analyse_game.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import csv\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "hero_names = [u'adagio',\n",
    " u'ardan',\n",
    " u'vox',\n",
    " u'krul',\n",
    " u'celeste',\n",
    " u'ringo',\n",
    " u'catherine',\n",
    " u'skaarf',\n",
    " u'koshka',\n",
    " u'taka',\n",
    " u'petal',\n",
    " u'rona',\n",
    " u'glaive',\n",
    " u'saw',\n",
    " u'joule',\n",
    " u'fortress']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def build_game(row_player_file, col_player_file):\n",
    "    \"\"\"Import the bi matrices and create the game object\"\"\"\n",
    "    bi_matrices = []\n",
    "    for fle in [row_player_file, col_player_file]:\n",
    "        f = open(fle, 'r')\n",
    "        csvrdr = csv.reader(f)\n",
    "        bi_matrices.append(-matrix([[float(ele) for ele in row] for row in csvrdr]))\n",
    "        f.close()\n",
    "\n",
    "    return NormalFormGame(bi_matrices)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "g = build_game(\"data/A.csv\", \"data/B.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us take a look at the payoff matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[ -1.0 -0.50 -0.19  -3.0  -1.0  -1.5  -4.0 -0.75  -3.0  -2.0  -2.0 -0.50  -3.0  -3.0  -2.0 -0.50]\n",
       "[ -1.5  -2.0  -1.5  -4.0  -1.5  -2.0  -2.0  -3.0  -3.0  -3.0  -2.0 -0.50  -3.0  -4.0  -3.0  -1.5]\n",
       "[ -3.0  -2.0  -3.0  -4.0  -3.0  -4.0  -1.5  -2.0  -6.0  -6.0  -2.0 -0.75  -3.0  -3.0  -2.0  -1.0]\n",
       "[ -3.0  -2.0  -3.0  -4.0  -3.0  -4.0  -4.0  -4.0  -4.0  -6.0  -3.0  -1.0  -4.0  -4.0  -4.0  -1.5]\n",
       "[ -1.5  -3.0  -2.0  -4.0  -3.0  -4.0  -4.0  -4.0  -8.0  -8.0  -4.0  0.00  -6.0  -3.0  -2.0  -2.0]\n",
       "[ -2.0  -1.5 -0.75  -3.0  -2.0  -1.5  -4.0  -2.0  -4.0  -4.0  -4.0  0.00  -4.0  -3.0  -3.0 -0.38]\n",
       "[ -3.0  -1.0 -0.50  -3.0  -1.0  -2.0  -2.0  -2.0  -2.0  -2.0  -4.0  -1.0  -3.0  -2.0  -2.0 -0.75]\n",
       "[ -2.0  -1.0  -2.0  -4.0  -1.0  -4.0  -4.0  -2.0  -4.0  -8.0  -4.0  0.00  -6.0  -1.5  -2.0 -0.25]\n",
       "[ -1.5 -0.38 -0.75  -4.0 -0.75  -2.0  -3.0  -1.0  -2.0  -2.0  -1.5 -0.19  -4.0  -1.5  -2.0 -0.12]\n",
       "[ -4.0  0.00  0.00  -3.0  0.00  -1.5  -6.0  -1.0  -3.0  -4.0  -2.0  0.00  -3.0  -4.0  -4.0  0.00]\n",
       "[ -2.0  -1.5  -1.5  -1.5  -1.0  -1.5  -1.0  -1.0  -4.0  -3.0  -3.0 -0.50  -2.0  -2.0  -1.5  -1.0]\n",
       "[ -2.0  -2.0  -3.0  -4.0  -4.0  -2.0  -3.0  -3.0  -3.0  -3.0  -1.5  -2.0  -4.0  -2.0  -2.0  -2.0]\n",
       "[ -2.0  -1.5  -2.0  -6.0  -1.5  -4.0  -4.0  -2.0  -3.0  -4.0  -4.0  -1.0  -2.0  -3.0  -3.0  -1.5]\n",
       "[ -2.0 -0.50  -1.0  -3.0  -1.5  -2.0  -4.0  -2.0  -4.0  -3.0  -2.0 -0.50  -4.0  -2.0  -4.0 -0.50]\n",
       "[ -3.0  -2.0  -1.5  -4.0  -2.0  -4.0  -3.0  -2.0  -4.0  -6.0  -3.0 -0.38  -4.0  -3.0  -3.0  -1.0]\n",
       "[ -2.0  -1.5  -2.0  -3.0  -3.0  -2.0  -2.0  -2.0  -2.0  -4.0  -2.0 -0.75  -3.0  -2.0  -3.0  -2.0]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = g.payoff_matrices()[0].n(digits=0)\n",
    "m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After a question on reddit finding the charachters which pose the greatest total threat:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[u'krul', u'catherine', u'koshka', u'taka', u'glaive']"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_of_threats = [sum([row[k] for row in m])  for k in range(16)]\n",
    "[hero_names[i] for i, score in enumerate(sum_of_threats) if score == min(sum_of_threats)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a graphical representation of this for the row player:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RDOL/z0UXXaSjR486HTt69CivP/gfhYWFLl8vNputWv6l4C1xcXGqW7eutm7dqubNm0s6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\nTA60oAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(g.payoff_matrices()[0], colorbar=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the same for the column player (as expected these are just reflections of each other in the diagonal):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hGAcAAAAMYZsKAAAAXMILOJ1HMw4AAAAYQjMOAAAAl9CMO49mHAAAADCEZhwA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\nqR93BgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(g.payoff_matrices()[1], colorbar=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check if the game is degenerate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g.is_degenerate()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us find the best responses to each player."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def get_best_response_dictionary(game):\n",
    "    \"\"\"Returns the best response dictionary for a given player\"\"\"\n",
    "    N = len(hero_names)\n",
    "    best_response_dictionary = {}\n",
    "    for i in range(1, N + 1):\n",
    "        strategy = [0 for k in range(i - 1)] + [1] + [0 for k in range(N - i)]\n",
    "        hero = hero_names[i - 1]\n",
    "        best_responses = [hero_names[br] for br in g.best_responses(strategy,0)]\n",
    "        best_response_dictionary[hero] = best_responses\n",
    "    return best_response_dictionary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "adagio: \n",
      "\tadagio\n",
      "koshka: \n",
      "\tfortress\n",
      "ardan: \n",
      "\ttaka\n",
      "joule: \n",
      "\tpetal\n",
      "catherine: \n",
      "\tpetal\n",
      "celeste: \n",
      "\ttaka\n",
      "krul: \n",
      "\tpetal\n",
      "ringo: \n",
      "\tadagio\n",
      "taka: \n",
      "\tadagio\n",
      "saw: \n",
      "\tkoshka\n",
      "petal: \n",
      "\tkoshka\n",
      "skaarf: \n",
      "\tadagio\n",
      "vox: \n",
      "\ttaka\n",
      "rona: \n",
      "\tceleste\n",
      "\tringo\n",
      "\tskaarf\n",
      "\ttaka\n",
      "fortress: \n",
      "\ttaka\n",
      "glaive: \n",
      "\tglaive\n"
     ]
    }
   ],
   "source": [
    "d = get_best_response_dictionary(g)\n",
    "for hero in d:\n",
    "    print hero +\": \" \n",
    "    for br in d[hero]:\n",
    "        print \"\\t\", br"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a graphical representation of the above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def digraph_representation(game):\n",
    "    \"\"\"Get a graphical representation of the best response dynamics\"\"\"\n",
    "    G = DiGraph(get_best_response_dictionary(game))\n",
    "    return G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LS+urbcrKysL+/fvh5+eH+Ph4kTQul4tBgwbBy8sLPXv2ZET18ePHcHJyEguk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\nMwkGg8FgFMj/AW2bXZGlwSE2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "Graphics object consisting of 51 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = digraph_representation(g)\n",
    "G.show(layout='circular')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Obtain the NE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "NEs = g.obtain_nash(algorithm='lrs')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How many NE are there?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(NEs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def analyse_set_of_NE(NEs):\n",
    "    \"\"\"Go through the NEs and analyse\"\"\"\n",
    "    \n",
    "    return [sum([vector(ne[player])/len(NEs) for ne in NEs]) for player in [0, 1]]       "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_mean_NE(game, output_file, title=None):\n",
    "    \"\"\"Obtain the plot of the mean NE for a game: save to a file given by `output_file` also return the mean ne\"\"\"\n",
    "    mean_ne = analyse_set_of_NE(NEs)\n",
    "\n",
    "    N = len(hero_names)\n",
    "    p1 = mean_ne[0]\n",
    "    p2 = mean_ne[1]\n",
    "\n",
    "\n",
    "    heroes = range(N)  # the x locations for the heroes\n",
    "    width = 0.35       # the width of the bars\n",
    "\n",
    "    fig, ax = plt.subplots()\n",
    "    rects1 = ax.bar(heroes, p1, width, color='black')\n",
    "    rects2 = ax.bar([h + width for h in heroes], p2, width, color='grey')\n",
    "\n",
    "    # add some text for labels, title and axes ticks\n",
    "    ax.set_ylabel('Probability')\n",
    "    if title:\n",
    "        ax.set_title(title)\n",
    "    else:\n",
    "        ax.set_title('Mean probability for both players accross all equilibria')\n",
    "    ax.set_xticks([h + width for h in heroes])\n",
    "    ax.set_xticklabels(hero_names, rotation='vertical')\n",
    "    plt.savefig(output_file, bbox_inches='tight')\n",
    "    return mean_ne"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mean_ne = plot_mean_NE(g, \"risk-averse-plot-ne-all.svg\", \"Risk Averse - All guides\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on this not all heroes are actually played."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def heroes_that_are_played(mean_ne):\n",
    "    return [hero_names[i] for i in range(len(hero_names)) if mean_ne[0][i] !=0]\n",
    "def heroes_that_are_not_played(mean_ne):\n",
    "    return [hero_names[i] for i in range(len(hero_names)) if mean_ne[0][i] ==0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[u'adagio', u'catherine', u'koshka', u'taka', u'petal', u'glaive', u'fortress']"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "played = heroes_that_are_played(mean_ne)\n",
    "played"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[u'ardan',\n",
       " u'vox',\n",
       " u'krul',\n",
       " u'celeste',\n",
       " u'ringo',\n",
       " u'skaarf',\n",
       " u'rona',\n",
       " u'saw',\n",
       " u'joule']"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "not_played = heroes_that_are_not_played(mean_ne)\n",
    "not_played"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us redraw the best response dynamics indicating heroes that should (blue) and should not be played (red)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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L6enpUWpq6ifb7+7uTjo6OhQbG6tKq1KlCgmFQpo1a1aW+0ilUvLx8aGaNWuSRCIhU1NT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\n",
      "text/plain": [
       "Graphics object consisting of 51 graphics primitives"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = G.plot(layout='circular', vertex_colors={(0,.75,1):played, (1,.05,0):not_played}, title=\"Risk Averse - All guides\")\n",
    "p.save(\"risk-averse-plot-br-all.svg\")\n",
    "p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Analysing all the games."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "N = 20\n",
    "number_of_equilibria = []\n",
    "for number_of_guides in range(1, N + 1):\n",
    "    a_file = 'data/A-%02d.csv' % number_of_guides\n",
    "    b_file = 'data/B-%02d.csv' % number_of_guides\n",
    "    g = build_game(a_file, b_file)\n",
    "    NEs = g.obtain_nash(algorithm='lrs')\n",
    "    number_of_equilibria.append(len(NEs))\n",
    "    mean_ne = plot_mean_NE(g, \"risk-averse-plot-ne-%02d.svg\" % number_of_guides, title=\"Risk Averse - %s guides\" % number_of_guides)\n",
    "    played = heroes_that_are_played(mean_ne)\n",
    "    not_played = heroes_that_are_not_played(mean_ne)\n",
    "    G = digraph_representation(g)\n",
    "    p = G.plot(layout='circular', vertex_colors={(0,.75,1):played, (1,.05,0):not_played}, title=\"Risk Averse - %s guides\" % number_of_guides)\n",
    "    p.save(\"risk-averse-plot-br-%02d.svg\"% number_of_guides)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[35, 1352, 607, 3, 135, 479, 12, 30, 6, 6, 11, 5, 11, 13, 13, 5, 5, 5, 13, 13]"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "number_of_equilibria"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.figure()\n",
    "plt.scatter(range(1, N + 1), number_of_equilibria)\n",
    "#plt.ylim(0,max(number_of_equilibria) * 1.1)\n",
    "plt.xlabel(\"Number of guides\")\n",
    "plt.ylabel(\"Number of equilibria (log scale)\")\n",
    "plt.yscale(\"log\")\n",
    "plt.title(\"Risk Averse\")\n",
    "plt.xlim(0, N + 1)\n",
    "plt.savefig(\"risk-averse_number_of_equilibria.svg\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Swapping the and negating matrices so that players now aim to maximise the threat they pose."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a_file = 'A.csv'\n",
    "b_file = 'B.csv'\n",
    "g = build_game(b_file, a_file)\n",
    "a, b = g.payoff_matrices()\n",
    "g = NormalFormGame([-a, -b])\n",
    "NEs = g.obtain_nash(algorithm='lrs')\n",
    "number_of_equilibria.append(len(NEs))\n",
    "mean_ne = plot_mean_NE(g, \"threatening-plot-ne-all.svg\", title=\"Threatening - All guides\")\n",
    "played = heroes_that_are_played(mean_ne)\n",
    "not_played = heroes_that_are_not_played(mean_ne)\n",
    "G = digraph_representation(g)\n",
    "p = G.plot(layout='circular', vertex_colors={(0,.75,1):played, (1,.05,0):not_played}, title=\"Threatening - All guides\")\n",
    "p.save(\"threatening-plot-br-all.svg\")\n",
    "\n",
    "N = 20\n",
    "number_of_equilibria = []\n",
    "for number_of_guides in range(1, N + 1):\n",
    "    a_file = 'A-%02d.csv' % number_of_guides\n",
    "    b_file = 'B-%02d.csv' % number_of_guides\n",
    "    g = build_game(b_file, a_file)\n",
    "    a, b = g.payoff_matrices()\n",
    "    g = NormalFormGame([-a, -b])\n",
    "    NEs = g.obtain_nash(algorithm='lrs')\n",
    "    number_of_equilibria.append(len(NEs))\n",
    "    mean_ne = plot_mean_NE(g, \"threatening-plot-ne-%02d.svg\" % number_of_guides, title=\"Threatening - %s guides\" % number_of_guides)\n",
    "    played = heroes_that_are_played(mean_ne)\n",
    "    not_played = heroes_that_are_not_played(mean_ne)\n",
    "    G = digraph_representation(g)\n",
    "    p = G.plot(layout='circular', vertex_colors={(0,.75,1):played, (1,.05,0):not_played}, title=\"Threatening - %s guides\" % number_of_guides)\n",
    "    p.save(\"threatening-plot-br-%02d.svg\"% number_of_guides)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.figure()\n",
    "plt.scatter(range(1, N + 1), number_of_equilibria)\n",
    "#plt.ylim(0,max(number_of_equilibria) * 1.1)\n",
    "plt.xlabel(\"Number of guides\")\n",
    "plt.ylabel(\"Number of equilibria (log scale)\")\n",
    "plt.title(\"Threatening\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlim(0, N + 1)\n",
    "plt.savefig(\"threatening_number_of_equilibria.svg\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the situation where the row player seeks to be a threat and the column player seeks to avoid threats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "b_file = 'B.csv'\n",
    "g = build_game(b_file, b_file)\n",
    "a, b = g.payoff_matrices()\n",
    "g = NormalFormGame([-a, b])\n",
    "NEs = g.obtain_nash(algorithm='lrs')\n",
    "number_of_equilibria.append(len(NEs))\n",
    "mean_ne = plot_mean_NE(g, \"asymmetric-plot-ne-all.svg\", title=\"Asymmetric - All guides\")\n",
    "\n",
    "N = 20\n",
    "number_of_equilibria = []\n",
    "for number_of_guides in range(1, N + 1) :\n",
    "    a_file = 'A-%02d.csv' % number_of_guides\n",
    "    #b_file = 'B-%02d.csv' % number_of_guides\n",
    "    g = build_game(a_file, a_file)\n",
    "    a, b = g.payoff_matrices()\n",
    "    g = NormalFormGame([-a, b])\n",
    "    NEs = g.obtain_nash(algorithm='lrs')\n",
    "    number_of_equilibria.append(len(NEs))\n",
    "    mean_ne = plot_mean_NE(g, \"asymmetric-plot-ne-%02d.svg\" % number_of_guides, title=\"Asymmetric - %s guides\" % number_of_guides)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.figure()\n",
    "plt.scatter(range(1, N + 1), number_of_equilibria)\n",
    "#plt.ylim(0,max(number_of_equilibria) * 1.1)\n",
    "plt.xlabel(\"Number of guides\")\n",
    "plt.ylabel(\"Number of equilibria (log scale)\")\n",
    "plt.title(\"Asymmetric\")\n",
    "plt.yscale(\"log\")\n",
    "plt.xlim(0, N + 1)\n",
    "plt.savefig(\"asymmetric_number_of_equilibria.svg\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Sage 6.9.beta4",
   "language": "",
   "name": "sage_6_9_beta4"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}