+g7WaoivrVVCU16NRo4dWZ0zIHcQAAB2ISURBVIBELISHVISwHl68t4ul0HUS33zzDZYsWYLvv//eaR9g2NqtW7fMgri4uBgDBgwwWb4WFhbm1EFcV1eHyMhI3LhxA//5z3/a1BS9tlGDxIzS2wcjVDQY+3LffTBCy9dl3T0RL/PF5JgAmx+MQKHbzhkMBixfvhx79+7FoUOHEBoayndJTu3WrVvIysoyWb5WUlKCiIgIsyB2lo/bwO3v08cffxynT59GYmIiRowYgTlz5mDbtm3o2rXrPV+X/ccRYMkWHAEW/8cRYHIbHQFGoduONTU1YebMmSgvL8ePP/54329ewp+GhgazIC4tLcXAgQNNVk3IZLJ2H8Qvv/wytm7dCn9/f5SXl+ODDz5otTm6VQ67DfbBmonWP+yWQredqqiowPjx4xEcHIyvvvqK1po6mJYgbpmWSE9PR1lZmVkQh4aGtqsgZowhLi4O58+fBwB06dIFFRUVJu/x2EUlFidmQ6U1QKN/8DvbPyMVCeEqEWLDFDniZb6cjXs3Ct12KC8vD+PGjcMLL7yAFStWOOyWXmKqvr7eLIivX7+OyMhIsyAWiUR8l9sme/bsMenbLBQK8f333+OZZ54BYwyrkxTYebYEzVq91Wpwk4gwPa4Xlo2WWeXvDoVuO9PSdPyzzz7DtGnT+C6HWNnNmzdNgjgjI8MYxHeumnCUIL558yZ++OEHJCUl4cSJE6itrYWLiwsqKyux+lgRDuRct2rgtnCTiDA+sifWTozgPHgpdNuRlqbjP/zwA4YOHcp3OYQndXV1ZkFcUVFhFsQhISF2H8SXLl3CokWLUNwpBoLgYVDpbBdXLXe8y8eEcTouhW47oNPp8MYbb+D48eM4fPiwUzcTIa2rq6tDZmamyfI1pVIJuVxuEsTBwcF2F8S/XKzAgv89Dx1sv5HHTSLCxmlRnM7xUug6uPr6ekydOhU6nQ579+6Ft7dtlr0Qx1dbW2sWxFVVVZDL5SbL14KDg3nbuVjXpMHwT06iXqXj5foA0NFNjNS3HudsVQOFrgMrKSnB2LFjMXToUGzcuNGpF9gTbty4ccMsiKurqxEVFWUSxP3797dJEL+8IwPHL1VyukrhYUlFQjwh64Yt02M4GY9C10GdO3cOCQkJeOutt/D666/TCgViNTU1NcYgbgnjmpoaREdHmwRxv379OA3i7NI6TNt+xiYPzv6Mm0SE3XMHI5KDDRQUug5o3759ePnll/HVV19h/PjxfJdDnFBNTY0xhFuCuLa21hjELWEcFBTU5iB+5ftMHMkvt2jjA1eEAmD0gB7Y9Gy0xWNR6DqQlqbjmzdvxoEDBxAVFcV3SYQYVVdXIzMz02Qd8c2bN1sN4j/7ZFbbqMHgtceh1vE3rXA3F7EQZ5Y8YXGvBgpdB6HRaPDSSy8hJycHBw8ehJ+fH98lEfKnqqqqTII4IyPDGMR3rpq4O4i3pV3FhuSCh+qlYG2uEiEWjwrB3GGBFo1DoesAampqMGnSJHh7e2Pnzp3UdJw4tKqqKpMHdRkZGWhoaDAJ4v8t74q8iuY2X6M+4yAa845DU1UED9kIdB37Bie1x/XtjD3zhlg0BoWunbty5QrGjBmDCRMmYO3atXa3hpIQLlRWVprMD2cFTYdA6t7m8ZounwYEAjT/ngmm1XAWul6uYuSufNKiMSh07VhqaiqmTJmCVatWYd68eXyXQ4hNKOtVGP7JSU7mc2vT/hf6+mrOQlcqFuLfbz9uUSN0OqvFTn377beYPHkydu7cSYFLnIqivB5SsX1Gk4tYCEVFg0VjtJ+ecO2EwWDAihUrsHv3bqSmpkImk/FdEiE21ajRw14/gDPG0Ki2bHccha4daW5uxvPPP4/y8nKcOXMGPj4+fJdEiM1pdQbYaeaCMUBj4bSHfd7DO6GKigqMHDkSUqkUycnJFLjEaUnEQtjrBkuBABZPfVDo2oG8vDwMHjwYY8aMwY4dO+Dqyu9ppYTwyUMqsnhbOzPowXQawKAHmAFMpwEzWL6dWCAQwMPFsgkCml7g2ZEjRzBz5kz8/e9/x7PPPst3OYTwgjGGoqIiZGRk4FR6Lm6xGEDY9ni6+etu3Px1l/HHjRdOouOj0+A9bLpFdap1Bsi6e1o0BoUujzZt2oTVq1fjX//6Fx599FG+yyHEJhhjKC4uNtkckZGRAVdXV+PmCFeNGM0W3Jh6D5tuccC2xlUstGi5GEChywudToc333wTycnJ+PXXXxEYaNm2QkLsFWMMJSUlJv0YMjIy4OLiYgzY1157DTExMejevbvxdfn/OI1zRbU8Vt46WQ8vi8eg0LWxhoYGTJ06FRqNBqdPn6am46TdaAnYO3eWZWRkQCKRGAN20aJFiImJQY8ePe47VrzMF7llN+2u9wIXJ0jQjjQbamk6PmTIEGzatImajhOHxRhDaWmpWcCKRCJjwLb8v2fPng89fnvuMkZ3ujZy/vx5/M///A8WL16MN954g5qOE4fBGMO1a9fMAlYoFBrDdcGCBcaA5eJ7u5OHFPEyX7vqpztK5mtx4AIUujbxww8/YP78+dR0nNg9xhjKysrMuoABMAbs/PnzERMTAz8/P6vePMwdFogTlyrt4uQIF7HI4paOLSh0rYgxhnXr1uGLL77A0aNHER1tedd5QrjCGMP169dNAjY9PR2MMWPAzps3DzExMfD397f5pzN5gDdGBvvYxRlpI0N8ODmqB6A5XavRaDSYP38+srOzqek4sQutBaxerzeZf42NjeUlYO/FXk4DTnv7L+joxs0zGLrTtYIbN25g0qRJ8PLyQlpaGjp06MB3ScTJlJeXmwWsVqs1husLL7yAzZs3IyAgwG4CtjXuYiBGewEntH0gkLjY/PpuEhHWT5ZzFrgA3ely7sqVKxg7dizGjRuHdevWUdNxYnUVFRUm86/p6elQq9Vmqwh69epl1wEL3F7Dfu7cOZw8eRIHDhzA+fPnIRQK8eaOf+PgxTqbzu+6SUSYHtcLy8eEcTouhS6HqOk4sTalUmkWsM3NzWYB27t3b7sP2NZ89913mDVrFiQSCbRaLQBg3bp1ePvtt7Fkfx4O5Fy3SfC6SUQYL++JtQkRnP8+Uuhy5LvvvsPbb7+NnTt3YtSoUXyXQ9oBpVJptkyrqanJ5GTdmJgY9OnTxyEDtjVarRbR0dHIz88HAHh4eKCyshLu7u5gjGF1kgI7z5ZYNXhb7nCXjZZZ5feV5nQtZDAY8P7772PXrl1ISUlBWBi3H0WIc7j7jLCMjAzcunXLGK7PPfccPv30U/Tt27fdBGxrvv76a1y4cAHu7u5Qq9V48cUX4e5++6w0gUCA5WPCENe3CxYnZkOlNXC6qkEqEsJNKsT6yXJOdp7dC93pWqC5uRkzZ85EWVkZfvzxR+qBSx5Iy2m4dwbs3afhxsTEIDAwsF0H7N0WLlyIzZs344MPPsCMGTMwevRoHDlyBH369DH7tXVNGizdn4eUgiqodXqLNlAIBbfX4Y4M8cGahAh4u1u+AeJ+KHTbSKlUYsKECQgKCsJXX31FPXBJq6qrq802Gty8edMsYIOCgpwqYO9kMBjwxBNP4NSpU9izZw8mTZr0wK/NKa3D9lOFOKZQQiDAQ/VqcJUIwdjtnWZzhwVytg73z1DotkF+fj7Gjh2L2bNn4/3333favyzEVE1NjVnA1tbWmgRsbGwsAgMDIRTS+QEAUFdXh6ioKFRVVeH06dMYOHBgm8apbdRgX+Y1JCuUUJTXQ6UzwEUsBGMMjN0+8UEgEECtM8BVLISshxfiZb54Otqfk629D4NC9yH9/PPPeP755/Hpp59i+nTu+3USx3Djxg2zdbAtAXvng66goCAK2HtQKBSIi4tDx44dkZOTg86dO3M2dmW9CoqKBjSqddDoDJCKhfBwEUPW3dPifriWotB9CJs3b8aqVauwb98+ajruRG7cuIHMzEyTgK2pqTEL2H79+lHAPqBDhw4hISEBcXFxSElJgVjsPM/0KXQfgF6vx5tvvolffvkFhw8fpqbj7Vhtba3JaQbp6emorq5GVFSUyTKt/v37U8C20ccff4wlS5Zgzpw52L59O9/l2ByF7p9oaGjAtGnToFKpsG/fPmo63o7U1tYiMzPTZJqgqqoKcrncJGCDg4MpYDny/PPPY+fOndiwYQNee+01vsvhBYXufZSUlGDcuHGIi4vDF198QU3HHVhdXZ1ZwCqVSsjlcpNVBMHBwbR12wo0Gg0effRR5OTk4PDhw069gYhC9x5amo6/+eabePPNN2mFggO5efOmWcBWVFQgMjLSJGBDQkIoYG2gsrISkZGRaG5uRkZGBoKCgvguiVcUuq3Yv38/XnrpJXz55ZeYMGEC3+WQ+6ivrzcL2OvXr5sFbGhoKAUsD9LT0zF8+HD4+fkhKyuLOu6BQtcEYwwff/wxNm3ahJ9++omajtuZ+vp6ZGVlmayDLSsrw8CBA03WwVLA2oddu3ZhxowZiI+PR1JSEs2L/4FC9w8ajQYvv/wysrKyqOm4HWhoaDAL2NLSUkRGRpos0woNDXWq5UaOYtmyZVizZg3eeOMNrF+/nu9y7AqFLm4/xZ40aRI8PT2xc+dO+ghkY7du3TIJ2PT0dJSWlmLgwIEmASuTyShg7ZzBYEBCQgIOHTqEL7/8ErNnz+a7JLvj9KH722+/YcyYMRg7diw+/vhj+lhqZS0Be+c62JKSEkRERJgFLK0WcSxNTU2IjY3F77//jhMnTmDIkCF8l2SXnDp009LSMGXKFHz44Yd46aWX+C6n3WlsbDQL2OLiYgwYMMBkHWxYWBgFrIMrLi5GdHQ0RCIRMjMz4e/vz3dJdstpQ/ef//wn3nrrLWo6zpHGxkZkZ2ebrCIoKipCeHi4ScCGh4dTwLYzaWlpGDVqFEJDQ3H27FnquPcnnC50W5qOf//99zh06BA1HW+DpqYms4AtLCxEeHi4yTKt8PBwSKW27eBEbOsf//gHFixYgIkTJyIxMZHvchyCU4Vuc3MzZs2ahdLSUvz444/o1q0b3yXZvaamJuTk5JgE7NWrVxEWFmYSsAMGDKCAdTKvvvoqvvjiC6xcuRIrV67kuxyH4TSh29J0PDAwEF9//TV9BGpFc3OzWcD+9ttvkMlkZgHr4mL747CJfbiz6fju3bvx9NNP812SQ7GL0FXWq6Aor0ejRg+tzgCJWAgPqQhhPbw46X2Zn5+PcePGYebMmVi5ciVt6cXtgM3NzTVZB3vlyhWEhoaabDSggCV34qrpuDPjJXRrGzVIzCi93eW9osHYZPjuLu8tX5d190S8zBeTYwIeusv70aNHMWPGDKduOq5SqcwCtqCgAKGhoSbLtCIiIihgyT3d2XQ8OzsbXbp04bskh2TT0M3+4zyjZAvOM4r/4zwj+QOcZ7RlyxZ89NFHSExMxGOPPWZJ6Q5DpVIhLy/PZKNBQUEBQkJCzAKWpljIg0pKSsKECRPwyCOPIC0tjTapWMAmoWuVkzuDfbBmYusnd+r1eixevBhHjx7FoUOH2m1XI7VajdzcXJN1sJcvX0ZwcLBJwA4cOJAClrTZJ598gnfffRezZ8/GV199xXc5Ds/qoXvsotJqZ9S7SoTYMMX0jPqGhgY8++yzaGpqwr59+9CpUyfOrskntVqNvLw8k4C9dOkS+vfvb7IOduDAgXBzc+O7XNJOPP/889ixYwc+/fRTp206zjWrhS5jDKuTFNh5tgTNWr01LgEAcJOIMD2uF5aNluHatWsYO3YsBg0ahM2bNzvsInyNRmMWsAqFAv369TMJ2MjISApYYhVarRaPPvoosrOzcfDgQTz55JN8l9RuWCV0GWNYsj8PB3KuWzVwW7hJRBjiJ8Evq2bi9ddfx+LFix1mhYJGo0F+fr7JMq2LFy8iKCjILGDd3d35Lpc4gTubjp8/fx79+/fnu6R2xSqhu+rwRXxv5TvcuzGtCo8HSPDta+Ntds2HpdFocOHCBbOA7du3r8k6WLlcTgFLeJGRkYFhw4ahZ8+eyM7Opo57VsB56B67qMSi3Vk2DdwWbhIRNk6LMpnj5YtWq8WFCxdMlmnl5+e3GrAeHh58l0sINR23EU5Dt65Jg+GfnES9SsfVkA+to5sYqW893uqqBmvRarW4ePGiWcD27t3bZKMBBSyxVytWrMDq1aup6bgNcBq6L+/IwPFLlZyuUnhYUpEQT8i6Ycv0GKuMr9PpzAI2Ly8PvXv3NlmmJZfL6aMZsXsGgwETJ07EwYMHsX37drzwwgt8l9TucbbCObu0DikFVbwGLgBo9AakXK5CTmkdIh9gA8X96HQ6KBQKk40GeXl56NWrlzFgp06dCrlcDk9PT47eASG20dTUhEceeQSFhYVIS0vDo48+yndJToGz0N1+qhBqne3ncVuj1umx/VQhNj3734Ml9Xo91q1bh3HjxiEiIsLsNS0Be+cyrby8PPj7+xvvXqdMmYKoqCgKWOLwiouLERMTA6FQiCtXrlDTcRviJHRrGzVIVigt2mnGJQMDjimUqG3UoJOHFFVVVRg/fjzOnTuHW7duISwszCxgc3Nz4efnZwzYp59+GlFRUfDy8uL77RDCqZam4yEhITh37hztVrQxTuZ0t6VdxYbkgofqpWBtrhIhFo8KwQCxEmPGjEF9fT30ej08PT1hMBjQs2dPk3WwUVFR6NixI99lE2JV27Ztw8svv4yEhATs27eP73KcEid3uskKJWeBq71RhutfLYRH6KPoOu6tNo+j0hpwOLsE8xY9bvJ1vV6PsrIyeHtbNt9LiKOhpuP2gZPQVVQ0cDEMAODGL1vh0oObHTCFN9S4cOECTp48if379+P06dNoamqCTsffkjZCbM1gMCA+Ph5paWnYu3cvNR3nmcWhq6xXQaPj5i638WIqhK4ekHQJha6u3OLxVDoDuvoH4pVXwvDKK69Aq9Xi0qVL1AeUOI36+nrI5XJUVlYiIyMDkZGRfJfk9CzecqIor4dUbPnOFYO6CXWndqLTX+ZYPFYLF7HQ5C5cIpEgIiLCYfoyEGKJy5cvIyAgABqNBkVFRRS4dsLitGzU6MHF/oq6tP9Fh8j/A7GXj8VjtWCMoVFNUwnE+SQlJWHAgAEIDw9HUVERunbtyndJ5A8Wh65WZ4ClmatRFkJVnAOvRyZYWo4JxsDZ1AchjuKTTz7B2LFjMWPGDJw+fZpOebAzFv9pSMRCWPppXVWSB91NJa5tng0AYBoVwAwor34NPWZ/1uZxBQJwMvVBiKNoaTq+YcMGvP7663yXQ1phceh6SEUWz5F2kD8JD9lw44/rz+2H7qYSnZ98xaJxBQIBPFzoX3nS/ul0OgwdOhTZ2dk4cuQINR23YxYnkqyHl8Uf4YUSV0Dy310xAokrBGIpRO6WbVZQ6wyQdactu6R9q6yshFwuR1NTEy5cuEBNx+2cxaHr6+UKqVgINYdzp97DuDkq3VUsRDcv2uJI2q/MzEw89thj6NmzJy5fvkx9QRwAJxOe9no3KetBfRNI+7Vnzx4MGjQIw4YNQ0FBAQWug+AkdONlvnCV2NcDK1eJ0C5OkCDEGlasWIFp06Zh0aJFOHr0KJ3y4EA4+ZOaHBNg8bIxrjEGPB1N7epI+2IwGJCQkIC//e1v2L59OzZs2MB3SeQhcfJov5OHFPEyXxzJL7eL9o5CATBK5otOHrY7socQa2tubkZsbCyuXr1KTccdGGefSeYOC4SLWMTVcBZxEYswd1gg32UQwpmSkhIEBASgsrISv/32GwWuA+MsdOUB3hgZ7AOpiN+5JalIiJEhPhYf1UOIvUhLS0NwcDB69uyJ0tJSOuXBwXGakGsmRvD+QM1NKsTaiQN5rYEQrmzbtg2PP/44xo4di9zcXDrloR3gNCG93aVYP1kONwk/0wxuEhHWT5ajo5uEl+sTwqVFixZh/vz5WLFiBZ3y0I5wvkd2VJgvpsf1ws6zJWjW2u6gSjeJCNPjetEyMeLwDAYDRo0ahdTUVGo63g5ZpTHBstEyNKh0OJBz3SbB6yYRYby8J5aNlln9WsS5KetVUJTXo1Gjh1ZngEQshIdUhLAeXpzsfryz6Xh6ejrkcjkHVRN7YpXQFQgEWDsxAp6uYqvf8bbc4S4bLaPm5IRztY0aJGaUIlmhhKKiARqdAVKxEIwxMHa7k51AIDB+XdbdE/EyX0yOCXjoJYuXL1/GoEGD4OnpST1w2zFOTgO+n2MXlVicmA2V1gCNnrv+DFKREG5SIdZPltOUAuFcdmkdtp8qRLJCCYEAD3XwqqtECMZu79ScOywQ8nuspNFqtYiLi8Mnn3wCtVqNCRMmIDY2FqdOnaIeuO2Y1UMXAOqaNFi6Pw8pBVVQ6/QWbaAQCm6vwx0Z4oM1CRHwdqcNEIQ7VvleDfbBmonm36uJiYmYMWMGGGPQarWYNWsWvv76awvfAbF3NgndFjl/3D0cs+DuYdQfdw+0DpdwzZqfylwlQmyYYvqpLCoqCtnZ2QAAT09PFBYW0pSCE7Bp6LaobdRgX+a12/Nk5fVQ6QxwaWWeTK0zwFUshKyHF+Jlvng62p+29hLOMcawOklh0+cPGRkZGDRoEBhjEAgEEIlEePHFF7FlyxarXZ/YB15C926V9SooKhrQqNYZH0h4uIgh6+5J/XCJVTHGsGR/nk1X2vzfcB/885UnUVNTg6CgIEyYMAHx8fEYNmwYOnToYPUaCL/sInQJ4cuqwxfxvY3XlEOnQfdbv+HAhzPRrVs3212X2AVqwkmc1rGLStsHLgCIpbjpE4HcGrrfcUYUusQp1TVpsDgx2/aB+4dmrR6LE7NR16Th5fqEPxS6xCkt3Z/3UKtnrKFZY8DSf+XxWgOxPQpd4nSyS+uQUlDF6bKwttDoDUi5XIWc0jpe6yC2RaFLnM72U4VQ6/iZVribWqfH9lOFfJdBbIhClziV2kYNkhVKuzhWCgAMDDimUKK2keZ2nQWFLnEqiRmlsLe+SAIBsC/zGt9lEBuhrhrEqSQrlBY/QKvYuQTq65chEN5u1i/y7AK/ef9o83gqrQHJCiWd6+ckKHSJU1FUNHAyTuf/Mx+ekU9yMhYAKMrrORuL2DeaXiBOQ1mvgkbH74qFe1HpDKisV/FdBrEButMlTkNRXg+pWAg1B8Fbl/Id6lK+g6SzH7yHz4Brb8sOQ3URC6GoaKBeI06AQpc4jUaNHly0Gun0+GxIugRAIJKgUZGGyh9WocfszyHp1KPNYzLG0KjWWVwbsX80vUCchlZnABftnVx6hkDo4g6BWIIOEU/AxU+G5qvpFo3JGOx26oNwi0KXOA2JWGid5WICAQDL0lwgAKRi+uvoDOhPmTgND6nI4sNLDapbaC7MANNpwAx63LpwEurSfLj1jbZoXIFAAA8Xmu1zBvSnTJyGrIeXxR/hmUGPurQd0N64BgiEkHTxh8/E5ZB08bdoXLXOAFl3T4vGII6BQpc4DV8vV4tXL4jcO6LHrE85rOo2V7GQVi44CZpeIE7FXu8mZT28+C6B2AiFLnEq8TJfuErs69veVSI0OSWYtG/29d1HiJVNjgngZNkYlxgDno62bE6YOA4KXeJUOnlIES/zhdBOOo0JBcAomS86eUj5LoXYCIUucTpzhwXCRSziuwwAgItYRN3FnAyFLnE68gBvjAz2gVTE77e/VCTEyBAfRAZ481oHsS0KXeKU1kyM4P2BmptUiLUTLWuUQxwPhS5xSt7uUqyfLIebhJ9pBjeJCOsny9HRTcLL9Ql/KHSJ0xoV5ovpcb1sHrxuEhGmx/WiZWJOikKXOLVlo2UYH9nTZsHrJhFhvLwnlo2W2eR6xP4IGBcNRglxYIwxrE5SYOfZEjRrrXc0e8sd7rLRMosb7xDHRaFLyB+OXVRicWI2VFoDNHruettKRUK4SYVYP1lOUwqEQpeQO9U1abB0fx5SCqqg1ulhsOBvh1Bwex3uyBAfrEmIgLc7bYAgFLqEtCqntA7bTxXimEIJgQAPdWy7q0QIxm7vNJs7LJDW4RITFLqE3Edtowb7Mq8hWaGEorweKp0BLmIhGGNg7PaJDwKBAGqdAa5iIWQ9vBAv88XT0f60tZe0ikKXEEJsiJaMEUKIDVHoEkKIDVHoEkKIDVHoEkKIDVHoEkKIDf1/GPrB+X0GBu8AAAAASUVORK5CYII=\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": [
    "### Set up the Directed network environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True Nature is: 1; Signal Informativeness: 0.7\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G=nx.from_pandas_edgelist(Alldata[Alldata.network==1], 'from', 'to', create_using=nx.DiGraph() )\n",
    "E = DirectedNetwork(G,1,0.7,1, 140, 40)\n",
    "# (self, Network, TrueNature, Sig_Acc,  waiting_cost, payoff_correct, payoff_wrong, period = 0, Decisions=[], InforSets=[])\n",
    "print(E)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Nash Equilibrium Prediction "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True Nature is: 1; Signal Informativeness: 0.7\n",
      "this is Period 0\n",
      "Agent 0\n",
      "    Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0        0           1         110.000  [1, 2, 5, 3, 4]\n",
      "1        1           3         117.400  [1, 2, 5, 3, 4]\n",
      "2        2           5         121.692  [1, 2, 5, 3, 4]\n",
      "3        3           5         120.692  [1, 2, 5, 3, 4]\n",
      "4        4           5         119.692  [1, 2, 5, 3, 4]\n",
      "5        5           5         118.692  [1, 2, 5, 3, 4]\n",
      "6        6           5         117.692  [1, 2, 5, 3, 4]\n",
      "7        7           5         116.692  [1, 2, 5, 3, 4]\n",
      "8        8           5         115.692  [1, 2, 5, 3, 4]\n",
      "9        9           5         114.692  [1, 2, 5, 3, 4]\n",
      "10      10           5         113.692  [1, 2, 5, 3, 4]\n",
      "Highest Payoff2\n",
      "Period                          2\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            121.692\n",
      "InforSet          [1, 2, 5, 3, 4]\n",
      "Name: 2, dtype: object\n",
      "Agent 1\n",
      "    Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0        0           1         110.000  [2, 1, 3, 4, 5]\n",
      "1        1           4         117.400  [2, 1, 3, 4, 5]\n",
      "2        2           5         121.692  [2, 1, 3, 4, 5]\n",
      "3        3           5         120.692  [2, 1, 3, 4, 5]\n",
      "4        4           5         119.692  [2, 1, 3, 4, 5]\n",
      "5        5           5         118.692  [2, 1, 3, 4, 5]\n",
      "6        6           5         117.692  [2, 1, 3, 4, 5]\n",
      "7        7           5         116.692  [2, 1, 3, 4, 5]\n",
      "8        8           5         115.692  [2, 1, 3, 4, 5]\n",
      "9        9           5         114.692  [2, 1, 3, 4, 5]\n",
      "10      10           5         113.692  [2, 1, 3, 4, 5]\n",
      "Highest Payoff2\n",
      "Period                          2\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            121.692\n",
      "InforSet          [2, 1, 3, 4, 5]\n",
      "Name: 2, dtype: object\n",
      "Agent 2\n",
      "    Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0        0           1         110.000  [3, 1, 2, 5, 4]\n",
      "1        1           2         109.000  [3, 1, 2, 5, 4]\n",
      "2        2           4         116.400  [3, 1, 2, 5, 4]\n",
      "3        3           5         120.692  [3, 1, 2, 5, 4]\n",
      "4        4           5         119.692  [3, 1, 2, 5, 4]\n",
      "5        5           5         118.692  [3, 1, 2, 5, 4]\n",
      "6        6           5         117.692  [3, 1, 2, 5, 4]\n",
      "7        7           5         116.692  [3, 1, 2, 5, 4]\n",
      "8        8           5         115.692  [3, 1, 2, 5, 4]\n",
      "9        9           5         114.692  [3, 1, 2, 5, 4]\n",
      "10      10           5         113.692  [3, 1, 2, 5, 4]\n",
      "Highest Payoff3\n",
      "Period                          3\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            120.692\n",
      "InforSet          [3, 1, 2, 5, 4]\n",
      "Name: 3, dtype: object\n",
      "Agent 3\n",
      "    Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0        0           1         110.000  [4, 1, 2, 5, 3]\n",
      "1        1           2         109.000  [4, 1, 2, 5, 3]\n",
      "2        2           4         116.400  [4, 1, 2, 5, 3]\n",
      "3        3           5         120.692  [4, 1, 2, 5, 3]\n",
      "4        4           5         119.692  [4, 1, 2, 5, 3]\n",
      "5        5           5         118.692  [4, 1, 2, 5, 3]\n",
      "6        6           5         117.692  [4, 1, 2, 5, 3]\n",
      "7        7           5         116.692  [4, 1, 2, 5, 3]\n",
      "8        8           5         115.692  [4, 1, 2, 5, 3]\n",
      "9        9           5         114.692  [4, 1, 2, 5, 3]\n",
      "10      10           5         113.692  [4, 1, 2, 5, 3]\n",
      "Highest Payoff3\n",
      "Period                          3\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            120.692\n",
      "InforSet          [4, 1, 2, 5, 3]\n",
      "Name: 3, dtype: object\n",
      "Agent 4\n",
      "    Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0        0           1         110.000  [5, 1, 2, 3, 4]\n",
      "1        1           2         109.000  [5, 1, 2, 3, 4]\n",
      "2        2           3         116.400  [5, 1, 2, 3, 4]\n",
      "3        3           5         120.692  [5, 1, 2, 3, 4]\n",
      "4        4           5         119.692  [5, 1, 2, 3, 4]\n",
      "5        5           5         118.692  [5, 1, 2, 3, 4]\n",
      "6        6           5         117.692  [5, 1, 2, 3, 4]\n",
      "7        7           5         116.692  [5, 1, 2, 3, 4]\n",
      "8        8           5         115.692  [5, 1, 2, 3, 4]\n",
      "9        9           5         114.692  [5, 1, 2, 3, 4]\n",
      "10      10           5         113.692  [5, 1, 2, 3, 4]\n",
      "Highest Payoff3\n",
      "Period                          3\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            120.692\n",
      "InforSet          [5, 1, 2, 3, 4]\n",
      "Name: 3, dtype: object\n",
      "this is Period 1\n",
      "Agent 0\n",
      "   Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0       1           3         117.400  [1, 2, 5, 3, 4]\n",
      "1       2           5         121.692  [1, 2, 5, 3, 4]\n",
      "2       3           5         120.692  [1, 2, 5, 3, 4]\n",
      "3       4           5         119.692  [1, 2, 5, 3, 4]\n",
      "4       5           5         118.692  [1, 2, 5, 3, 4]\n",
      "5       6           5         117.692  [1, 2, 5, 3, 4]\n",
      "6       7           5         116.692  [1, 2, 5, 3, 4]\n",
      "7       8           5         115.692  [1, 2, 5, 3, 4]\n",
      "8       9           5         114.692  [1, 2, 5, 3, 4]\n",
      "9      10           5         113.692  [1, 2, 5, 3, 4]\n",
      "Highest Payoff1\n",
      "Period                          2\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            121.692\n",
      "InforSet          [1, 2, 5, 3, 4]\n",
      "Name: 1, dtype: object\n",
      "Agent 1\n",
      "   Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0       1           4         117.400  [2, 1, 3, 4, 5]\n",
      "1       2           5         121.692  [2, 1, 3, 4, 5]\n",
      "2       3           5         120.692  [2, 1, 3, 4, 5]\n",
      "3       4           5         119.692  [2, 1, 3, 4, 5]\n",
      "4       5           5         118.692  [2, 1, 3, 4, 5]\n",
      "5       6           5         117.692  [2, 1, 3, 4, 5]\n",
      "6       7           5         116.692  [2, 1, 3, 4, 5]\n",
      "7       8           5         115.692  [2, 1, 3, 4, 5]\n",
      "8       9           5         114.692  [2, 1, 3, 4, 5]\n",
      "9      10           5         113.692  [2, 1, 3, 4, 5]\n",
      "Highest Payoff1\n",
      "Period                          2\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            121.692\n",
      "InforSet          [2, 1, 3, 4, 5]\n",
      "Name: 1, dtype: object\n",
      "Agent 2\n",
      "   Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0       1           2         109.000  [3, 1, 2, 5, 4]\n",
      "1       2           4         116.400  [3, 1, 2, 5, 4]\n",
      "2       3           5         120.692  [3, 1, 2, 5, 4]\n",
      "3       4           5         119.692  [3, 1, 2, 5, 4]\n",
      "4       5           5         118.692  [3, 1, 2, 5, 4]\n",
      "5       6           5         117.692  [3, 1, 2, 5, 4]\n",
      "6       7           5         116.692  [3, 1, 2, 5, 4]\n",
      "7       8           5         115.692  [3, 1, 2, 5, 4]\n",
      "8       9           5         114.692  [3, 1, 2, 5, 4]\n",
      "9      10           5         113.692  [3, 1, 2, 5, 4]\n",
      "Highest Payoff2\n",
      "Period                          3\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            120.692\n",
      "InforSet          [3, 1, 2, 5, 4]\n",
      "Name: 2, dtype: object\n",
      "Agent 3\n",
      "   Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0       1           2         109.000  [4, 1, 2, 5, 3]\n",
      "1       2           4         116.400  [4, 1, 2, 5, 3]\n",
      "2       3           5         120.692  [4, 1, 2, 5, 3]\n",
      "3       4           5         119.692  [4, 1, 2, 5, 3]\n",
      "4       5           5         118.692  [4, 1, 2, 5, 3]\n",
      "5       6           5         117.692  [4, 1, 2, 5, 3]\n",
      "6       7           5         116.692  [4, 1, 2, 5, 3]\n",
      "7       8           5         115.692  [4, 1, 2, 5, 3]\n",
      "8       9           5         114.692  [4, 1, 2, 5, 3]\n",
      "9      10           5         113.692  [4, 1, 2, 5, 3]\n",
      "Highest Payoff2\n",
      "Period                          3\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            120.692\n",
      "InforSet          [4, 1, 2, 5, 3]\n",
      "Name: 2, dtype: object\n",
      "Agent 4\n",
      "   Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0       1           2         109.000  [5, 1, 2, 3, 4]\n",
      "1       2           3         116.400  [5, 1, 2, 3, 4]\n",
      "2       3           5         120.692  [5, 1, 2, 3, 4]\n",
      "3       4           5         119.692  [5, 1, 2, 3, 4]\n",
      "4       5           5         118.692  [5, 1, 2, 3, 4]\n",
      "5       6           5         117.692  [5, 1, 2, 3, 4]\n",
      "6       7           5         116.692  [5, 1, 2, 3, 4]\n",
      "7       8           5         115.692  [5, 1, 2, 3, 4]\n",
      "8       9           5         114.692  [5, 1, 2, 3, 4]\n",
      "9      10           5         113.692  [5, 1, 2, 3, 4]\n",
      "Highest Payoff2\n",
      "Period                          3\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            120.692\n",
      "InforSet          [5, 1, 2, 3, 4]\n",
      "Name: 2, dtype: object\n",
      "this is Period 2\n",
      "Agent 0\n",
      "   Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0       2           5         121.692  [1, 2, 5, 3, 4]\n",
      "1       3           5         120.692  [1, 2, 5, 3, 4]\n",
      "2       4           5         119.692  [1, 2, 5, 3, 4]\n",
      "3       5           5         118.692  [1, 2, 5, 3, 4]\n",
      "4       6           5         117.692  [1, 2, 5, 3, 4]\n",
      "5       7           5         116.692  [1, 2, 5, 3, 4]\n",
      "6       8           5         115.692  [1, 2, 5, 3, 4]\n",
      "7       9           5         114.692  [1, 2, 5, 3, 4]\n",
      "8      10           5         113.692  [1, 2, 5, 3, 4]\n",
      "Highest Payoff0\n",
      "Period                          2\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            121.692\n",
      "InforSet          [1, 2, 5, 3, 4]\n",
      "Name: 0, dtype: object\n",
      "Agent 1\n",
      "   Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0       2           5         121.692  [2, 1, 3, 4, 5]\n",
      "1       3           5         120.692  [2, 1, 3, 4, 5]\n",
      "2       4           5         119.692  [2, 1, 3, 4, 5]\n",
      "3       5           5         118.692  [2, 1, 3, 4, 5]\n",
      "4       6           5         117.692  [2, 1, 3, 4, 5]\n",
      "5       7           5         116.692  [2, 1, 3, 4, 5]\n",
      "6       8           5         115.692  [2, 1, 3, 4, 5]\n",
      "7       9           5         114.692  [2, 1, 3, 4, 5]\n",
      "8      10           5         113.692  [2, 1, 3, 4, 5]\n",
      "Highest Payoff0\n",
      "Period                          2\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            121.692\n",
      "InforSet          [2, 1, 3, 4, 5]\n",
      "Name: 0, dtype: object\n",
      "Agent 2\n",
      "   Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0       2           4         116.400  [3, 1, 2, 5, 4]\n",
      "1       3           5         120.692  [3, 1, 2, 5, 4]\n",
      "2       4           5         119.692  [3, 1, 2, 5, 4]\n",
      "3       5           5         118.692  [3, 1, 2, 5, 4]\n",
      "4       6           5         117.692  [3, 1, 2, 5, 4]\n",
      "5       7           5         116.692  [3, 1, 2, 5, 4]\n",
      "6       8           5         115.692  [3, 1, 2, 5, 4]\n",
      "7       9           5         114.692  [3, 1, 2, 5, 4]\n",
      "8      10           5         113.692  [3, 1, 2, 5, 4]\n",
      "Highest Payoff1\n",
      "Period                          3\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            120.692\n",
      "InforSet          [3, 1, 2, 5, 4]\n",
      "Name: 1, dtype: object\n",
      "Agent 3\n",
      "   Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0       2           4         116.400  [4, 1, 2, 5, 3]\n",
      "1       3           5         120.692  [4, 1, 2, 5, 3]\n",
      "2       4           5         119.692  [4, 1, 2, 5, 3]\n",
      "3       5           5         118.692  [4, 1, 2, 5, 3]\n",
      "4       6           5         117.692  [4, 1, 2, 5, 3]\n",
      "5       7           5         116.692  [4, 1, 2, 5, 3]\n",
      "6       8           5         115.692  [4, 1, 2, 5, 3]\n",
      "7       9           5         114.692  [4, 1, 2, 5, 3]\n",
      "8      10           5         113.692  [4, 1, 2, 5, 3]\n",
      "Highest Payoff1\n",
      "Period                          3\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            120.692\n",
      "InforSet          [4, 1, 2, 5, 3]\n",
      "Name: 1, dtype: object\n",
      "Agent 4\n",
      "   Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0       2           3         116.400  [5, 1, 2, 3, 4]\n",
      "1       3           5         120.692  [5, 1, 2, 3, 4]\n",
      "2       4           5         119.692  [5, 1, 2, 3, 4]\n",
      "3       5           5         118.692  [5, 1, 2, 3, 4]\n",
      "4       6           5         117.692  [5, 1, 2, 3, 4]\n",
      "5       7           5         116.692  [5, 1, 2, 3, 4]\n",
      "6       8           5         115.692  [5, 1, 2, 3, 4]\n",
      "7       9           5         114.692  [5, 1, 2, 3, 4]\n",
      "8      10           5         113.692  [5, 1, 2, 3, 4]\n",
      "Highest Payoff1\n",
      "Period                          3\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            120.692\n",
      "InforSet          [5, 1, 2, 3, 4]\n",
      "Name: 1, dtype: object\n",
      "this is Period 3\n",
      "Agent 2\n",
      "   Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0       3           5         120.692  [3, 1, 2, 5, 4]\n",
      "1       4           5         119.692  [3, 1, 2, 5, 4]\n",
      "2       5           5         118.692  [3, 1, 2, 5, 4]\n",
      "3       6           5         117.692  [3, 1, 2, 5, 4]\n",
      "4       7           5         116.692  [3, 1, 2, 5, 4]\n",
      "5       8           5         115.692  [3, 1, 2, 5, 4]\n",
      "6       9           5         114.692  [3, 1, 2, 5, 4]\n",
      "7      10           5         113.692  [3, 1, 2, 5, 4]\n",
      "Highest Payoff0\n",
      "Period                          3\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            120.692\n",
      "InforSet          [3, 1, 2, 5, 4]\n",
      "Name: 0, dtype: object\n",
      "Agent 3\n",
      "   Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0       3           5         120.692  [4, 1, 2, 5, 3]\n",
      "1       4           5         119.692  [4, 1, 2, 5, 3]\n",
      "2       5           5         118.692  [4, 1, 2, 5, 3]\n",
      "3       6           5         117.692  [4, 1, 2, 5, 3]\n",
      "4       7           5         116.692  [4, 1, 2, 5, 3]\n",
      "5       8           5         115.692  [4, 1, 2, 5, 3]\n",
      "6       9           5         114.692  [4, 1, 2, 5, 3]\n",
      "7      10           5         113.692  [4, 1, 2, 5, 3]\n",
      "Highest Payoff0\n",
      "Period                          3\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            120.692\n",
      "InforSet          [4, 1, 2, 5, 3]\n",
      "Name: 0, dtype: object\n",
      "Agent 4\n",
      "   Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0       3           5         120.692  [5, 1, 2, 3, 4]\n",
      "1       4           5         119.692  [5, 1, 2, 3, 4]\n",
      "2       5           5         118.692  [5, 1, 2, 3, 4]\n",
      "3       6           5         117.692  [5, 1, 2, 3, 4]\n",
      "4       7           5         116.692  [5, 1, 2, 3, 4]\n",
      "5       8           5         115.692  [5, 1, 2, 3, 4]\n",
      "6       9           5         114.692  [5, 1, 2, 3, 4]\n",
      "7      10           5         113.692  [5, 1, 2, 3, 4]\n",
      "Highest Payoff0\n",
      "Period                          3\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            120.692\n",
      "InforSet          [5, 1, 2, 3, 4]\n",
      "Name: 0, dtype: object\n",
      "NE.Decisions: \n",
      "[2. 2. 3. 3. 3.]\n",
      "True Nature is: 1; Signal Informativeness: 0.7\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-88-9988908262bd>:24: DeprecationWarning: elementwise comparison failed; this will raise an error in the future.\n",
      "  if Decisions == [] :\n",
      "<ipython-input-88-9988908262bd>:24: DeprecationWarning: elementwise comparison failed; this will raise an error in the future.\n",
      "  if Decisions == [] :\n",
      "<ipython-input-88-9988908262bd>:24: DeprecationWarning: elementwise comparison failed; this will raise an error in the future.\n",
      "  if Decisions == [] :\n",
      "<ipython-input-88-9988908262bd>:24: DeprecationWarning: elementwise comparison failed; this will raise an error in the future.\n",
      "  if Decisions == [] :\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# *******************************************************\n",
    "# Nash Equilibrium Prediction \n",
    "# *******************************************************\n",
    "NE = copy.deepcopy(E)\n",
    "print(NE)\n",
    "#Note: Since in order to calculate the N.E. The environment will change every time people make a decision,so assign values is\n",
    "while -1 in NE.Decisions:\n",
    "    NE.SimultaneousMove()\n",
    "    NE.NextPeriod()\n",
    "    NE = DirectedNetwork(NE.NextNetwork, NE.TrueNature, NE.Sig_Acc,  NE.Waiting_Cost, NE.Payoff_Correct, NE.Payoff_Wrong, NE.NextPeriod, NE.Decisions, NE.NextInforsets)\n",
    "#This one will help calculate the payoffs\n",
    "print('NE.Decisions: ')\n",
    "print(NE.Decisions)\n",
    "# This one will give the signals each subject will obtain eventually\n",
    "NE.InforSets\n",
    "print(NE)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Linear Reward Function Equilibrium Prediction "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True Nature is: 1; Signal Informativeness: 0.7\n",
      "this is Period 0\n",
      "Agent 0\n",
      "    Period  NumSignals  ExpectedPayoff InforSet\n",
      "0        0           1         111.554   [1, 5]\n",
      "1        1           2         113.977   [1, 5]\n",
      "2        2           2         112.977   [1, 5]\n",
      "3        3           2         111.977   [1, 5]\n",
      "4        4           2         110.977   [1, 5]\n",
      "5        5           2         109.977   [1, 5]\n",
      "6        6           2         108.977   [1, 5]\n",
      "7        7           2         107.977   [1, 5]\n",
      "8        8           2         106.977   [1, 5]\n",
      "9        9           2         105.977   [1, 5]\n",
      "10      10           2         104.977   [1, 5]\n",
      "Highest Payoff1\n",
      "Period                  1\n",
      "NumSignals              2\n",
      "ExpectedPayoff    113.977\n",
      "InforSet           [1, 5]\n",
      "Name: 1, dtype: object\n",
      "Agent 1\n",
      "    Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0        0           1         111.554  [2, 1, 3, 4, 5]\n",
      "1        1           4         120.823  [2, 1, 3, 4, 5]\n",
      "2        2           5         123.246  [2, 1, 3, 4, 5]\n",
      "3        3           5         122.246  [2, 1, 3, 4, 5]\n",
      "4        4           5         121.246  [2, 1, 3, 4, 5]\n",
      "5        5           5         120.246  [2, 1, 3, 4, 5]\n",
      "6        6           5         119.246  [2, 1, 3, 4, 5]\n",
      "7        7           5         118.246  [2, 1, 3, 4, 5]\n",
      "8        8           5         117.246  [2, 1, 3, 4, 5]\n",
      "9        9           5         116.246  [2, 1, 3, 4, 5]\n",
      "10      10           5         115.246  [2, 1, 3, 4, 5]\n",
      "Highest Payoff2\n",
      "Period                          2\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            123.246\n",
      "InforSet          [2, 1, 3, 4, 5]\n",
      "Name: 2, dtype: object\n",
      "Agent 2\n",
      "    Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0        0           1         111.554  [3, 1, 2, 4, 5]\n",
      "1        1           3         117.400  [3, 1, 2, 4, 5]\n",
      "2        2           5         123.246  [3, 1, 2, 4, 5]\n",
      "3        3           5         122.246  [3, 1, 2, 4, 5]\n",
      "4        4           5         121.246  [3, 1, 2, 4, 5]\n",
      "5        5           5         120.246  [3, 1, 2, 4, 5]\n",
      "6        6           5         119.246  [3, 1, 2, 4, 5]\n",
      "7        7           5         118.246  [3, 1, 2, 4, 5]\n",
      "8        8           5         117.246  [3, 1, 2, 4, 5]\n",
      "9        9           5         116.246  [3, 1, 2, 4, 5]\n",
      "10      10           5         115.246  [3, 1, 2, 4, 5]\n",
      "Highest Payoff2\n",
      "Period                          2\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            123.246\n",
      "InforSet          [3, 1, 2, 4, 5]\n",
      "Name: 2, dtype: object\n",
      "Agent 3\n",
      "    Period  NumSignals  ExpectedPayoff   InforSet\n",
      "0        0           1         111.554  [4, 1, 5]\n",
      "1        1           2         113.977  [4, 1, 5]\n",
      "2        2           3         116.400  [4, 1, 5]\n",
      "3        3           3         115.400  [4, 1, 5]\n",
      "4        4           3         114.400  [4, 1, 5]\n",
      "5        5           3         113.400  [4, 1, 5]\n",
      "6        6           3         112.400  [4, 1, 5]\n",
      "7        7           3         111.400  [4, 1, 5]\n",
      "8        8           3         110.400  [4, 1, 5]\n",
      "9        9           3         109.400  [4, 1, 5]\n",
      "10      10           3         108.400  [4, 1, 5]\n",
      "Highest Payoff2\n",
      "Period                    2\n",
      "NumSignals                3\n",
      "ExpectedPayoff        116.4\n",
      "InforSet          [4, 1, 5]\n",
      "Name: 2, dtype: object\n",
      "Agent 4\n",
      "    Period  NumSignals  ExpectedPayoff InforSet\n",
      "0        0           1         111.554   [5, 1]\n",
      "1        1           2         113.977   [5, 1]\n",
      "2        2           2         112.977   [5, 1]\n",
      "3        3           2         111.977   [5, 1]\n",
      "4        4           2         110.977   [5, 1]\n",
      "5        5           2         109.977   [5, 1]\n",
      "6        6           2         108.977   [5, 1]\n",
      "7        7           2         107.977   [5, 1]\n",
      "8        8           2         106.977   [5, 1]\n",
      "9        9           2         105.977   [5, 1]\n",
      "10      10           2         104.977   [5, 1]\n",
      "Highest Payoff1\n",
      "Period                  1\n",
      "NumSignals              2\n",
      "ExpectedPayoff    113.977\n",
      "InforSet           [5, 1]\n",
      "Name: 1, dtype: object\n",
      "this is Period 1\n",
      "Agent 0\n",
      "   Period  NumSignals  ExpectedPayoff InforSet\n",
      "0       1           2         113.977   [1, 5]\n",
      "1       2           2         112.977   [1, 5]\n",
      "2       3           2         111.977   [1, 5]\n",
      "3       4           2         110.977   [1, 5]\n",
      "4       5           2         109.977   [1, 5]\n",
      "5       6           2         108.977   [1, 5]\n",
      "6       7           2         107.977   [1, 5]\n",
      "7       8           2         106.977   [1, 5]\n",
      "8       9           2         105.977   [1, 5]\n",
      "9      10           2         104.977   [1, 5]\n",
      "Highest Payoff0\n",
      "Period                  1\n",
      "NumSignals              2\n",
      "ExpectedPayoff    113.977\n",
      "InforSet           [1, 5]\n",
      "Name: 0, dtype: object\n",
      "Agent 1\n",
      "   Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0       1           4         120.823  [2, 1, 3, 4, 5]\n",
      "1       2           5         123.246  [2, 1, 3, 4, 5]\n",
      "2       3           5         122.246  [2, 1, 3, 4, 5]\n",
      "3       4           5         121.246  [2, 1, 3, 4, 5]\n",
      "4       5           5         120.246  [2, 1, 3, 4, 5]\n",
      "5       6           5         119.246  [2, 1, 3, 4, 5]\n",
      "6       7           5         118.246  [2, 1, 3, 4, 5]\n",
      "7       8           5         117.246  [2, 1, 3, 4, 5]\n",
      "8       9           5         116.246  [2, 1, 3, 4, 5]\n",
      "9      10           5         115.246  [2, 1, 3, 4, 5]\n",
      "Highest Payoff1\n",
      "Period                          2\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            123.246\n",
      "InforSet          [2, 1, 3, 4, 5]\n",
      "Name: 1, dtype: object\n",
      "Agent 2\n",
      "   Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0       1           3         117.400  [3, 1, 2, 4, 5]\n",
      "1       2           5         123.246  [3, 1, 2, 4, 5]\n",
      "2       3           5         122.246  [3, 1, 2, 4, 5]\n",
      "3       4           5         121.246  [3, 1, 2, 4, 5]\n",
      "4       5           5         120.246  [3, 1, 2, 4, 5]\n",
      "5       6           5         119.246  [3, 1, 2, 4, 5]\n",
      "6       7           5         118.246  [3, 1, 2, 4, 5]\n",
      "7       8           5         117.246  [3, 1, 2, 4, 5]\n",
      "8       9           5         116.246  [3, 1, 2, 4, 5]\n",
      "9      10           5         115.246  [3, 1, 2, 4, 5]\n",
      "Highest Payoff1\n",
      "Period                          2\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            123.246\n",
      "InforSet          [3, 1, 2, 4, 5]\n",
      "Name: 1, dtype: object\n",
      "Agent 3\n",
      "   Period  NumSignals  ExpectedPayoff   InforSet\n",
      "0       1           2         113.977  [4, 1, 5]\n",
      "1       2           3         116.400  [4, 1, 5]\n",
      "2       3           3         115.400  [4, 1, 5]\n",
      "3       4           3         114.400  [4, 1, 5]\n",
      "4       5           3         113.400  [4, 1, 5]\n",
      "5       6           3         112.400  [4, 1, 5]\n",
      "6       7           3         111.400  [4, 1, 5]\n",
      "7       8           3         110.400  [4, 1, 5]\n",
      "8       9           3         109.400  [4, 1, 5]\n",
      "9      10           3         108.400  [4, 1, 5]\n",
      "Highest Payoff1\n",
      "Period                    2\n",
      "NumSignals                3\n",
      "ExpectedPayoff        116.4\n",
      "InforSet          [4, 1, 5]\n",
      "Name: 1, dtype: object\n",
      "Agent 4\n",
      "   Period  NumSignals  ExpectedPayoff InforSet\n",
      "0       1           2         113.977   [5, 1]\n",
      "1       2           2         112.977   [5, 1]\n",
      "2       3           2         111.977   [5, 1]\n",
      "3       4           2         110.977   [5, 1]\n",
      "4       5           2         109.977   [5, 1]\n",
      "5       6           2         108.977   [5, 1]\n",
      "6       7           2         107.977   [5, 1]\n",
      "7       8           2         106.977   [5, 1]\n",
      "8       9           2         105.977   [5, 1]\n",
      "9      10           2         104.977   [5, 1]\n",
      "Highest Payoff0\n",
      "Period                  1\n",
      "NumSignals              2\n",
      "ExpectedPayoff    113.977\n",
      "InforSet           [5, 1]\n",
      "Name: 0, dtype: object\n",
      "this is Period 2\n",
      "Agent 1\n",
      "   Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0       2           5         123.246  [2, 1, 3, 4, 5]\n",
      "1       3           5         122.246  [2, 1, 3, 4, 5]\n",
      "2       4           5         121.246  [2, 1, 3, 4, 5]\n",
      "3       5           5         120.246  [2, 1, 3, 4, 5]\n",
      "4       6           5         119.246  [2, 1, 3, 4, 5]\n",
      "5       7           5         118.246  [2, 1, 3, 4, 5]\n",
      "6       8           5         117.246  [2, 1, 3, 4, 5]\n",
      "7       9           5         116.246  [2, 1, 3, 4, 5]\n",
      "8      10           5         115.246  [2, 1, 3, 4, 5]\n",
      "Highest Payoff0\n",
      "Period                          2\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            123.246\n",
      "InforSet          [2, 1, 3, 4, 5]\n",
      "Name: 0, dtype: object\n",
      "Agent 2\n",
      "   Period  NumSignals  ExpectedPayoff         InforSet\n",
      "0       2           5         123.246  [3, 1, 2, 5, 4]\n",
      "1       3           5         122.246  [3, 1, 2, 5, 4]\n",
      "2       4           5         121.246  [3, 1, 2, 5, 4]\n",
      "3       5           5         120.246  [3, 1, 2, 5, 4]\n",
      "4       6           5         119.246  [3, 1, 2, 5, 4]\n",
      "5       7           5         118.246  [3, 1, 2, 5, 4]\n",
      "6       8           5         117.246  [3, 1, 2, 5, 4]\n",
      "7       9           5         116.246  [3, 1, 2, 5, 4]\n",
      "8      10           5         115.246  [3, 1, 2, 5, 4]\n",
      "Highest Payoff0\n",
      "Period                          2\n",
      "NumSignals                      5\n",
      "ExpectedPayoff            123.246\n",
      "InforSet          [3, 1, 2, 5, 4]\n",
      "Name: 0, dtype: object\n",
      "Agent 3\n",
      "   Period  NumSignals  ExpectedPayoff   InforSet\n",
      "0       2           3           116.4  [4, 1, 5]\n",
      "1       3           3           115.4  [4, 1, 5]\n",
      "2       4           3           114.4  [4, 1, 5]\n",
      "3       5           3           113.4  [4, 1, 5]\n",
      "4       6           3           112.4  [4, 1, 5]\n",
      "5       7           3           111.4  [4, 1, 5]\n",
      "6       8           3           110.4  [4, 1, 5]\n",
      "7       9           3           109.4  [4, 1, 5]\n",
      "8      10           3           108.4  [4, 1, 5]\n",
      "Highest Payoff0\n",
      "Period                    2\n",
      "NumSignals                3\n",
      "ExpectedPayoff        116.4\n",
      "InforSet          [4, 1, 5]\n",
      "Name: 0, dtype: object\n",
      "NE.Decisions: \n",
      "[1. 2. 2. 2. 1.]\n",
      "True Nature is: 1; Signal Informativeness: 0.7\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-88-9988908262bd>:24: DeprecationWarning: elementwise comparison failed; this will raise an error in the future.\n",
      "  if Decisions == [] :\n",
      "<ipython-input-88-9988908262bd>:24: DeprecationWarning: elementwise comparison failed; this will raise an error in the future.\n",
      "  if Decisions == [] :\n",
      "<ipython-input-88-9988908262bd>:24: DeprecationWarning: elementwise comparison failed; this will raise an error in the future.\n",
      "  if Decisions == [] :\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# *******************************************************\n",
    "# Linear Reward Function Equilibrium Prediction \n",
    "# *******************************************************\n",
    "LinearEq = copy.deepcopy(E)\n",
    "print(LinearEq)\n",
    "#Note: Since in order to calculate the N.E. The environment will change every time people make a decision,so assign values is\n",
    "while -1 in LinearEq.Decisions:\n",
    "    LinearEq.SimultaneousMove_linear()\n",
    "    LinearEq.NextPeriod()\n",
    "    LinearEq = DirectedNetwork(LinearEq.NextNetwork, LinearEq.TrueNature, LinearEq.Sig_Acc,  LinearEq.Waiting_Cost, LinearEq.Payoff_Correct, \n",
    "                               LinearEq.Payoff_Wrong, LinearEq.NextPeriod, LinearEq.Decisions, LinearEq.NextInforsets)\n",
    "#This one will help calculate the payoffs\n",
    "print('NE.Decisions: ')\n",
    "print(LinearEq.Decisions)\n",
    "# This one will give the signals each subject will obtain eventually\n",
    "LinearEq.InforSets\n",
    "print(LinearEq)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### In this section, I want to simulate all possible networks' NE predictions in an excel "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nash Equilibrium Data Generations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "E.AssignSignals()\n",
    "# *******************************************************\n",
    "#  Data Generations\n",
    "# *******************************************************\n",
    "# Obtain the NE's agent's guesses\n",
    "NE_Half_Guess = np.zeros(len(NE.Decisions))\n",
    "NE_Self_Guess = np.zeros(len(NE.Decisions))\n",
    "for i in range(len(NE.Decisions)):\n",
    "    # Subject 2's inforset\n",
    "    # print(E.Signals)\n",
    "    Decide = 0\n",
    "\n",
    "    for x in NE.InforSets[i]:\n",
    "        Decide += E.Signals[x-1]\n",
    "\n",
    "    if Decide > 0:\n",
    "        NE_Half_Guess[i] = 1\n",
    "        NE_Self_Guess[i] = 1\n",
    "    elif Decide < 0 :\n",
    "        NE_Half_Guess[i] = -1\n",
    "        NE_Self_Guess[i] = -1\n",
    "    elif Decide == 0 :\n",
    "        NE_Half_Guess[i] = 2*np.random.randint(2)-1\n",
    "        NE_Self_Guess[i] =  E.Signals[i]\n",
    "\n",
    "print(E.TrueNature)\n",
    "print(E.Signals)\n",
    "print(NE_Half_Guess)\n",
    "print(NE_Self_Guess)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "NVE= copy.deepcopy(E)\n",
    "print(NVE)\n",
    "NVE.Network.in_degree(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Behavioral Predictions  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Behavioral Prediction (Rule 1) Data Generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# *******************************************************\n",
    "# Behavioral Prediction (Rule 1)\n",
    "# *******************************************************\n",
    "\n",
    "NVE= DirectedNetworkAndRealizedSignals(E, E.Signals)\n",
    "print(NVE)\n",
    "# while -1 in NVE.Decisions:\n",
    "NVE.SimultaneousMove()\n",
    "NVE.NextPeriod()\n",
    "NVEDirected = DirectedNetwork(NVE.NextNetwork, NVE.DirectedNetwork.TrueNature, NVE.DirectedNetwork.Sig_Acc, \n",
    "                              NVE.DirectedNetwork.Waiting_Cost, NVE.DirectedNetwork.Payoff_Correct, \n",
    "                              NVE.DirectedNetwork.Payoff_Wrong, NVE.NextPeriod, NVE.Decisions, NVE.NextInforsets)\n",
    "NVE=DirectedNetworkAndRealizedSignals(NVEDirected, E.Signals, NVE.Half_Guess,  NVE.Self_Guess)\n",
    "NVE.SimultaneousMove()\n",
    "NVE.NextPeriod()\n",
    "\n",
    "print(NVE.Decisions)\n",
    "print(NVE.Half_Guess)\n",
    "print(NVE.Self_Guess)\n",
    "\n",
    "#This one will help calculate the payoffs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "NVE.Half_Guess"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(NVEDirected)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "NVE.Decisions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # In real simulations, NE predictions can be used \n",
    "# # This step, assign the same signals to all different simulations\n",
    "# E.AssignSignals()\n",
    "\n",
    "# # Obtain the Naive agent's guesses\n",
    "# NVE= copy.deepcopy(E)\n",
    "# NVE_Half_Guess = np.zeros(nx.number_of_nodes(NVE.Network))\n",
    "# NVE_Self_Guess = np.zeros(nx.number_of_nodes(NVE.Network))\n",
    "\n",
    "\n",
    "# period = 0\n",
    "# for j in range(nx.number_of_nodes(NVE.Network)):  \n",
    "#     # If one node's own indegree is 1, make deciion immediately\n",
    "#     if NVE.Network.in_degree(j+1) == 1 : \n",
    "#         NVE.Decisions[j] = 0\n",
    "#         NVE_Half_Guess[j] = NVE.InforSets[j][0]\n",
    "#         NVE_Self_Guess[j] = NVE.InforSets[j][0]\n",
    "        \n",
    "        \n",
    "# period = 1\n",
    "# NewInforsets = copy.deepcopy(NVE.InforSets)\n",
    "# for j in range(nx.number_of_nodes(NVE.Network) ):  \n",
    "#     if NVE.Decisions[j]== 0 :\n",
    "#         # Update each node's inforsets\n",
    "#         temp = NVE.InforSets[j]\n",
    "#         for i in range(nx.number_of_nodes(NVE.Network)):\n",
    "#             if (i != j) and NVE.Network.has_edge(i+1,j+1) :\n",
    "#                 for x in NVE.InforSets[i] :\n",
    "#                     if x not in temp:\n",
    "#                                 temp.append(x)         \n",
    "#                 NewInforsets[j]=temp\n",
    "\n",
    "#         # Based on the signals' realization, makes a decision        \n",
    "#         Decide = 0\n",
    "#         for x in temp :\n",
    "#             Decide += E.Signals[x-1]\n",
    "#         if Decide > 0 :\n",
    "#             NVE.Decisions[j] = period\n",
    "#             NVE_Half_Guess[j] = 1\n",
    "#             NVE_Self_Guess[j] = 1\n",
    "#         elif  Decide < 0 :\n",
    "#             NVE.Decisions[j] = period\n",
    "#             NVE_Half_Guess[j] = -1\n",
    "#             NVE_Self_Guess[j] = -1\n",
    "\n",
    "#             # Secondly, based on decisions, \"down-grade\" the network structure\n",
    "#             NextNetwork = copy.deepcopy(NVE.Network)\n",
    "#             for j in range(NVE.Network.number_of_nodes()) :\n",
    "#                 if  NVE.Decisions[j] == period :\n",
    "#                     NextNetwork.remove_edges_from(list(NextNetwork.in_edges(j+1)))\n",
    "\n",
    "# if -1 in NVE.Decisions :\n",
    "#     NVE = DirectedNetwork(NextNetwork, NVE.TrueNature, NVE.Sig_Acc,  NVE.waiting_cost, NVE.payoff_correct, NVE.payoff_wrong, period, NVE.Decisions, NewInforsets)\n",
    "#     period += 1\n",
    "#     for j in range(nx.number_of_nodes(NVE.Network)):  \n",
    "#         if NVE.Decisions[j] == -1 :\n",
    "#         # If one node's own indegree is 1, make deciion immediately\n",
    "#             if NVE.Network.in_degree(j+1) == 1 : \n",
    "#                 NVE.Decisions[j] = period\n",
    "#                 NVE_Half_Guess[j] = 2*np.random.randint(2)-1\n",
    "#                 NVE_Self_Guess[j] = E.Signals[j]\n",
    "#             else :\n",
    "#                 print(\"something's off, since it's 5 nodes; may need to loop back if n>5\")\n",
    "\n",
    "\n",
    "# #This one will help calculate the payoffs\n",
    "              "
   ]
  }
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