logitdyn_py.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logit Response Dynamics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Yuya Furusawa**\n",
    "\n",
    "*Graduate School of Economics, University of Tokyo*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook demonstrates how to study logit best response dynamics model using the `logitdyn` Python library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import quantecon.game_theory as gt\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logit Response Dynamics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Logit response dynamics model is one of the learning models.\n",
    "There is much literature that studies the learning in games, for example, fictitious play, (myopic) best response dynamics, Kandori-Mailath-Rob, sampling best response models.\n",
    "Please refer these notes:\n",
    "- fictitious play\n",
    "- best response dynamics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The learning model with random mistakes, including KMR model, is criticised by the absense of the foundation of mistakes.\n",
    "\n",
    "In contrast, **Logit response dynamics**, which incorporates the random mistakes, is based on a theory about the origin of mistakes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $\\Gamma = (I, {(S_i, u_i)}_{i \\in I})$ be a finite normal form game.\n",
    "- $I=\\{1,\\ldots,N\\}$ : player set\n",
    "- $S_i$ : strategies set ($S$ : pure strategy profile)\n",
    "- $u_i$ : payoff function\n",
    "\n",
    "Denote $s=(s_i, s_{-i}) \\in S$ and $u_i(s_i, s_{-i})=u_i(s)$.\n",
    "\n",
    "In logit response dynamics model, players behave as myopic best replier, but have mistakes in thier decisions.\n",
    "A player is chosen to update her action given other players' actions every period (**asynchronous learning**)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When player $i$ is chosen, she will update her action to $s_i$ given actions $s_{-i}$.\n",
    "The probability of choosing action $s_i$ is given by **logit choice function** :\n",
    "$$\n",
    "    p_i(s_i, s_{-i}) = \\frac{\\exp(\\beta u_i(s_i, s_{-i}))}{\\sum_{s_i' \\in S_i} \\exp(\\beta u_i(s_i', s_{-i}))}\n",
    "$$\n",
    "where $0 < \\beta < \\infty$.\n",
    "\n",
    "$\\beta$ can be interpreted as an inverse measure of the level of noise in players' decisions.\n",
    "As $\\beta$ becomes larger, the size of noise becomes smaller.\n",
    "From the microeconomic point of view, this modeling is based on a random-utility model, decision thoretic foundation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Logit response dynamics can converge to the set of Nash equilibria in the potential game.\n",
    "We call this converged state as stabel state.\n",
    "First, we introduce the definition of potential game.\n",
    "\n",
    "**Definition(potential game)**\n",
    "\n",
    "The $\\Gamma$ is a *potential game* if there exists a function $\\rho:S \\rightarrow \\mathbb{R}$ such that for all $i \\in I$, $s_i, s_i' \\in S_i$, $s_{-i} \\in S_{-i}$,\n",
    "$$\n",
    "    u_i(s_i, s_{-i}) - u_i(s_i', s_{-i}) = \\rho(s_i, s_{-i}) - \\rho(s_i', s_{-i})\n",
    "$$\n",
    "\n",
    "$\\rho$ is called the potential."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following game is the potential game:\n",
    "\n",
    "1$\\backslash$2 | $A$           | $B$ \n",
    " ------------- |---------------| ---------\n",
    " $A$           | 4, 4          |   0, 3   \n",
    " $B$           | 3, 0          |   2, 2     \n",
    " \n",
    "To see this, the potential $\\rho$ can be defined\n",
    "\n",
    "1$\\backslash$2 | $A$        | $B$ \n",
    " ------------- |------------| ---------\n",
    " $A$           | 1          |   0  \n",
    " $B$           | 0          |   2     \n",
    "\n",
    "(Note every $2 \\times 2$ symmetric game is the potential game)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Theorem**\n",
    "\n",
    "In the potential game, the set of stable states of logit response dynamics is equal to the set of maximizers of $\\rho$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will check this later."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `logitdyn.py` usage"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To create `LogitDynamics` class instance, you need the played game and the parameter $\\beta$.\n",
    "The game has to be `NormalFormGame` instance or array like.\n",
    "As argued before, $\\beta$ is the level of noise in the players' decisions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "payoff = [[4, 0],\n",
    "          [3, 2]]\n",
    "game = gt.NormalFormGame(payoff)\n",
    "beta = 2.0\n",
    "ldy = gt.LogitDynamics(game, beta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can check the cumulative elements of logit choice function(normalized $\\exp(\\beta u_i(s_i, s_{-i}))$) for each player by `logit_choice_cdfs` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[1.        , 1.13533528],\n",
       "        [0.01831564, 1.01831564]]),\n",
       " array([[1.        , 1.13533528],\n",
       "        [0.01831564, 1.01831564]]))"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ldy.logit_choice_cdfs()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `play` method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`play` method returns a new action profile in the model.\n",
    "You can specify the initial action profile.\n",
    "If not provided, it is determined randomly.\n",
    "In addition, you can proceed the dynamics multiple times by specifying `num_reps`, which is set to 1 by default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 0)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "init_actions = (0, 0) # both players take action 0\n",
    "ldy.play(init_actions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 0)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ldy.play(init_actions, num_reps=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `time_series` method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`time_series` method returns a time series of action distributions.\n",
    "You have to specify the length of time series.\n",
    "In addition, you can choose initial action distribution from which the dynamics proceeds.\n",
    "If not specified, it is randomly choosed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0],\n",
       "       [0, 0],\n",
       "       [0, 0],\n",
       "       [0, 0],\n",
       "       [0, 0]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts_length = 5\n",
    "init_actions = (0, 0)\n",
    "ldy.time_series(ts_length, init_actions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see the convergence of the logit response dynamics in the potential game.\n",
    "We use the coordination game defined above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "payoff = [[4,0],\n",
    "          [3,2]]\n",
    "beta = 4.0\n",
    "ldy = gt.LogitDynamics(payoff, beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "ts_length = 1000\n",
    "init_actions = (0,0)\n",
    "series = ldy.time_series(ts_length, init_actions)\n",
    "seriesB = np.where(series==1, 1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 5))\n",
    "ax.set_prop_cycle('color', ['b', 'g'])\n",
    "ax.plot(np.cumsum(seriesB[:, 0], axis=0)/np.arange(1,ts_length+1), linewidth=2, label=\"Player 1\")\n",
    "ax.plot(np.cumsum(seriesB[:, 1], axis=0)/np.arange(1,ts_length+1), linewidth=2, label=\"Player 2\")\n",
    "ax.set_ylim(0, 1)\n",
    "plt.legend()\n",
    "plt.title(\"Cumulative Frequency of Action B\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, (B,B) is a stable state of this dynamics, and this state maximizers of the potential $\\rho$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we simulate the logit reponse dynamics in the Young's game.\n",
    "Young's game is defined as follows:\n",
    "\n",
    "1$\\backslash$2 | $A$           | $B$      | $C$\n",
    " ------------- |---------------| ---------| --------\n",
    " $A$           | 6, 6          |   0, 0   |   0, 0\n",
    " $B$           | 5, 5          |   7, 7   |   5, 5\n",
    " $C$           | 0, 0          |   5, 5   |   8, 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "young_game_matrix = [[6, 0, 0],\n",
    "                     [5, 7, 5],\n",
    "                     [0, 5, 8]]\n",
    "beta = 4.0\n",
    "ldy = gt.LogitDynamics(young_game_matrix, beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ts_length = 1000\n",
    "init_actions = (0,0)\n",
    "series = ldy.time_series(ts_length, init_actions)\n",
    "seriesB = np.where(series==1, 1, 0)\n",
    "fig, ax = plt.subplots(figsize=(8, 5))\n",
    "ax.set_prop_cycle('color', ['b', 'g'])\n",
    "ax.plot(np.cumsum(seriesB[:, 0], axis=0)/np.arange(1,ts_length+1), linewidth=2, label=\"Player 1\")\n",
    "ax.plot(np.cumsum(seriesB[:, 1], axis=0)/np.arange(1,ts_length+1), linewidth=2, label=\"Player 2\")\n",
    "ax.set_ylim(0, 1)\n",
    "plt.legend()\n",
    "plt.title(\"Cumulative Frequency of Action B\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reference\n",
    "- Alós-Ferrer, Carlos, and Nick Netzer. \"The logit-response dynamics.\" Games and Economic Behavior 68.2 (2010): 413-427."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}