nashpy_axelrod_example.ipynb

nashpy_axelrod_example.ipynb

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        "<a href=\"https://colab.research.google.com/gist/pikulet/17006a04fa40a613fb91627b4178bd32/nashpy_axelrod_example.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "cell_type": "markdown",
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      "source": [
        "# Example of how to use nashpy, axelrod"
      ]
    },
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      "cell_type": "markdown",
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      "source": [
        "## Prisoner's Dilemma\n",
        "\n",
        "![picture](https://drive.google.com/uc?id=1fw7j7O8XLGQR3Rt_c9UK_PE6KgLsFeEw)\n"
      ]
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      "source": [
        "# Import packages\n",
        "!pip install nashpy\n",
        "!pip install axelrod\n",
        "\n",
        "import nashpy as nash\n",
        "import numpy as np"
      ],
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      "outputs": []
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    {
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      "source": [
        "# Create payoff matrix\n",
        "\n",
        "# p1 is the row player, p2 is the column player\n",
        "p1 =  np.array([[8,1], [15,3]])\n",
        "p2 =  np.array([[8,15], [1,3]])\n",
        "prisoner_dilemma = nash.Game(P1, P2)\n",
        "prisoner_dilemma"
      ],
      "execution_count": null,
      "outputs": []
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    {
      "cell_type": "code",
      "metadata": {
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      "source": [
        "# Calculate utilities for Mixed Strategy\n",
        "sigma_r = np.array([0.2, 0.8])\n",
        "sigma_c = np.array([0.6, 0.4])\n",
        "prisoner_dilemma = nash.Game(P1, P2)\n",
        "prisoner_dilemma[sigma_r, sigma_c]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sF4K0KlOI5A7",
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      "source": [
        "Strict and unique Nash Equilibrium\n",
        "\n",
        "![picture](https://drive.google.com/uc?id=1_B9Wk5Sb1jwK1AADXR1xj9n0tmALNykM)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
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      "source": [
        "# Find Nash Equilibria\n",
        "equilibria = prisoner_dilemma.support_enumeration()\n",
        "for eq in equilibria:\n",
        "  print(eq)\n",
        "\n",
        "# expected: single equilibrium point for each p1 and p2"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NY2yrKJNI5BG",
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      },
      "source": [
        "## Hawk Dove - Multiple Nash Equilibria\n",
        "\n",
        "![picture](https://drive.google.com/uc?id=1b8kKho3qu1s5b7Qriq6NYWqJxd5uKI6x)"
      ]
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      "source": [
        "# p3 is the row player, p4 is the column player\n",
        "p3 =  np.array([[3, 1], [4, 0]])\n",
        "p4 =  np.array([[3, 4], [1, 0]])\n",
        "hawk_dove = nash.Game(P3, P4)\n",
        "hawk_dove"
      ],
      "execution_count": null,
      "outputs": []
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      "source": [
        "![picture](https://drive.google.com/uc?id=1JJxdwZ3y6U_hxMH-0l4i6LpuuTVhF5w0)\n"
      ]
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      "source": [
        "equilibria = hawk_dove.support_enumeration()\n",
        "for eq in equilibria:\n",
        "  print(eq)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5NhqPum6I5BX",
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      },
      "source": [
        "## Zero Sum Game - Matching coins\n",
        "\n",
        "![picture](https://drive.google.com/uc?id=1DJhLFiRbUah8Cvku03oGP5C2eFuDPxBQ)"
      ]
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      "cell_type": "code",
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      "source": [
        "p5 = np.array([[1, -1], [-1, 1]])\n",
        "mp = nash.Game(p5)"
      ],
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      "outputs": []
    },
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      "source": [
        "equilibria = mp.support_enumeration()\n",
        "for eq in equilibria:\n",
        "  print(eq)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eVM0LDlfI5Br",
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      "source": [
        "## Repeat games with Axelrod"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-qiWUNZ2I5Bs",
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      "source": [
        "!pip install -U pyYAML\n",
        "import axelrod as axl"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xAlZskFMI5Bv",
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      "source": [
        "players = (axl.Cooperator(), axl.Alternator())  # specify strategies\n",
        "match = axl.Match(players, turns=5)\n",
        "match.play()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "InpWBSpII5Bx",
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      "source": [
        "# view all strategies\n",
        "axl.all_strategies "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eD9qeCgEI5B_",
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      },
      "source": [
        "# analyse payoffs\n",
        "match1.game\n",
        "#R: Reward (default 3) C-C\n",
        "#P: Punishment (default 1) D-D\n",
        "#S: Loss (default 0) C-D\n",
        "#T: Temptation (default 5) D-C"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xs7rQEyZI5CC",
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      "source": [
        "# retrieve scores\n",
        "match1.scores()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zCkP68lJI5CF",
        "colab_type": "code",
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      "source": [
        "# visualise results using sparklines\n",
        "# solid = cooperate, blank = defection\n",
        "print(match1.sparklines())"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
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      "source": [
        "#### References:\n",
        "\n",
        "Package Documentations\n",
        "\n",
        "https://nashpy.readthedocs.io/en/stable/index.html#\n",
        "\n",
        "https://axelrod.readthedocs.io/en/stable/#"
      ]
    }
  ]
}