brd_py.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Best Response Dynamics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Author: Yuya Furusawa\n",
    "\n",
    "*Graduate School of Economics, University of Tokyo*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This note demonstrates the best response dynamics model and its related models with `quantecon.game_theory` Python library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from quantecon.game_theory.brd import BRD, KMR, SamplingBRD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Best response dynamics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Best response dynamics is one of the strategy updating methods.\n",
    "At each round, the set of players is chosen, and they take best responses given other players' current strategy.\n",
    "Players who take best response only consider the next round payoff, that is they don't consider the future payoffs.\n",
    "From this feature, best response dynamics, is called **myopic best response**. \n",
    "\n",
    "In the potential game, you can find a Nash equilibrium by best response dynamics."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### KMR model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kandori-Mailath-Rob model(KMR model) is an evolutional model, similar to best response dynamics model.\n",
    "In KMR model, agents do not always take a strategy which delivers highest payoff, they sometimes take another strategy.\n",
    "Unlike best response dynamics, in KMR model, the system is not deterministic evolution.\n",
    "Startegy flips can occur in every period.\n",
    "\n",
    "KMR model gives a **[risk-dominance](https://en.wikipedia.org/wiki/Risk_dominance) equilibrium** as stationary equilibrium.\n",
    "In contrast, best response dynamics does not always give a risk-dominance equilibrium.\n",
    "(We see these contrast later.)\n",
    "\n",
    "KMR model is sometimes criticised by the absense of the foundation of strategy flips.\n",
    "To overcome this point, logit response dynamics model incorporates decision theoretic foundation of strategy chooice (See this note)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sampling best response dynamics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sampling best response dynamics model is also evolutional model.\n",
    "In this model, agents who get a chance to revise an action observe the randomly sampled opponents' actions, and then take a best resoponse.\n",
    "If $k$ sample observed, we call **$k$-sampling best response dynamics**.\n",
    "\n",
    "Under some conditions, this dynamics gives p-dominant equilibrium as stationary equilibirum (To refer the *p-dominant equilibrium*, see Morris, Rob and Shin(1995))."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `brd.py` usage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# payoff matrix\n",
    "payoff_matrix = [[4, 0],\n",
    "                 [3, 2]]\n",
    "# the number of players\n",
    "N = 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To create `BRD` class instance, you need payoff matrix and the integer representing the number of players."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Best Response Dynamics\n",
    "brd = BRD(payoff_matrix, N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You need additionally specify `epsilon`, the probability of strategy flips, and `k`, sample size, to create `KMR` and `SamplingBRD` class instances respectively.\n",
    "If not provided, these are set to `epsilon=0.1` and `k=2` by default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# KMR model\n",
    "epsilon = 0.1\n",
    "kmr = KMR(payoff_matrix, N, epsilon)\n",
    "\n",
    "# Sampling Best Response Dynamics\n",
    "k = 2\n",
    "sbrd = SamplingBRD(payoff_matrix, N, k)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `play` method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`play` method proceeds the game by one step.\n",
    "`play` method requires two arguments: `action` and `action_dist`.\n",
    "\n",
    "`action_dist` is the current action distribution(in other words \"frquency\", not probability distribution) where first element indicates the number of players who takes action 0.\n",
    "`action` is the pure action of a player who taks an action."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 3]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Two players take action 0 and the other two take action 1\n",
    "# A player who takes action 0 take her best reponse given opponents' actions.\n",
    "action = 0\n",
    "action_dist = [2, 2]\n",
    "brd.play(action, action_dist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can use `play` similarly in KMR model and sampling best response dynamics model."
   ]
  },
  {
   "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 chosen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 2],\n",
       "       [3, 1],\n",
       "       [3, 1],\n",
       "       [3, 1],\n",
       "       [3, 1]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts_length = 5\n",
    "init_action_dist = [2, 2]\n",
    "brd.time_series(ts_length, init_action_dist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can use `time_series` similarly KMR model and sampling best response dynamics model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We illustrate the dynamics of players' actions with **coordination game** and **Young's game**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Coordination game is defined as follows:\n",
    "\n",
    "1$\\backslash$2 | $A$           | $B$ \n",
    " ------------- |---------------| ---------\n",
    " $A$           | 2, 2          |   0, 0   \n",
    " $B$           | 0, 0          |   1, 1   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "coordination_game_matrix = [[2, 0],\n",
    "                            [0, 1]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "young_game_matrix = [[6, 0, 0],\n",
    "                     [5, 7, 5],\n",
    "                     [0, 5, 8]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The number of agents is set to 10 and the length of time series is 200."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 10\n",
    "ts_length = 200"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the function to plot the graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_graph(brd, ts_length, init_action_dist, random_state=None):\n",
    "    series = brd.time_series(ts_length, init_action_dist=init_action_dist, random_state=random_state)\n",
    "    action_label = ['A', 'B', 'C']\n",
    "    fig, ax = plt.subplots(figsize=(8,5))\n",
    "    for h in range(brd.num_actions):\n",
    "        ax.plot(series[:, h], linewidth=2, label='action {0}'.format(action_label[h]))\n",
    "    ax.set_ylim(0, N+1)\n",
    "    plt.legend(loc=4)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the graphs below, vertical axis represents the number of players who take each actions, and holizontal axis represents the periods."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Best Response Dynamics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In evolutionary game theory, best response dynamics represents a class of strategy updating rules, where each player's strategy in the next round is determined by their best response to subset of population."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Coordination Game"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "brd_coor = BRD(coordination_game_matrix, N=N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Only 2 players take action A initially.\n",
    "m = 2\n",
    "plot_graph(brd_coor, ts_length, [m, N-m])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Eight players take action A initially.\n",
    "m = 8\n",
    "plot_graph(brd_coor, ts_length, [m, N-m])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see converged action profile depends on the initial action distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kandori-Mailath-Rob model (KMR model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Coordination Game"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "kmr_coor = KMR(coordination_game_matrix, N=N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = 2\n",
    "plot_graph(kmr_coor, ts_length, [m, N-m])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This graph shows (A,A) is the long-run equilibrium which is a risk-dominance equilibrium (if not, pick larger `ts_length`).\n",
    "\n",
    "To compare the results from best response dynamics see the above, (A,A) becomes stationary equilibrium even if the number of player who initially takes action A is small. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Young's Game"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "kmr_young = KMR(young_game_matrix, N=N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = 2\n",
    "plot_graph(kmr_young, ts_length, [N-2*m, m, m])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sampling Best Response Dynamics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Coordination Game"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "sbrd_coor = SamplingBRD(coordination_game_matrix, N=N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = 2\n",
    "plot_graph(sbrd_coor, ts_length, [m, N-m])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see (A,A) is the converged action profile, which is the risk-dominance equilibrium."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Young's Game"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "sbrd_young = SamplingBRD(young_game_matrix, N=N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = 2\n",
    "plot_graph(sbrd_young, ts_length, [N-2*m, m, m])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Kandori, Mailath and Rob(1993), \"Learning, Mutation, and Long Run Equilibria in Games.\", Econometrica, vol.61, No.1, 26-59\n",
    "- Morris, Rob, and Shin(1995), \"p-Dominance and belief potential\", Econometrica 63, 145-157.\n",
    "- Oyama, Sandholm and Tercieux(2015), \"Sampling best response dynamics and deterministic equilibirum selection\", Theoretical Economics, 10, 243-281"
   ]
  }
 ],
 "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
}