Prospect_Theory.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Prospect Theory.ipynb",
      "provenance": [],
      "collapsed_sections": [
        "TCuqjo5t9xNN"
      ],
      "authorship_tag": "ABX9TyOZoUjnGAYeM/ENjeFmh9mc",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Skezzowski/CPT-Calculator/blob/master/Prospect_Theory.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ip1Lyw3e2SH6",
        "colab_type": "text"
      },
      "source": [
        "#Imports"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sjvAZKer2GhX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "from matplotlib import pyplot as pl"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Eg9TvtYd2RRy",
        "colab_type": "text"
      },
      "source": [
        "#Value function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DnUhX49L2Yse",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "beta = 0.88\n",
        "c = 2.25\n",
        "\n",
        "def valueFunction(x):\n",
        "  x = np.atleast_1d(x)\n",
        "  y = np.array([])\n",
        "  for idx,val in enumerate(x):\n",
        "    if(val>=0):\n",
        "       y = np.append(y, val**(1./beta))\n",
        "    else:\n",
        "       y = np.append(y,c * (-(-val)**(1./beta)))\n",
        "  return y\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TCuqjo5t9xNN",
        "colab_type": "text"
      },
      "source": [
        "#Weighting (π) function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XeJbY26q-Gck",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "alfa = 0.6\n",
        "\n",
        "\n",
        "def weightFunction(x):\n",
        "  x = np.atleast_1d(x)\n",
        "  y = np.array([])\n",
        "  for idx,val in enumerate(x):\n",
        "      up = val**alfa\n",
        "      down = pow(val**alfa + (1-val)**alfa, 1/alfa)\n",
        "      y = np.append(y,up/down)\n",
        "  return y"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4mrUfQ1TFYrm",
        "colab_type": "text"
      },
      "source": [
        "#Prospect Theory"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NLPfJSHrFX4M",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def cpt(x,p):\n",
        "  if  p > 1 or p < 0:\n",
        "    print(\"Probability is out of bounds: [0,1]\")\n",
        "    return\n",
        "  x = np.atleast_1d(x)\n",
        "  p = np.atleast_1d(p)\n",
        "  return np.sum(weightFunction(p) * valueFunction(x))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9i4La57o29SJ",
        "colab_type": "code",
        "outputId": "ce593385-091f-4090-c4a6-9dd724f4e204",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 578
        }
      },
      "source": [
        "X = np.linspace(-5,5)\n",
        "X2 = np.linspace(0,1,10)\n",
        "\n",
        "pl.grid(True, which='both')\n",
        "pl.axhline(y=0, color='k')\n",
        "pl.axvline(x=0, color='k')\n",
        "pl.xlabel(\"Gain\")\n",
        "pl.ylabel(\"Value\")\n",
        "pl.plot(X,valueFunction(X))\n",
        "pl.title(\"Value Function\")\n",
        "pl.show()\n",
        "\n",
        "pl.grid(True, which='both')\n",
        "pl.plot(X2,X2)\n",
        "pl.plot(X2,weightFunction(X2))\n",
        "pl.title(\"Weight Function\")\n",
        "pl.show()\n",
        "\n",
        "print(cpt(-15,1))"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "-48.825855100872175\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5KAz2woJ3Z9K",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}