ZIAgentsGames.ipynb

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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "<font color=\"red\">Games in a Population of ZI Agents</font>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Jose Manuel MAGALLANES**  \n",
      "PhD Program in Computational Social Science  \n",
      "George Mason University  \n",
      "SPRING 2014"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PART A:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Section 1:**"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Instantiate a population of 100-1000 agents and have them play a game that does not have a dominant strategy (e.g., coordination, battle of the sexes,chicken). Initially the agents have **random strategies**. Treat them as innocent of the actual payoffs and of game theoretic-type reasoning (e.g., about dominant strategies). "
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "<font color=\"darkblue\">Here we will creat our **Player** (ZI agent) and out game class. We first present the libraries needed, as well as the coding of the classes:</font>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* <font color=\"blue\">**Importing functions to use:**</font>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from random import choice, sample, shuffle\n",
      "from numpy import mean\n",
      "import matplotlib.pyplot as plot\n",
      "from collections import Counter\n",
      "import time\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* <font color=\"blue\">**Initial Player class (agent) with random strategy:**</font>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class BasicPlayer(object):\n",
      "    '''\n",
      "    The BasicPlayer is initilized with a code (see method createAgents in Game below).\n",
      "    At the begining they will have a random strategy, which may change according to\n",
      "    what is specified in the method get_strategy.\n",
      "    This initial strategy is inmediately store in a list called record, which\n",
      "    will have the history of his moves and payoffs.\n",
      "    '''\n",
      "    \n",
      "    def __init__(self,code):\n",
      "        '''\n",
      "        constructor of agent with code, initial strategy \n",
      "        and a list recording that strategy, and the subsequent ones\n",
      "        '''\n",
      "        self.code=code\n",
      "        self.strategy=choice(('Dancing','Football'))\n",
      "        self.record=[(self.strategy,0)]\n",
      "        \n",
      "    def get_strategy(self):\n",
      "        '''\n",
      "        This is the basic method to return a strategy \n",
      "        to any other method that calls it.\n",
      "        In this basic version, it just returns the same strategy which\n",
      "        was assigned when the agent was initialized.\n",
      "        '''\n",
      "        return self.strategy\n",
      "\n",
      "    def update_record(self,strategy,payoff):\n",
      "        ''' \n",
      "        method in charge of updating \n",
      "        the history of strategies and payoffs \n",
      "        of the player\n",
      "        '''\n",
      "        self.record.append((strategy,payoff))\n",
      "        \n",
      "    def last_strategy(self):\n",
      "        '''\n",
      "        method that returns the\n",
      "        previous strategy played\n",
      "        '''\n",
      "        last_strategy,payoff=self.record[len(self.record)-1]\n",
      "        return last_strategy\n",
      "    \n",
      "    def getPlayer(self):\n",
      "        ''' \n",
      "        method that returns an\n",
      "        integer containing the index or code\n",
      "        of the agent.\n",
      "        '''\n",
      "        return self.code"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* <font color=\"blue\">**Game class:**</font>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class Game(object):\n",
      "    '''\n",
      "    This class will make the agents play the game; for that\n",
      "    a list of agents must be supplied.\n",
      "    The game depends on the payoff_matrix given.\n",
      "    The game saves the history of Payoffs and Strategies played\n",
      "    every moment.\n",
      "    '''\n",
      "    def __init__(self,list_of_agents,payoff_matrix):  \n",
      "        '''\n",
      "        Constructor initializing\n",
      "        game variables.\n",
      "        '''\n",
      "        self.players=list_of_agents\n",
      "        self.payoffmat = payoff_matrix\n",
      "        self.historyPayoff = list()\n",
      "        self.historyStrategy = list()\n",
      "\n",
      "    def run(self):\n",
      "        '''\n",
      "        The run makes a couple of agents play the game.\n",
      "        Here me make a call to a method that will give the\n",
      "        order of activation of agents.\n",
      "        '''\n",
      "        activated=self.activateAgents(self.players)\n",
      "        self.players=activated[:]\n",
      "        for agent in self.players:\n",
      "            p1=agent\n",
      "            i=p1.code\n",
      "            if i==len(self.players)-1:\n",
      "                index=0\n",
      "            else:\n",
      "                index= i+1\n",
      "            p2=self.players[index]\n",
      "            strategy_p1,strategy_p2 = p1.get_strategy(), p2.get_strategy()\n",
      "            payoff_p1, payoff_p2= self.payoffmat[strategy_p1,strategy_p2] #here they play the game!\n",
      "            self.historyStrategy.append((strategy_p1,strategy_p2))\n",
      "            self.historyPayoff.append((payoff_p1,payoff_p2))\n",
      "            p1.update_record(strategy_p1,payoff_p1)\n",
      "            p2.update_record(strategy_p2,payoff_p2)\n",
      "    \n",
      "    def activateAgents(self,agent_list):\n",
      "        '''\n",
      "        A different sequence of agents will be given\n",
      "        every time this method is called.\n",
      "        '''\n",
      "        activatedPlayers=agent_list[:]\n",
      "        shuffle(activatedPlayers)\n",
      "        return activatedPlayers\n",
      "\n",
      "    def result(self):\n",
      "        '''\n",
      "        Here we give the mean payoff \n",
      "        of the history game, as it is being played.\n",
      "        '''\n",
      "        payoffs = self.historyPayoff\n",
      "        pay1, pay2 = zip(*payoffs) \n",
      "        return  mean([mean(pay1), mean(pay2)])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**<font color=\"darkblue\">Here we have our helping and *main* function and parameters that will be used in all the experiments:</font>**"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* <font color=\"blue\">**Helping functions:**</font>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def createPlayers(population,agentType):\n",
      "    \"\"\"\n",
      "    Here, we will return a LIST\n",
      "    containing a population of Agents\n",
      "    \"\"\"\n",
      "    return [agentType(code=i) for i in range(population)]\n",
      "\n",
      "def plot_game_distribution(list_of_average_performance_per_round):\n",
      "    '''\n",
      "    procedure to plot the player performance;\n",
      "    a list of averages per player must be supplied\n",
      "    '''\n",
      "    plot.figure(figsize=(20,5))\n",
      "    plot.xlabel('mean payoff', fontsize=18)\n",
      "    plot.ylabel('count', fontsize=16)\n",
      "    plot.title(\"Distribution of the mean payoff per agent\",fontsize=20)\n",
      "    plot.hist(list_of_average_performance_per_player)\n",
      "    plot.show()\n",
      "\n",
      "def plot_game_timeSeries(list_of_average_performance_per_round):\n",
      "    '''\n",
      "    procedure to plot the game performance;\n",
      "    a list of averages per round must be supplied\n",
      "    '''\n",
      "    plot.figure(figsize=(20,5))\n",
      "    plot.xlabel('matches', fontsize=18)\n",
      "    plot.ylabel('average payoff', fontsize=16)\n",
      "    plot.plot(list_of_average_performance_per_round)\n",
      "    plot.axhline(y=1.5,color='r',ls='--',lw=2)\n",
      "    plot.ylim(0,2)\n",
      "    plot.title(\"Trend of the cummulative average payoff of the total ZI agents\",fontsize=20)\n",
      "    plot.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* <font color=\"blue\">**Main:**</font>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def main(rounds,list_of_Agents,payoff_matrix):\n",
      "    '''\n",
      "    Main function determines how many rounds should be played.\n",
      "    '''\n",
      "    game = Game(list_of_Agents,payoff_matrix)\n",
      "    performance_per_round=[]\n",
      "    for i in xrange(rounds):\n",
      "        game.run()\n",
      "        x=game.result()\n",
      "        performance_per_round.append(x) #collecting performance per round\n",
      "    return performance_per_round"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* <font color=\"blue\">**Parameters:**</font>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "PAYOFFMAT= {('Dancing','Dancing'):(2,1), ('Dancing','Football'):(0,0),\n",
      "            ('Football','Dancing'):(0,0), ('Football','Football'):(1,2)}\n",
      "POPULATION=100\n",
      "RUNS=1000"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## <font color=\"blue\">**Testing Basic Player:**</font>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**<font color=\"darkblue\">Here we will test the behavior of the game with this basic player:</font>**"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* <font color=\"blue\">**Initialization:**</font>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "list_of_BasicAgents=createPlayers(POPULATION,agentType=BasicPlayer)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* <font color=\"blue\">**Executing main:**</font>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gamePayoffs=main(RUNS,list_of_BasicAgents,PAYOFFMAT)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_game_distribution(gamePayoffs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
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       "output_type": "display_data",
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AAHFxccjJyUFOTg6Cg4OxYcMGdO/eHe3btze1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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e40c5d0>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_game_timeSeries(gamePayoffs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10e434790>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Section 2:**"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Coding the agents to **\u2018grope\u2019 for better payoffs**. That is they play their current strategy a few times and see what kinds of payoffs they get. They occasionally sample other strategies. They cannot observe other agents playing the game but they have perfect memory of their past plays. The population coevolves.\n",
      "Run the  model long enough that some steady-state is attained."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**<font color=\"darkblue\">To grope for better payoffs, we need to make some changes to the BasicPlayer class:</font>**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class BetterPlayer(BasicPlayer):\n",
      "    '''\n",
      "    BetterPlayer is a 'child' of the BasicPlayer class.\n",
      "    It will inherit the constructor and the methods. \n",
      "    Some changes are proposed (below)\n",
      "    '''\n",
      "        \n",
      "    def get_strategy(self):\n",
      "        '''\n",
      "        This inherited methos will be modified.\n",
      "        Here, the agent will check its performance\n",
      "        every ten games played; and \n",
      "        if 0 payoff is predominant, it will change its current strategy.\n",
      "        '''\n",
      "        if len(self.record)%10==0:\n",
      "            check=Counter(zip(*self.record)[1]) #here we get the mode as a tuple\n",
      "            if 0 in check.most_common(1)[0]:    #the first value indicates the payoff (index 0)\n",
      "                self.strategy=self.get_otherStrategy(self.last_strategy())\n",
      "                return self.get_otherStrategy(self.last_strategy())\n",
      "        return self.strategy\n",
      "    \n",
      "    def get_otherStrategy(self,strategy):\n",
      "        '''\n",
      "        this will give the strategy that was not being played\n",
      "        '''\n",
      "        if strategy=='Dancing':\n",
      "            return 'Football'\n",
      "        else:\n",
      "            return 'Dancing'   "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* <font color=\"blue\">**Initialization:**</font>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "list_of_BetterAgents=createPlayers(POPULATION,agentType=BetterPlayer)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* <font color=\"blue\">**Experimenting with \"BETTER AGENT\":**</font>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gamePayoffs=main(RUNS,list_of_BetterAgents,PAYOFFMAT)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* <font color=\"blue\">**Results:**</font>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_game_distribution(gamePayoffs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10df23550>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_game_timeSeries(gamePayoffs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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CCZwAAAAAKJTACQAAAIBCCZwAAAAAKJTACQAA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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10df1c3d0>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**<font color=\"darkblue\">Here we offer a different version, now a \"BEST PLAYER\":</font>**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class BestPlayer(BetterPlayer):\n",
      "    '''\n",
      "    BestPlayer is a 'child' of the BetterPlayer class.\n",
      "    It will inherit the constructor and the methods. \n",
      "    Some changes are proposed (below)\n",
      "    '''\n",
      "        \n",
      "    def get_strategy(self):\n",
      "        '''\n",
      "        This inherited method will a light modification.\n",
      "        After the agent verifies its performance, it will only check\n",
      "        the strategies after the last checkpoint. \n",
      "        '''\n",
      "        flag=len(self.record)\n",
      "        if flag%10==0:\n",
      "            if flag>=20:\n",
      "                checkpoint=Counter(zip(*self.record[flag-20:])[1])\n",
      "                if 0 in checkpoint.most_common(1)[0]: \n",
      "                    self.strategy=self.get_otherStrategy(self.last_strategy())\n",
      "                    return self.get_otherStrategy(self.last_strategy())\n",
      "            else:\n",
      "                checkpoint=Counter(zip(*self.record)[1])\n",
      "                if 0 in checkpoint.most_common(1)[0]: \n",
      "                    self.strategy=self.get_otherStrategy(self.last_strategy())\n",
      "                    return self.get_otherStrategy(self.last_strategy())\n",
      "        return self.strategy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* <font color=\"blue\">**Initialization:**</font>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "list_of_BestAgents=createPlayers(POPULATION,agentType=BestPlayer)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* <font color=\"blue\">**Experimenting with \"BEST AGENT\":**</font>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gamePayoffs=main(RUNS,list_of_BestAgents,PAYOFFMAT)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* <font color=\"blue\">**Results:**</font>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_game_distribution(gamePayoffs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10bdd59d0>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_game_timeSeries(gamePayoffs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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XXnopDz74YO6///7s2LEjf/nLX9Ki\nRYt07do1zz33XCZPnpwlS5bk2muvzeGHH57Kysr069dvl+r9z3MHHHBAnnjiiUybNi2///3vc+ed\nd2bbtm059thj069fv1x88cVJkkMOOSSTJk3KY489lgULFmT79u3p169fJk+enAsuuCAtWrTYrZ8R\nAMDuKit5Ty4AAAAABbKHEwAAAACFEjgBAAAAUCiBEwAAAACFEjgBAAAAUCiBEwAAAACFEjgBAAAA\nUCiBEwAAAACFEjgBAAAAUCiBEwAAAACFEjgBAAAAUKj/Add20lGtodfOAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11011a110>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Part B:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Run your model multiple times with the same population size and for the same game.\n",
      "Characterize the run-to-run variation you observe."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gamePayoffs_listBETTER=[]\n",
      "for i in xrange(10):\n",
      "    list_of_BetterAgents=createPlayers(POPULATION,agentType=BetterPlayer)\n",
      "    gamePayoffsBT=main(RUNS,list_of_BetterAgents,PAYOFFMAT)\n",
      "    gamePayoffs_listBETTER.append(gamePayoffsBT)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gamePayoffs_listBEST=[]\n",
      "for i in xrange(10):\n",
      "    list_of_BestAgents=createPlayers(POPULATION,agentType=BestPlayer)\n",
      "    gamePayoffsBS=main(RUNS,list_of_BestAgents,PAYOFFMAT)\n",
      "    gamePayoffs_listBEST.append(gamePayoffsBS)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "BEST=[mean (x) for x in gamePayoffs_listBEST]\n",
      "BETTER=[mean (x) for x in gamePayoffs_listBETTER]\n",
      "BOTH=[BEST,BETTER]\n",
      "data = [data for data in BOTH]\n",
      "plot.figure(figsize=(12,5))\n",
      "box = plot.boxplot(data, notch=True, patch_artist=True)\n",
      "colors = ['green', 'blue']\n",
      "for patch, color in zip(box['boxes'], colors):\n",
      "    patch.set_facecolor(color)\n",
      "plot.xticks([1, 2], ['BestPlayer', 'BetterPlayer'])\n",
      "plot.axhline(y=0.755,color='r',ls='--',lw=2)\n",
      "plot.ylabel('average payoff', fontsize=16)\n",
      "plot.title(\"Comparisson of BestPlayer vs BetterPlayer\",fontsize=20)\n",
      "plot.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Kh787qTLimG8iIiIionLEMd9ERERERBUAk28iIiIiIj1h8k1EREREpCdMvomI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\nAd6LR85wJwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x111944750>"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**<font color=\"darkblue\">As the boxplots show, there might be a significant variation between the performance of those two kinds of agents. In each case each set of agents went 1000 rounds.</font>**"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Part C:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Do your agents arrive at either pure or mixed strategy Nash equilibria? Is it reasonable to say that agent-level equilibria emerge in your model runs? Do social norms arise? Can you imagine long run configurations of your model that are different from what you obtained."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**<font color=\"darkblue\">By the nature of the experiment the agents follow a mixed strategy. Besides, as no top-down constraint or rule has been given, it is fair to say that the equilibrium seen in the results emerges out the game among the ZI agents.\n",
      "It is not clear if social normas may arise, as the norm of changing the strategy has been explicitly coded.\n",
      "A different long-run may appear if the period to decide when to asses performance varies.</font>**"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Part D:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "How do your results depend on the number of agents? Phrase your answer in terms of the speed of convergence, stability of steady-state, character of the transient dynamics, and so on."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**<font color=\"darkblue\">To get some ideas related to this question, we are going to run the game 500 rounds for different populations of agents, starting from 100 agents until 1000 agents, with a population increase of 100.</font>**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gamePayoffs_listBETTER=[]\n",
      "timeGame=[]\n",
      "start=100\n",
      "step=100\n",
      "stop=1000\n",
      "while start<=stop:\n",
      "    timeStart=time.time()\n",
      "    listBetter=createPlayers(population=start,agentType=BetterPlayer)\n",
      "    gamePayoffsBT=main(rounds=1000,list_of_Agents=listBetter,payoff_matrix=PAYOFFMAT) # we keep 1000\n",
      "    gamePayoffs_listBETTER.append(gamePayoffsBT)\n",
      "    timeEnd=time.time()\n",
      "    timeGame.append(timeEnd-timeStart)\n",
      "    start+=step"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = [data for data in gamePayoffs_listBETTER]\n",
      "\n",
      "plot.figure(figsize=(18,5))\n",
      "box = plot.boxplot(data, notch=True, patch_artist=True)\n",
      "plot.xticks(range(1,11),range(100,1001,100) )\n",
      "plot.title(\"Comparisson of Performance at different number of agents using BetterPlayer\",fontsize=10)\n",
      "plot.xlabel('Number of Agents', fontsize=16)\n",
      "plot.ylabel('Average payoff', fontsize=16)\n",
      "plot.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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R6bOmGw8crcOE+fsDv/widRREpomfD6KGcUQb02NvD1RWSh2Fdat7kr9okaJs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\n+6Q4WgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e40c590>"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot.figure(figsize=(20,5))\n",
      "plot.xlabel('# Agents', fontsize=18)\n",
      "plot.ylabel('time taken', fontsize=16)\n",
      "plot.plot(timeGame,lw=2)\n",
      "plot.title(\"Time as number of agents increases (1000 rounds in each case)\",fontsize=20)\n",
      "plot.xlabel('Number of Agents ', fontsize=16)\n",
      "plot.ylabel('Time consumed', fontsize=16)\n",
      "plot.xticks(range(0,10),range(100,1001,100) )\n",
      "for x in range(0,11):\n",
      "    plot.axvline(x,color='k',ls='--',lw=0.5)\n",
      "\n",
      "\n",
      "# ytikcs\n",
      "\n",
      "plot.yticks(timeGame, [round(x/60,2) for x in timeGame])\n",
      "for y in [x for x in timeGame]:\n",
      "    plot.axhline(y ,color='r',ls='--',lw=0.5)\n",
      "plot.ylabel('minutes')\n",
      "plot.xlim(-1,10)\n",
      "plot.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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cuXPo16+fVQGpefPmaNOmDRISEvDpp59a2m/dumUZvWGO416ZryWffvqpVVHs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       "text": [
        "<matplotlib.figure.Figure at 0x122d11e90>"
       ]
      }
     ],
     "prompt_number": 79
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**<font color=\"darkblue\">As we see, the number of agents do not present clear cut different results respect to the emergent equilibrium; that is, the output from the process coded is indifferent to the number of agents.  \n",
      "On the other hand, the speed increases in a linear fashion as the number of the agents increases, and the previous result makes this finding consistent (no non-linear behavior was expected).</font>**"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}