Hider_Interactive.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Annaother/Active-Inference-Tutorial-Scripts/blob/main/Hider_Interactive.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "mUy58P4847qe",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "da61dc21-bbc3-4d90-84af-b0eba2fdc6fe"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "pymdp package is not installed\n",
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting git+https://github.com/infer-actively/pymdp.git\n",
            "  Cloning https://github.com/infer-actively/pymdp.git to /tmp/pip-req-build-co9yce9q\n",
            "  Running command git clone --filter=blob:none --quiet https://github.com/infer-actively/pymdp.git /tmp/pip-req-build-co9yce9q\n",
            "  Resolved https://github.com/infer-actively/pymdp.git to commit 2d2152c79d4b28c8efc4a7a77012a5d1c146ec32\n",
            "  Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
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          ]
        }
      ],
      "source": [
        "## Import relevant packages\n",
        "\n",
        "import pkg_resources #to check if certain packages are installed\n",
        "\n",
        "import os\n",
        "import sys\n",
        "import pathlib\n",
        "import numpy as np\n",
        "import seaborn as sns\n",
        "import matplotlib.pyplot as plt\n",
        "import copy\n",
        "\n",
        "\n",
        "#check if pymd package is installed in the env\n",
        "if 'pymdp' in {pkg.key for pkg in pkg_resources.working_set}:\n",
        "    print(\"pymdp package is installed\")\n",
        "else:\n",
        "    print(\"pymdp package is not installed\")\n",
        "    !pip install git+https://github.com/infer-actively/pymdp.git \n",
        " \n",
        "\n",
        "from pymdp import utils \n",
        "from pymdp.agent import Agent\n",
        "from pymdp.maths import softmax\n",
        "from pymdp.utils import plot_likelihood\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "kRpDICL_47qg"
      },
      "outputs": [],
      "source": [
        "## Specify dimensionalities of hidden state factors, control factors and observation modalities\n",
        "\n",
        "context_names = ['Left Hand', 'Right Hand'] ## 2 contexts controlled by other agent: seeker chose penny left or right\n",
        "choice_names = ['Hide left', 'Hide right']\n",
        "\n",
        "\"\"\" Define `num_states` and `num_factors` below \"\"\"\n",
        "num_states = [len(context_names), len(choice_names)]\n",
        "num_factors = len(num_states)\n",
        "\n",
        "context_action_names = ['Do-nothing']\n",
        "choice_action_names = ['Hide penny left', 'Hide penny right'] ## 2 actions: choose to hide penny left and hide penny right\n",
        "\n",
        "\"\"\" Define `num_controls` below \"\"\"\n",
        "num_controls = [len(context_action_names), len(choice_action_names)]\n",
        "\n",
        "reward_obs_names = ['Loss', 'Reward']\n",
        "choice_obs_names = ['Left Hand', 'Right Hand']\n",
        "\n",
        "\"\"\" Define `num_obs` and `num_modalities` below \"\"\"\n",
        "num_obs = [len(reward_obs_names), len(choice_obs_names)]\n",
        "num_modalities = len(num_obs)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6wGg56WQ47qc"
      },
      "source": [
        "The *0-ToM hider* is an active inference agent that learns to predict its reward outcomes and infer the other player's choices in a matching pennies paradigm\n",
        "The agent architecture is based on the agent class introduced by Conor Heins, Alexander Tschantz, Daphne Demekas, Brennan Klein"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3bxGYFIr47qh"
      },
      "source": [
        "## Hidden states\n",
        "\n",
        "Context states (other-states that need to be inferred)\n",
        "    1. Seeker chose to seek penny in left hand\n",
        "    2. Hider chose to seek penny in right hand \n",
        "\n",
        "\n",
        "Choice states (self-states that are directly accessible)\n",
        "    1. Hide in left hand \n",
        "    2. Hide in right hand \n",
        "\n",
        "\n",
        "Observation modalities\n",
        "    1. Self-choices (directly accessible)\n",
        "    2. Reward outcomes (noisy) \n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9HoiutjH47qk"
      },
      "source": [
        "## Likelihood Matrix A"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "x2nOV47t47ql",
        "outputId": "f38f70b2-2597-45bb-80cd-e5a5af817001",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "## Likelihood matrix A of observations O given hidden states S\n",
        "\n",
        "\"\"\" Generate the A array \"\"\"\n",
        "A = utils.obj_array(num_modalities)\n",
        "\n",
        "#### 1. Likelihood of proprioceptive/interoceptive observations (left choice or right choice) given beliefs about self-choice (left or right) and where the penny is hidden (context states left or right)\n",
        "A_choice = np.zeros((len(choice_obs_names), len(choice_names), len(context_names)))\n",
        "\n",
        "\n",
        "    #### 1.1. Likelihood of observing left choice given beliefs left choice and sought left\n",
        "    #### 1.2. Likelihood of observing left choice given beliefs left choice and sought right\n",
        "    #### 1.3. Likelihood of observing left choice given beliefs right choice and sought left\n",
        "    #### 1.4. Likelihood of observing left choice given beliefs right choice and sought right\n",
        "\n",
        "    #### 1.5. Likelihood of observing right choice given beliefs left choice and sought left\n",
        "    #### 1.6. Likelihood of observing right choice given beliefs left choice and sought right\n",
        "    #### 1.7. Likelihood of observing left choice given beliefs right choice and sought left\n",
        "    #### 1.8. Likelihood of observing right choice given beliefs right choice and sought right\n",
        "\n",
        "\n",
        "for choice_id in range(len(choice_names)):\n",
        "\n",
        "  A_choice[choice_id, :, choice_id] = 1.0 ## self-choices are fully transparant \n",
        "\n",
        "A[0] = A_choice\n",
        "\n",
        "plot_likelihood(A[0][:,0,:], \"Mapping between sensed states and true states\") ##plot likelihood mapping between choice observation and inferred choice state\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3j5zCScz47qn",
        "outputId": "61ef2781-b252-4d74-d287-da62a256ad6c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "['Hide left', 'Hide right']\n",
            "['Left Hand', 'Right Hand']\n",
            "[[[1. 0.]\n",
            "  [0. 1.]]\n",
            "\n",
            " [[0. 1.]\n",
            "  [1. 0.]]]\n"
          ]
        }
      ],
      "source": [
        "#### 2. Likelihood of reward observations (win or loose) given beliefs about self-choices (left or right) and where the penny is hidden (context states left or right)\n",
        "\n",
        "\"\"\" Initialize matrix storing likelihood mapping reward opbservations to hidden states\"\"\"\n",
        "from difflib import context_diff\n",
        "\n",
        "\n",
        "A_reward = np.zeros((len(reward_obs_names), len(context_names), len(choice_names)))\n",
        "\n",
        "## Likelihood mappings for each reward observation\n",
        "for choice_id, choice_name in enumerate(choice_names):\n",
        "    \n",
        "    for context_id, context_name in enumerate(context_names):\n",
        "      \n",
        "      if choice_name == 'Hide left':\n",
        "        \n",
        "        if context_name == 'Left Hand': \n",
        "          A_reward[1,context_id, choice_id] = 0 #### 1.1. Likelihood of observing a win given left choice and hid left\n",
        "      \n",
        "        elif context_name == 'Right Hand':\n",
        "          A_reward[1, context_id, choice_id] = 1 #### 1.2. Likelihood of observing a win given left choice and hid right\n",
        "\n",
        "      elif choice_name == 'Hide right':\n",
        "         \n",
        "          if context_name == 'Left Hand':\n",
        "            A_reward[1, context_id,choice_id] = 1 #### 1.3. Likelihood of observing a win given right choice and hid left\n",
        "          \n",
        "          elif context_name == 'Right Hand':\n",
        "            A_reward[1, context_id, choice_id] =  0 #### 1.4. Likelihood of Sobserving a win given right choice and hid right\n",
        "\n",
        "      A_reward[0,context_id,choice_id] = 1 - A_reward[1, context_id, choice_id] #### Likelihood of observing a loss is just 1- observing a win for each case\n",
        "\n",
        "print(choice_names)\n",
        "\n",
        "print(context_names)\n",
        "\n",
        "\n",
        "## Assign reward and choice-likelihoods to datastructure for A\n",
        "A[1] = A_reward\n",
        "\n",
        "print(A_reward)\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#function to normalize multidimensional arr\n",
        "A_reward = utils.norm_dist(A_reward)\n",
        "\n",
        "print(A_reward)\n"
      ],
      "metadata": {
        "id": "jPQQYkmS5Lsi",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "98738529-b0ca-4b42-a75b-993953016c05"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[[1. 0.]\n",
            "  [0. 1.]]\n",
            "\n",
            " [[0. 1.]\n",
            "  [1. 0.]]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "iv3ZPJ8T47qq",
        "outputId": "6f53c94a-6b47-41d8-9426-b95236c9de87",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 425
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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PyxPMvaXkGp9xxhkB68yePdsk2YIFC/xlwbYNFd3DQ7n/FhUV2SmnnGIxMTG2Y8cOu+aaa6xevXplEnwVjYFMTEw86GcGqjWQJS0tTdHR0Wrbtq0uueQSNWzYUC+88ILi4uIkSZGRkf51f/jhB+3Zs0epqan68MMP/eVNmjTRueeeq6efflpmJkkqKirS4sWLNWTIEDVo0ECStGzZMoWFhem6664LqMP1118vM9Orr75anUMoV8k4lBdffLHaYwF9Pp9GjhxZ7To899xzSkxM1HnnnVfmf4diqo6MjIyA67V+/Xpt3LhRw4cP186dO7Vjxw7t2LFD+fn5Ov300/XOO+9Uem6WLVum2NhYDRs2zF9Wv359XXfdddq7d6/efvvtkOu4dOlSFRcXa9KkSWXGXpU+J127dlVqaqr/7+joaB133HH65ptvAurYt29fnXLKKf6yhg0b6oorrtCWLVu0YcOGkI6ladOmys/P1xtvvBHysTVs2FB//OMf/X+Hh4erb9++AfVdvny54uLidM455/jLIiIiNHr06JD3d6Bly5ZJkjIzMwPKr7/+eknSK6+8EtR2/vznPwf8nZqaGlD/0oqKivTaa69pyJAhOvbYY/3lxx9/vNLT0wPWff7551VcXKyLL77Y/17csWOHYmNj1alTJ61cuTKoOl5zzTUBf48ZM0bS/85BqPsJ5rqVGDlypMLDw/1/l7w/D1x3xIgR+uc//6lNmzb5y5588km1bdtW/fv3D+oYS0tLS1NCQoL/7x49eqhx48aVXpsDlW4byvPBBx9o586dGj16dMAY1z/84Q9q1qxZua8J5nxURzDHe+Dx/Prrr9q5c6c6duyopk2bBtyfSlxxxRUBbUxqaqqKior07bffSpLefPNNFRYWasyYMQHrHexUPKG2oxdccIGio6MPap8lyvs879y5Uz/++KOkmvtMltarVy81bNhQ77zzjiRp1apVatOmjUaMGKEPP/xQP//8s8xM7777bkAbH2x7Xp5g7i0l13jcuHEB64wePVqNGzcu006G0jaUFsr91+v1auHChdq7d6/OOusszZ07V1lZWerdu3eV+5H237f+9a9/aePGjUGtX55qBZBz5szRG2+8oZUrV2rDhg365ptvAhr+l19+Wb/73e8UERGh5s2bKzo6Wg888ID27NkTsJ0RI0Zo69atWrVqlaT9FyovLy9gGoNvv/1WrVu3VqNGjQJee/zxx/v/X1OGDh2qk08+WaNGjVJMTIwuueQS/e1vfwspmIyLiwtoHEO1adMmde/evdqvD1X79u0D/i55M2VkZCg6Ojpgefjhh1VQUFDmOh7o22+/VadOncp8GA/mem3atEler1ddu3atct0DA5ISzZo10w8//BBQx+OOO67MeqXrGOyxXH311ercubPOOusstWnTRpdffrmWL18e1LG1adOmTBBcXn0TEhLKrNexY8eg9lGRb7/9Vl6vt8x2YmNj1bRp06CuVURERJkbV+n6l7Z9+3b98ssv6tSpU5n/lb4uGzdulJmpU6dOZd6Pn3/+ubZt21ZlHSWV2VdCQoK8Xq+2bNlSrf0Ec91KlH5PlgRWB647dOhQ+Xw+Pfnkk5KkPXv26OWXX9Yf/vCHan9xDOazUJnSbUN5St4jpd9D9erVU3x8fFD1Ku98VEcwx/vLL79o0qRJatu2rXw+n6KiohQdHa3du3eX265VVdeS4y/9/oqOjq4wgA5GqO1oMNcqWFUdc019JksLCwtTSkqKPx5YtWqVUlNTdcopp6ioqEhr1qzRhg0btGvXroAAMtj2vDzB3FtKXl96H+Hh4erQoUOZ7YfSNpQW6v03ISFB2dnZev/999WtWzfdeuutVe6jxNSpU7V792517txZJ5xwgm688UZ98sknQb9ekqr1WGTfvn0rjHJXrVqlc845R/369dPcuXPVqlUr1a9fX48++qieeuqpgHXT09MVExOjJ554Qv369dMTTzyh2NhYpaWlVadaBy0yMlLvvPOOVq5cqVdeeUXLly/X4sWLNWDAAL3++usKCwsLahuhKCoqqm51y1XRzaaoqKjc+peub0mwPG3aNPXs2bPcbQU7eXRdqOgalWS5D4WWLVtq/fr1eu211/Tqq6/q1Vdf1aOPPqoRI0boscceq/S1dVHf0g4msx3MZ+JgFBcXy+Px6NVXXy13X9V9L5Y+5lD3E8p1C2bdZs2a6eyzz9aTTz6pSZMmacmSJSooKAjIZITqYN9bobZlwTpU7/lgtjtmzBg9+uijGjdunFJSUtSkSRN5PB5dcskl5SYKXPh8BqMmr1VVx3yoPpOSdMopp+iOO+7Qvn37tGrVKk2cOFFNmzZV9+7dtWrVKsXExEhSQADpmoN5z1Tn/vv6669L2j+35M6dOxUbGxtUPfv166dNmzbpxRdf1Ouvv66HH35YM2bM0Lx58zRq1KigtlHj82o899xzioiI0GuvvSafz+cvf/TRR8usGxYWpuHDh2vhwoW6++67tXTpUo0ePTrgArRr105vvvmmfvrpp4As5BdffOH/f03yer06/fTTdfrpp2v69Om68847NXHiRK1cuVJpaWnVvtk2a9aszMSphYWF+v777wPKEhIS9Nlnn1W6rcrqUN5+pP3fojp06FBlPUu6gBo3blytQL5du3b65JNP/FN+lDiY65WQkKDi4mJt2LChwg9VqHX88ssvy5SXrmMoxxIeHq7Bgwdr8ODBKi4u1tVXX60HH3xQt95660FnCtu1a6cNGzbIzAKu/ddffx3U6yt6v7Rr107FxcXauHGj/9u6JOXl5Wn37t01/tkqER0drcjIyHK7Tkpfl4SEBJmZ2rdvr86dO1d7nxs3bgzI0nz99dcqLi72Z8lqaj8HY8SIETr33HP1/vvv68knn1SvXr3UrVu3OqlLsEreI19//bVOO+00f/lvv/2mLVu2qEePHtXa7qH6ZZ0lS5YoIyND9957r79s37591Z7UuuT4N27cGNC+bt++/aAyqoeiHS1xsOf2YD8rle0/NTVVhYWFevrpp/Xdd9/5A8V+/fr5A8jOnTv7A0kp+Pa8omOp6t5S8vovv/wy4BoXFhZq8+bN1bpPVnQOQr3/zps3T2+88YbuuOMO5eTk6MorrywznWJl57t58+YaOXKkRo4cqb1796pfv37Kzs4OOoCs8cm8wsLC5PF4AjJrW7ZsqXDm+0svvVQ//PCDrrzySu3du7fMN+6BAweqqKhIs2fPDiifMWOGPB6PzjrrrBqr+65du8qUlbypCgoKJMk/NjPUBichIcE/tqPEQw89VCYDecEFF+jjjz/WCy+8UGYbJd9gKqtDQkKC1qxZEzAP2Msvv6x///vfQdUzKSlJCQkJuueee7R3794y/9++fXulrx84cKByc3O1ePFif9lvv/2mWbNmqWHDhtUazzVkyBB5vV5NnTq1TJagOpmAgQMHau3atVq9erW/LD8/Xw899JDi4+P93RnBHsvOnTsDtu/1ev03zpL3zcFIT0/Xd999p5deeslftm/fPs2fPz+o11f0fhk4cKAklfnFj+nTp0uSBg0aVM0aVy4sLEzp6elaunSptm7d6i///PPP9dprrwWse/755yssLExTpkwpc63NrMy5r8icOXMC/p41a5Yk+duPmtrPwTjrrLMUFRWlu+++W2+//fZBZR9rS+/evdWiRQvNnz9fv/32m7/8ySefPKgAqkGDBpUOlamusLCwMtd31qxZ1e4JSktLU/369TVr1qyA7R7sr+gcina0RIMGDQ7qV2AO9rNS2f0rOTlZ9evX1913363mzZv7v0ClpqZqzZo1evvtt8tkH4Ntz8sTzL0lLS1N4eHhuv/++wOO95FHHtGePXuq1U5WdA5Cuf9u3rxZN954oy644AJNmDBB99xzj1566SU9/vjjZfZV3rkufZ0aNmyojh07hnTPqvEM5KBBgzR9+nSdeeaZGj58uLZt26Y5c+aoY8eO5fav9+rVS927d9ezzz6r448/XieeeGLA/wcPHqzTTjtNEydO1JYtW5SYmKjXX39dL774osaNGxcwaPpgTZ06Ve+8844GDRqkdu3aadu2bZo7d67atGnjH6CbkJCgpk2bat68eWrUqJEaNGig5OTkKsegjBo1Sn/+8591wQUX6Pe//70+/vhjvfbaa4qKigpY78Ybb9SSJUt00UUX6fLLL1dSUpJ27dqll156SfPmzVNiYmKldRg1apSWLFmiM888UxdffLE2bdqkJ554Iujz5PV69fDDD+uss85St27dNHLkSMXFxem7777TypUr1bhxY/3973+v8PVXXHGFHnzwQV122WVat26d4uPjtWTJEv3jH//QzJkzy4xlDUbHjh01ceJE3XbbbUpNTdX5558vn8+n999/X61bt1ZOTk5I27v55pv19NNP66yzztJ1112n5s2b67HHHtPmzZv13HPP+b/xB3sso0aN0q5duzRgwAC1adNG3377rWbNmqWePXsGZPaq68orr9Ts2bM1bNgwjR07Vq1atdKTTz7pnzy6qoxCUlKSJGnixIm65JJLVL9+fQ0ePFiJiYnKyMjQQw89pN27d6t///5au3atHnvsMQ0ZMiQgo1TTpkyZouXLlys1NVVXX321/+bYrVu3gHYiISFBt99+u7KysrRlyxYNGTJEjRo10ubNm/XCCy/oiiuu0A033FDl/jZv3qxzzjlHZ555plavXq0nnnhCw4cPV2JiYo3u52DUr19fl1xyiWbPnq2wsLCAByhcFR4eruzsbI0ZM0YDBgzQxRdfrC1btmjhwoXljtsNVlJSkhYvXqzMzEz16dNHDRs21ODBgw+6vmeffbYWLVqkJk2aqGvXrlq9erXefPNNtWjRolrbi46O1g033KCcnBydffbZGjhwoD766CO9+uqrZdr2UByKdrREUlKS3nzzTU2fPl2tW7dW+/btlZycHPTrD/azUlF71KBBAx1zzDFKSkrSmjVrNHjwYP/7p1+/fsrPz1d+fn6ZADLY9rw8wdxboqOjlZWVpSlTpujMM8/UOeecoy+//FJz585Vnz59qvVFr7J7eDD3XzPT5ZdfrsjISD3wwAOS9t8nnnvuOY0dO1ZpaWlq3bq1/3w/8MADuv3229WxY0e1bNlSAwYMUNeuXXXqqacqKSlJzZs31wcffKAlS5aE9pvyoTyyXdE8kKU98sgj1qlTJ/P5fNalSxd79NFHK/2Jsr/+9a8mye68885y///TTz/Z+PHjrXXr1la/fn3r1KlTwETiJQ52Gp8VK1bYueeea61bt7bw8HBr3bq1DRs2zL766quA9V588UXr2rWr1atXL+BR/Ir2b7b/kfubbrrJPyFtenq6ff311+VOu7Nz50679tprLS4uzsLDw61NmzaWkZERMJ9ZRXUw2z/tS8kkvSeffLJ98MEHFU7jU9HPin300Ud2/vnnW4sWLczn81m7du3s4osvthUrVlR5HvPy8mzkyJEWFRVl4eHhdsIJJ1Q45VAo0wgsWLDAevXqZT6fz5o1a2b9+/e3N954o8rtlT52s/9NPNu0aVOLiIiwvn37VjiReFXHsmTJEjvjjDOsZcuWFh4ebscee6xdeeWV9v333/vXqWwi8dIyMjLKTGHyzTff2KBBgywyMtKio6Pt+uuvt+eee84k2Zo1ayo5a/uVTHTs9XoDptD49ddfbcqUKda+fXurX7++tW3bNuSJxEuraFqZ0tNYvf3225aUlGTh4eFVTiT+3HPP2SmnnGINGjSwBg0aWJcuXeyaa66xL7/8stI6lmxvw4YNduGFF1qjRo2sWbNmdu2115Y7OXcw+wn2ulX0GSuZeqW8z0TJPLgH/pBCVSqbSLy0YH5er7K2oaKJxO+//35r166d+Xw+69u3r/3jH/+wpKQkO/PMM6vcbnnnY+/evTZ8+HBr2rSpScFPJF7V8f7www/+z3PDhg0tPT3dvvjiizLrVXSvK+/4i4qKbMqUKdaqVauQJhI/sI7ltVvBtD0HTiQerC+++ML69etnkZGRAVMNVfRThiXnovS0O9X9TJpV3B6Zmd14440mqczE/B07djRJ/vkSDxRse16Rqu4tZvun7enSpYvVr1/fYmJi7KqrrqpwIvHSymvTK7uHV3X/LZn66rnnngvY5tatW61x48Y2cOBAf1lubq4NGjTIGjVqFDC11u233259+/a1pk2bWmRkpHXp0sXuuOOOgHktq+Ixq/vRwPfdd5/Gjx+vLVu2lPskHYCyZs6cqfHjx+s///mPfwotBMrOztaUKVO0ffv2g8oI1ZaPP/5YPXv21OOPPx4wG8Xhpri4WNHR0Tr//PODHmoB4PBS5z9oamZ65JFH1L9/f4JHoAK//PJLwN/79u3Tgw8+qE6dOhE8HkHmz5+vhg0b6vzzz6/rqgRt3759ZcbCPf7449q1a5dOPfXUuqkUgEOuxsdABis/P18vvfSSVq5cqU8//bTMk0MA/uf888/Xscceq549e2rPnj164okn9MUXX/jnDcTh7e9//7s2bNighx56SNdee61/kP3hYM2aNRo/frwuuugitWjRQh9++KEeeeQRde/eXRdddFFdVw/AIVJnAeT27ds1fPhwNW3aVBMmTAj4lQ0AgdLT0/Xwww/rySefVFFRkbp27apnnnlGQ4cOreuqoQaMGTNGeXl5GjhwoKZMmVLX1QlJfHy82rZtq/vvv1+7du1S8+bNNWLECN11110H9aMKANzmxBhIAACAuvbOO+9o2rRpWrdunb7//nu98MILGjJkSKWveeutt5SZmal//etfatu2rW655RZddtlltVLfulTnYyABAABckJ+fr8TExDJzx1Zk8+bNGjRokE477TStX79e48aN06hRo8rMaXskIgMJAABQisfjqTIDedNNN+mVV14J+AW5Sy65RLt379by5ctroZZ1p87GQKLuFBQUlJlt3ufzBfz0JAAAR4JDec9bvXp1mZ8dTE9P17hx4w56264jgDwK5eTklBmoP3nyZGVnZ9dNhQAAKCW7pn4TffLkQ3bPy83NDfhtbkmKiYnRjz/+qF9++UWRkZEHvQ9XEUAehbKyspSZmRlQRvYRAOCSmnpI4ybueYcEAeRRiO5qAMDR4lDe82JjY5WXlxdQlpeXp8aNGx/R2UeJABLl2bezrmsA1K2IFmWKaqw7DTiMZdfic7eHwycuJSVFy5YtCyh74403lJKSUkc1qj1M4wMAAJzjraElFHv37tX69eu1fv16Sfun6Vm/fr22bt0qaf8QsBEjRvjX//Of/6xvvvlGf/nLX/TFF19o7ty5+tvf/qbx48dX76APIwSQAAAAkj744AP16tVLvXr1kiRlZmaqV69emjRpkiTp+++/9weTktS+fXu98soreuONN5SYmKh7771XDz/8sNLT0+uk/rWJeSBRFl3YONrRhQ2Uqza7sHNq6DOXRZhzSDAGEgAAOIevbG6jCxsAAAAhIQMJAACcQ4bLbQSQAADAOXRhu40AEgAAOIcMpNu4PgAAAAgJGUgAAOAcMlxuI4AEAADOYQyk2wjwAQAAEBIykAAAwDlkuNxGAAkAAJxDAOk2rg8AAABCQgYSAAA4h4do3EYACQAAnEMXqdu4PgAAAAgJGUgAAOAcurDdRgAJAACcQxep2wggAQCAcwgg3cb1AQAAQEjIQAIAAOcwBtJtBJAAAMA5dJG6jesDAACAkJCBBAAAziHD5TYCSAAA4BzGQLqNAB8AAAAhIQMJAACcQ4bLbQSQAADAOQSQbuP6AAAAICRkIAEAgHN4iMZtBJAAAMA5dJG6jQASAAA4hwyk2wjwAQAAEBIykAAAwDlkuNxGAAkAAJxDAOk2rg8AAABCQgYSAAA4h4do3EYACQAAnEMXqdu4PgAAAAgJGUgAAOAcMlxuI4AEAADOYQyk2wjwAQAAEBIykAAAwDkeLzlIlxFAAgAA53g8BJAuI4AEAADO8ZKBdBpjIAEAABASMpAAAMA5dGG7jQASAAA4h4do3EYXNgAAAEJCBhIAADiHLmy3EUACAADn0IXtNrqwAQAAEBIykAAAwDl0YbuNABIAADiHLmy30YUNAACAkJCBBAAAzqEL220EkAAAwDn8FrbbCCABAIBzyEC6jTGQAAAACAkZSAAA4ByewnYbASQAAHAOXdhuowsbAAAAISEDCQAAnEMXttsIIAEAgHPownYbXdgAAAAHmDNnjuLj4xUREaHk5GStXbu20vVnzpyp4447TpGRkWrbtq3Gjx+vffv21VJt6wYZSAAA4Jy66sJevHixMjMzNW/ePCUnJ2vmzJlKT0/Xl19+qZYtW5ZZ/6mnntLNN9+sBQsW6KSTTtJXX32lyy67TB6PR9OnT6+DI6gdZCABAIBzPB5PjSyhmj59ukaPHq2RI0eqa9eumjdvno455hgtWLCg3PXfe+89nXzyyRo+fLji4+N1xhlnaNiwYVVmLQ93BJAAAOCIVVBQoB9//DFgKSgoKHfdwsJCrVu3Tmlpaf4yr9ertLQ0rV69utzXnHTSSVq3bp0/YPzmm2+0bNkyDRw4sOYPxiEEkAAAwDler6dGlpycHDVp0iRgycnJKXefO3bsUFFRkWJiYgLKY2JilJubW+5rhg8frqlTp+qUU05R/fr1lZCQoFNPPVUTJkyo8XPiEgJIAADgnJrqws7KytKePXsClqysrBqr51tvvaU777xTc+fO1Ycffqjnn39er7zyim677bYa24eLeIgGAAA4p6YeovH5fPL5fEGtGxUVpbCwMOXl5QWU5+XlKTY2ttzX3Hrrrbr00ks1atQoSdIJJ5yg/Px8XXHFFZo4caK83iMzV3dkHhUAAECIwsPDlZSUpBUrVvjLiouLtWLFCqWkpJT7mp9//rlMkBgWFiZJMrNDV9k6RgYSAAA4p64mEs/MzFRGRoZ69+6tvn37aubMmcrPz9fIkSMlSSNGjFBcXJx/HOXgwYM1ffp09erVS8nJyfr666916623avDgwf5A8khEAAkAAJzjqaM+0qFDh2r79u2aNGmScnNz1bNnTy1fvtz/YM3WrVsDMo633HKLPB6PbrnlFn333XeKjo7W4MGDdccdd9TNAdQSjx3J+VVUz76ddV0DoG5FtChTlM3PqgHKrsWQ4cOOMVWvFIQTv86reiWEjAwkAABwDr+F7TYCSAAA4Jy6+ilDBIensAEAABASMpAAAMA5XrqwnUYACQAAnEMXttvowgYAAEBIyEACAADn8BS22wggAQCAc+jCdhsBJAAAcA4ZSLcxBhIAAAAhIQMJAACcQxe22wggAQCAc+jCdhtd2AAAAAgJGUgAAOAcj5ccl8sIIAEAgHMYA+k2wnsAAACEhAwkAABwDw/ROI0AEgAAOIcubLfRhQ0AAICQkIEEAADO4SlstxFAAgAA5zCRuNsIIAEAgHsYA+k08sMAAAAICRlIAADgHMZAuo0AEgAAOIcxkG4jvAcAAEBIyEACAADnMJG42wggAQCAewggnUYXNgAAAEJCBhIAADjH4yHH5TICSAAA4BzGQLqN8B4AAAAhIQMJAACcQwbSbQSQAADAPYyBdBoBJAAAcA4ZSLcR3gMAACAkZCABAIBzyEC6jQASAAA4x+MhgHQZXdgAAAAICRlIAADgHi85LpcRQAIAAOcwBtJthPcAAAAICRlIAADgHB6icRsBJAAAcI6HMZBO4+oAAAAgJGQgAQCAc3iIxm0EkAAAwD2MgXQaASQAAHAOGUi3MQYSAAAAISEDCQAAnMNT2G4jgAQAAM5hHki3Ed4DAAAgJGQgAQCAe3iIxmkEkAAAwDmMgXQbVwcAAAAhIQMJAACcw0M0biOABAAAzmEicbfRhQ0AAICQkIEEAADuoQvbaQSQAADAOXRhu40AEgAAuIf40WmMgQQAAEBIyEACAAD3MAbSaWQgAQCAczyemlmqY86cOYqPj1dERISSk5O1du3aStffvXu3rrnmGrVq1Uo+n0+dO3fWsmXLqrfzwwQZSAAAgP9avHixMjMzNW/ePCUnJ2vmzJlKT0/Xl19+qZYtW5ZZv7CwUL///e/VsmVLLVmyRHFxcfr222/VtGnT2q98LSKABAAA7qmjp7CnT5+u0aNHa+TIkZKkefPm6ZVXXtGCBQt08803l1l/wYIF2rVrl9577z3Vr19fkhQfH1+bVa4TdGEDAADn1FQXdkFBgX788ceApaCgoNx9FhYWat26dUpLS/OXeb1epaWlafXq1eW+5qWXXlJKSoquueYaxcTEqHv37rrzzjtVVFR0SM6LKwggAQDAESsnJ0dNmjQJWHJycspdd8eOHSoqKlJMTExAeUxMjHJzc8t9zTfffKMlS5aoqKhIy5Yt06233qp7771Xt99+e40fi0vowgYAAO6poaews7KylJmZGVDm8/lqZNuSVFxcrJYtW+qhhx5SWFiYkpKS9N1332natGmaPHlyje3HNQSQAADAPTXUR+rz+YIOGKOiohQWFqa8vLyA8ry8PMXGxpb7mlatWql+/foKCwvzlx1//PHKzc1VYWGhwsPDq195h9GFDQAAnOPxeGpkCUV4eLiSkpK0YsUKf1lxcbFWrFihlJSUcl9z8skn6+uvv1ZxcbG/7KuvvlKrVq2O2OBRIoAEAADwy8zM1Pz58/XYY4/p888/11VXXaX8/Hz/U9kjRoxQVlaWf/2rrrpKu3bt0tixY/XVV1/plVde0Z133qlrrrmmrg6hVtCFDQAA3FNHv0QzdOhQbd++XZMmTVJubq569uyp5cuX+x+s2bp1q7ze/+Xf2rZtq9dee03jx49Xjx49FBcXp7Fjx+qmm26qk/rXFo+ZWV1XAo7Zt7OuawDUrYgWZYqy+Vk1QNm1GDLk33BujWynwT0v1sh2EIgubAAAAISELmwAAOCeOvolGgSHABIAALiH+NFpdGEDAAAgJGQgAQCAc0KdwxG1iwASAAC4h/jRaXRhAwAAICRkIAEAgHM8PIXtNAJIAADgHuJHpxFAAgAA9/AQjdMYAwkAAICQkIEEAADOIQHpNgJIAADgHh6icRpd2AAAAAgJGUgAAOAcurDdRgAJAADcQwTpNLqwAQAAEBIykAAAwDkkIN1GAAkAANzDU9hOowsbAAAAISEDCQAA3EMfttMIIAEAgHOIH91GAAkAANxDBOk0xkACAAAgJGQgAQCAczykuJxGAAkAANxDF7bTiO8BAAAQEjKQAADAPSQgnUYAibIiWtR1DQDnZJvVdRWAo4qHLmynEUAehQoKClRQUBBQ5vP55PP56qhGAADgcMIYyKNQTk6OmjRpErDk5OTUdbUAAPgfr6dmFhwSHjP6ZY42ZCABAK4rmvnHGtlO2LgnamQ7CEQX9lGIYBEAABwMAkiUkc3AZRzlyn1gZt/O2q8I4JrafMiS7menEUACAAD38FM0TiOABAAA7qE3zGmE9wAAAAgJGUgAAOAexkA6jQASAAC4hzGQTuPqAAAAICRkIAEAgHvownYaASQAAHAPT2E7jS5sAAAAhIQMJAAAcI+XHJfLCCABAIB76MJ2GuE9AAAAQkIGEgAAuIcubKcRQAIAAPfQhe00AkgAAOAeAkinkR8GAABASMhAAgAA9zAG0mkEkAAAwD10YTuN8B4AAAAhIQMJAACc4/GSgXQZASQAAHCPh05Sl3F1AAAAEBIykAAAwD10YTuNABIAALiHp7CdRhc2AAAAQkIGEgAAuIeJxJ1GAAkAANxDF7bTCCABAIB7CCCdRn4YAAAAISGABAAA7vF6a2aphjlz5ig+Pl4RERFKTk7W2rVrg3rdM888I4/HoyFDhlRrv4cTAkgAAOAej6dmlhAtXrxYmZmZmjx5sj788EMlJiYqPT1d27Ztq/R1W7Zs0Q033KDU1NTqHvFhhQASAADgv6ZPn67Ro0dr5MiR6tq1q+bNm6djjjlGCxYsqPA1RUVF+sMf/qApU6aoQ4cOtVjbukMACQAA3OP11MhSUFCgH3/8MWApKCgod5eFhYVat26d0tLS/lcNr1dpaWlavXp1hVWdOnWqWrZsqT/96U81fhpcRQAJAADc4/HWyJKTk6MmTZoELDk5OeXucseOHSoqKlJMTExAeUxMjHJzc8t9zbvvvqtHHnlE8+fPr/FT4DKm8QEAAEesrKwsZWZmBpT5fL4a2fZPP/2kSy+9VPPnz1dUVFSNbPNwQQAJAADc462ZeSB9Pl/QAWNUVJTCwsKUl5cXUJ6Xl6fY2Ngy62/atElbtmzR4MGD/WXFxcWSpHr16unLL79UQkLCQdTeXXRhAwAA99TBU9jh4eFKSkrSihUr/GXFxcVasWKFUlJSyqzfpUsXffrpp1q/fr1/Oeecc3Taaadp/fr1atu27UGfBleRgQQAAPivzMxMZWRkqHfv3urbt69mzpyp/Px8jRw5UpI0YsQIxcXFKScnRxEREerevXvA65s2bSpJZcqPNASQAADAPdWcBPxgDR06VNu3b9ekSZOUm5urnj17avny5f4Ha7Zu3SpvHdXNJR4zs7quBNySze+P4iiXXV6zuG9n7VcEcE1Ei1rbVfHrt9XIdrxn3Foj20EgMpAAAMA9JDOcRg4WAAAAISEDCQAA3OMhx+UyAkgAAOAeerCdRngPAACAkJCBBAAA7uEhGqcRQAIAAPcQQDqNLmwAAACEhAwkAABwDxlIpxFAAgAABxFAuowubAAAAISEDCQAAHAPCUinEUACAAD3MAbSaQSQAADAPQSQTmMMJAAAAEJCBhIAALiHDKTTCCABAICDCCBdRhc2AAAAQkIGEgAAuIcEpNMIIAEAgHsYA+k0urABAAAQEjKQAADAPWQgnUYACQAAHEQA6TK6sAEAABASMpAAAMA9dGE7jQASAAC4hwDSaQSQAADAPcSPTmMMJAAAAEJCBhIAALiHLmynEUACAAAHEUC6jC5sAAAAhIQMJAAAcA9d2E4jgAQAAO4hgHQaXdgAAAAICRlIAADgHhKQTiOABAAA7qEL22l0YQMAACAkZCABAICDyEC6jAASAAC4hy5spxFAAgAA9xBAOo0xkAAAAAgJGUgAAOAeMpBOIwMJAACAkBBAAgAAICR0YQMAAPfQhe00AkgAAOAeAkin0YUNAACAkJCBBAAA7iED6TQCSAAA4CACSJfRhQ0AAICQkIEEAADuoQvbaQSQAADAPR46SV1GAAkAABxEBtJlhPcAAAAICRlIAADgHsZAOo0AEgAAuIcxkE7j6gAAACAkZCABAICD6MJ2GQEkAABwD2MgnUYXNgAAAEJCBhIAADiIHJfLCCABAIB76MJ2GuE9AAAAQkIACQAA3OPx1MxSDXPmzFF8fLwiIiKUnJystWvXVrju/PnzlZqaqmbNmqlZs2ZKS0urdP0jBQEkAABwkKeGltAsXrxYmZmZmjx5sj788EMlJiYqPT1d27ZtK3f9t956S8OGDdPKlSu1evVqtW3bVmeccYa+++67kPd9OPGYmdV1JeCWbMad4CiXXV6zuG9n7VcEcE1Ei1rbVfGmpTWyHW/CkJDWT05OVp8+fTR79uz99SguVtu2bTVmzBjdfPPNVb6+qKhIzZo10+zZszVixIjqVPmwQAYSAAAcsQoKCvTjjz8GLAUFBeWuW1hYqHXr1iktLc1f5vV6lZaWptWrVwe1v59//lm//vqrmjdvXiP1dxUBJAAAcE8NjYHMyclRkyZNApacnJxyd7ljxw4VFRUpJiYmoDwmJka5ublBVfumm25S69atA4LQIxHT+AAAAAfVzHCqrKwsZWZmBpT5fL4a2XZpd911l5555hm99dZbioiIOCT7cAUBJAAAOGL5fL6gA8aoqCiFhYUpLy8voDwvL0+xsbGVvvaee+7RXXfdpTfffFM9evSodn0PF3RhAwAA93i8NbOEIDw8XElJSVqxYoW/rLi4WCtWrFBKSkqFr/vrX/+q2267TcuXL1fv3r2rfciHEzKQAADAOZ46mhEkMzNTGRkZ6t27t/r27auZM2cqPz9fI0eOlCSNGDFCcXFx/nGUd999tyZNmqSnnnpK8fHx/rGSDRs2VMOGDevkGGoDASQAAMB/DR06VNu3b9ekSZOUm5urnj17avny5f4Ha7Zu3Sqv93+ZzQceeECFhYW68MILA7YzefJkZWdn12bVaxXzQKIM5oHE0Y55IIEK1OI8kLZlWY1sxxM/sEa2g0BkIAEAgHtCHL+I2sXVAQAAQEjIQAIAAAcxnMplBJAAAMA9jMd3GgEkAABwD2MgncbVAQAAQEjIQAIAAAfRhe0yAkgAAOAexkA6jS5sAAAAhIQMJAAAcA8P0TiNABIAADiILmyXEd4DAAAgJGQgAQCAe3iIxmkEkAAAwEF0krqMqwMAAICQkIEEAADuoQvbaQSQAADAPQSQTiOABAAADmKUncu4OgAAAAgJGUgAAOAeurCdRgAJAAAcRADpMrqwAQAAEBIykAAAwD10YTuNABIAADiIANJldGEDAAAgJGQgAQCAe+jCdhoBJAAAcBCdpC7j6gAAACAkZCABAIB76MJ2GgEkAABwEAGkywggAQCAe8hAOo0xkAAAAAgJGUgAAOAgMpAuI4AEAADuoQvbaXRhAwAAICRkIAEAgIPIQLqMABIAALiHLmyn0YUNAACAkJCBBAAADiLH5TICSAAA4B66sJ1GeA8AAICQkIEEAAAOIgPpMgJIAADgIAJIlxFAAgAA53gYA+k0xkACAAAgJGQgAQCAg8hAuowAEgAAuIcubKfRhQ0AAICQkIEEAAAOIgPpMgJIAADgHg+dpC7j6gAAACAkZCABAICD6MJ2GQEkAABwD09hO40ubAAAAISEDCQAAHAQGUiXEUACAAD30IXtNAJIAADgIAJIlzEGEgAAACEhAwkAANxDF7bTCCABAICDCCBdRhc2AAAAQkIGEgAAuIffwnYaVwcAADjIU0NL6ObMmaP4+HhFREQoOTlZa9eurXT9Z599Vl26dFFERIROOOEELVu2rFr7PZwQQAIAAPzX4sWLlZmZqcmTJ+vDDz9UYmKi0tPTtW3btnLXf++99zRs2DD96U9/0kcffaQhQ4ZoyJAh+uyzz2q55rXLY2ZW15WAW7J58g1HuezymsV9O2u/IoBrIlrU3r727aiZ7UREhbR6cnKy+vTpo9mzZ0uSiouL1bZtW40ZM0Y333xzmfWHDh2q/Px8vfzyy/6y3/3ud+rZs6fmzZt3cHV3GGMgUUa5N0/gaFebN04AqounsAsLC7Vu3TplZWX5y7xer9LS0rR69epyX7N69WplZmYGlKWnp2vp0qWHsqp1jgDyKFRQUKCCgoKAMp/PJ5/PV0c1AgDg0Ajlnrdjxw4VFRUpJiYmoDwmJkZffPFFudvPzc0td/3c3NyDrLnbGAN5FMrJyVGTJk0ClvT09DIfMOBoVlBQoOzsbD4XQCm19tmIaFEjS3n3vJycnENb96MAAeRRKCsrS3v27PEv//73v/X2229zowQOUFBQoClTpvC5AEo53D4bpe95e/bsCeiiPlBUVJTCwsKUl5cXUJ6Xl6fY2NhyXxMbGxvS+kcKAsijkM/nU+PGjQMWAACOROXd8yoashUeHq6kpCStWLHCX1ZcXKwVK1YoJSWl3NekpKQErC9Jb7zxRoXrHykYAwkAAPBfmZmZysjIUO/evdW3b1/NnDlT+fn5GjlypCRpxIgRiouL83eDjx07Vv3799e9996rQYMG6ZlnntEHH3yghx56qC4P45AjgAQAAPivoUOHavv27Zo0aZJyc3PVs2dPLV++3P+gzNatW+X1/q8D96STTtJTTz2lW265RRMmTFCnTp20dOlSde/eva4OoVYwDyRUUFCgnJwcZWVl8SQ28F98LoDy8dmARAAJAACAEPEQDQAAAEJCAAkAAICQEEACAAAgJASQAAAACAkBJAAAAEJCAAkAAICQEEACAAAgJASQAAAACAkBJAAAAEJCAAkAAICQEEACAAAgJP8fRQjwmzqRBpkAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plot_likelihood(A[1][:,:,1], 'Payoff structure of choosing to hide penny in right hand for the two contexts')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "S6qm9qIt47qr",
        "outputId": "96aaa895-b557-4a9f-caa6-fd7a73fedc11",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 394
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plot_likelihood(A[1][:,:,0], 'Payoff structure of choosing to hide the penny in the left hand for the two contexts') "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nhxSRh-647qt"
      },
      "source": [
        "## State transitions B"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "v7baZg7347qt",
        "outputId": "967378ef-ce7a-4e22-b38a-3207ec3f7bd4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[array([[[1.],\n",
            "         [0.]],\n",
            "\n",
            "        [[0.],\n",
            "         [1.]]]) array([[[1., 0.],\n",
            "                         [1., 0.]],\n",
            "\n",
            "                        [[0., 1.],\n",
            "                         [0., 1.]]])]\n"
          ]
        }
      ],
      "source": [
        "## State transitions between hidden states B\n",
        "\n",
        "\"\"\" Initialize B-array\"\"\"\n",
        "B = utils.obj_array(num_factors)\n",
        "\n",
        "\"\"\" Fill in transition probabilities for the context (Hider actions) which are uncontrollable\"\"\" \n",
        "B_context = np.zeros( (len(context_names), len(context_names), len(context_action_names)) )\n",
        "B_context[:,:,0] = np.eye(len(context_names))\n",
        "B[0] = B_context\n",
        "\n",
        "\"\"\" Fill in transition probabilities for choice state factor, which are controllable\"\"\"\n",
        "B_choice = np.zeros( (len(choice_names), len(choice_names), len(choice_action_names)) )\n",
        "\n",
        "for choice_i in range(len(choice_names)):\n",
        "  \n",
        "  B_choice[choice_i, :, choice_i] = 1.0 #action x leads to to choice state x, independently of previous state\n",
        "\n",
        "B[1] = B_choice\n",
        "B[1]= utils.norm_dist(B[1])\n",
        "\n",
        "print(B)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "eo59HC_A47qv"
      },
      "outputs": [],
      "source": [
        "## Prior preferences C for outcomes \n",
        "\n",
        "\"\"\" Initialize C based on the number of observation modalities\"\"\"\n",
        "C = utils.obj_array_zeros(num_obs)\n",
        "C_reward = np.zeros(len(reward_obs_names))\n",
        "\n",
        "### 1. Reward outcomes (noisy): preference (win)> preference (loose)\n",
        "C_reward[0] = -4.0 ## strong aversion to loss observation\n",
        "C_reward[1] = 2.0  ## slight preference for win\n",
        "\n",
        "### 2. Self-choices (directly accessible): no prior preferences, so C[2] remains flat\n",
        "C[0] = C_reward\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XIu8qAjG47qw"
      },
      "outputs": [],
      "source": [
        "## Starting state D: random starting state\n",
        "\n",
        "\"\"\" Initialize D based on hidden state factors: choice and context\"\"\"\n",
        "D = utils.obj_array(num_factors)\n",
        "\n",
        "## Starting-point context hidden state: no beliefs about context or choices or contexts\n",
        "D_context = np.array([0.5,0.5]) #random starting context-state\n",
        "D[0] = D_context\n",
        "\n",
        "## Starting point choice hidden state\n",
        "D_choice = np.zeros(len(choice_names)) # random starting choice-state\n",
        "D_choice = np.array([0.5,0.5])\n",
        "\n",
        "D[1] = D_choice"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Q5AboRa547qw"
      },
      "outputs": [],
      "source": [
        "## Prior preference over actions E: no prior preference\n",
        "E = utils.obj_array_zeros(num_controls)\n",
        "E = np.array([0.5,0.5]) "
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Additional parameters"
      ],
      "metadata": {
        "id": "7qEIUfbmas7F"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Active inference allows for the specificafion of parameters alpha and gamma that control randomness in action selection and prior precision, respectively. \n",
        "\n",
        "For alpha > 16...., for alpha < 16 ...\n",
        "For gamma > 16...., for gamma < 16..."
      ],
      "metadata": {
        "id": "arDkUsqCZ5XM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "alpha = 16\n",
        "gamma = 16  #default value = 16"
      ],
      "metadata": {
        "id": "PBo26Au5a3jL"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "l6Y9R_br47qx"
      },
      "outputs": [],
      "source": [
        "# Use agent class to construct active inference agent \n",
        "OToM_agent = Agent(A,B,C,D,E,alpha, gamma)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "id": "NHfG7Pxk47qx",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "35c206c7-a186-4b70-a1b2-83589cc802a6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "fatal: not in a git directory\n",
            "fatal: not in a git directory\n"
          ]
        }
      ],
      "source": [
        "!git \n",
        "\n",
        "!git config –global user.email “nvrmindny7@gmail.com”\n",
        "!git config –global user.name “Annaother”"
      ]
    }
  ],
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      "display_name": "base",
      "language": "python",
      "name": "python3"
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