{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 6) Using Gambit with OpenSpiel\n", "\n", "This tutorial demonstrates the interoperability of the Gambit and OpenSpiel Python packages for game-theoretic analysis.\n", "\n", "Where Gambit is used to compute exact equilibria for games, OpenSpiel provides a variety of iterative learning algorithms that can be used to approximate strategies. Another key distinction is that the PyGambit API allows the user a simple way to define custom games (see tutorials 1-3). This is also possible in OpenSpiel for normal form games, and you can load `.efg` files created from Gambit for extensive form, however some of the key functionality for iterated learning of strategies is only available for games from the built-in library (see the [OpenSpiel documentation](https://openspiel.readthedocs.io/en/latest/games.html)).\n", "\n", "This tutorial demonstrates:\n", "\n", "1. Transferring examples of normal (strategic) form and extensive form games between OpenSpiel and Gambit\n", "2. Simulating evolutionary dynamics of populations of strategies in OpenSpiel for normal form games\n", "3. Training agents using self-play of extensive form games in OpenSpiel to create strategies\n", "4. Comparing the strategies from OpenSpiel against equilibria strategies computed with Gambit\n", "\n", "Note:\n", "- The version of OpenSpiel used in this tutorial is `1.6.1`. If you are running this tutorial locally, this will be the version installed via the included `requirements.txt` file.\n", "- The OpenSpiel code was adapted from the introductory tutorial for the OpenSpiel API on colab [here](https://colab.research.google.com/github/deepmind/open_spiel/blob/master/open_spiel/colabs/OpenSpielTutorial.ipynb)." ] }, { "cell_type": "code", "execution_count": 1, "id": "ebb78322", "metadata": {}, "outputs": [], "source": [ "from io import StringIO\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from open_spiel.python import rl_environment\n", "from open_spiel.python.algorithms import tabular_qlearner\n", "from open_spiel.python.algorithms.gambit import export_gambit\n", "from open_spiel.python.egt import dynamics\n", "from open_spiel.python.egt.utils import game_payoffs_array\n", "\n", "import pyspiel\n", "\n", "import pygambit as gbt" ] }, { "cell_type": "markdown", "id": "fd324814", "metadata": {}, "source": [ "## OpenSpiel game library\n", "\n", "The [library of games](https://openspiel.readthedocs.io/en/latest/games.html) included in OpenSpiel is extensive. Many of these games will not be amenable to equilibrium computation with Gambit, due to their size. For the purposes of this tutorial, we'll pick small games from the list below." ] }, { "cell_type": "code", "execution_count": 2, "id": "b3eb3671", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "['2048', 'add_noise', 'amazons', 'backgammon', 'bargaining', 'battleship', 'blackjack', 'blotto', 'breakthrough', 'bridge', 'bridge_uncontested_bidding', 'cached_tree', 'catch', 'checkers', 'chess', 'cliff_walking', 'clobber', 'coin_game', 'colored_trails', 'connect_four', 'coop_box_pushing', 'coop_to_1p', 'coordinated_mp', 'crazy_eights', 'cribbage', 'cursor_go', 'dark_chess', 'dark_hex', 'dark_hex_ir', 'deep_sea', 'dots_and_boxes', 'dou_dizhu', 'efg_game', 'einstein_wurfelt_nicht', 'euchre', 'first_sealed_auction', 'gin_rummy', 'go', 'goofspiel', 'hanabi', 'havannah', 'hearts', 'hex', 'hive', 'kriegspiel', 'kuhn_poker', 'laser_tag', 'leduc_poker', 'lewis_signaling', 'liars_dice', 'liars_dice_ir', 'lines_of_action', 'maedn', 'mancala', 'markov_soccer', 'matching_pennies_3p', 'matrix_bos', 'matrix_brps', 'matrix_cd', 'matrix_coordination', 'matrix_mp', 'matrix_pd', 'matrix_rps', 'matrix_rpsw', 'matrix_sh', 'matrix_shapleys_game', 'mfg_crowd_modelling', 'mfg_crowd_modelling_2d', 'mfg_dynamic_routing', 'mfg_garnet', 'misere', 'mnk', 'morpion_solitaire', 'negotiation', 'nfg_game', 'nim', 'nine_mens_morris', 'normal_form_extensive_game', 'oh_hell', 'oshi_zumo', 'othello', 'oware', 'pathfinding', 'pentago', 'phantom_go', 'phantom_ttt', 'phantom_ttt_ir', 'pig', 'quoridor', 'rbc', 'repeated_game', 'restricted_nash_response', 'sheriff', 'skat', 'solitaire', 'spades', 'start_at', 'stones_and_gems', 'tarok', 'tic_tac_toe', 'tiny_bridge_2p', 'tiny_bridge_4p', 'tiny_hanabi', 'trade_comm', 'turn_based_simultaneous_game', 'twixt', 'ultimate_tic_tac_toe', 'universal_poker', 'y', 'zerosum']\n" ] } ], "source": [ "print(pyspiel.registered_names())" ] }, { "cell_type": "markdown", "id": "e628a86d", "metadata": {}, "source": [ "## Normal form games from the OpenSpiel library\n", "\n", "Let's start with a simple normal form game of rock-paper-scissors, in which the payoffs can be represented by a 3x3 matrix.\n", "\n", "Load matrix rock-paper-scissors from OpenSpiel:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "ops_matrix_rps_game = pyspiel.load_game(\"matrix_rps\")" ] }, { "cell_type": "markdown", "id": "fda1204e", "metadata": {}, "source": [ "In order to simulate a playthrough of the game, you can first initialise a game state:" ] }, { "cell_type": "code", "execution_count": 4, "id": "1bcdb97b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Terminal? false\n", "Row actions: Rock Paper Scissors \n", "Col actions: Rock Paper Scissors \n", "Utility matrix:\n", "0,0 -1,1 1,-1 \n", "1,-1 0,0 -1,1 \n", "-1,1 1,-1 0,0 " ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "state = ops_matrix_rps_game.new_initial_state()\n", "state" ] }, { "cell_type": "markdown", "id": "eeee015a", "metadata": {}, "source": [ "The possible actions for both players (player 0 and player 1) are Rock, Paper and Scissors, but these are not labelled and must be accessed via integer indices:" ] }, { "cell_type": "code", "execution_count": 5, "id": "70575dc7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0, 1, 2]\n", "[0, 1, 2]\n" ] } ], "source": [ "print(state.legal_actions(0)) # Player 0 (row) actions\n", "print(state.legal_actions(1)) # Player 1 (column) actions" ] }, { "cell_type": "markdown", "id": "fdea7e5b", "metadata": {}, "source": [ "Since Rock-paper-scissors is a 1-step simultaneous-move normal form game, we'll apply a list of player actions in one step to reach the terminal state.\n", "\n", "Let's simulate player 0 playing Rock (0) and player 1 playing Paper (1):" ] }, { "cell_type": "code", "execution_count": 6, "id": "a532321e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Terminal? true\n", "History: 0, 1\n", "Returns: -1,1\n", "Row actions: \n", "Col actions: \n", "Utility matrix:\n", "0,0 -1,1 1,-1 \n", "1,-1 0,0 -1,1 \n", "-1,1 1,-1 0,0 " ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "state.apply_actions([0, 1])\n", "state" ] }, { "cell_type": "markdown", "id": "045cf8dd", "metadata": {}, "source": [ "OpenSpiel can generate an NFG representation of the game loadable in Gambit:" ] }, { "cell_type": "code", "execution_count": 7, "id": "f5fa4e42", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'NFG 1 R \"OpenSpiel export of matrix_rps()\"\\n{ \"Player 0\" \"Player 1\" } { 3 3 }\\n\\n0 0\\n1 -1\\n-1 1\\n-1 1\\n0 0\\n1 -1\\n1 -1\\n-1 1\\n0 0\\n'" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nfg_matrix_rps_game = pyspiel.game_to_nfg_string(ops_matrix_rps_game)\n", "nfg_matrix_rps_game" ] }, { "cell_type": "markdown", "id": "70d1df64", "metadata": {}, "source": [ "Now let's load the NFG in Gambit. Since Gambit's `read_nfg` function expects a file like object, we'll convert the string with `io.StringIO`.\n", "We can also add labels for the actions to make the output more interpretable." ] }, { "cell_type": "code", "execution_count": 8, "id": "b684325e", "metadata": {}, "outputs": [ { "data": { "text/html": [ "

Rock-Paper-Scissors

\n", "
RockPaperScissors
Rock0,0-1,11,-1
Paper1,-10,0-1,1
Scissors-1,11,-10,0
\n" ], "text/plain": [ "Game(title='Rock-Paper-Scissors')" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gbt_matrix_rps_game = gbt.read_nfg(StringIO(nfg_matrix_rps_game))\n", "\n", "gbt_matrix_rps_game.title = \"Rock-Paper-Scissors\"\n", "\n", "for player in gbt_matrix_rps_game.players:\n", " player.strategies[0].label = \"Rock\"\n", " player.strategies[1].label = \"Paper\"\n", " player.strategies[2].label = \"Scissors\"\n", "\n", "gbt_matrix_rps_game" ] }, { "cell_type": "markdown", "id": "6d7da6f3", "metadata": {}, "source": [ "The equilibrium mixed strategy profile for both players is to choose rock, paper, and scissors with equal probability:" ] }, { "cell_type": "code", "execution_count": 9, "id": "707c6c30", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\left[\\left[\\frac{1}{3},\\frac{1}{3},\\frac{1}{3}\\right],\\left[\\frac{1}{3},\\frac{1}{3},\\frac{1}{3}\\right]\\right]$" ], "text/plain": [ "[[Rational(1, 3), Rational(1, 3), Rational(1, 3)], [Rational(1, 3), Rational(1, 3), Rational(1, 3)]]" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gbt.nash.lcp_solve(gbt_matrix_rps_game).equilibria[0]" ] }, { "cell_type": "markdown", "id": "966e7e3f", "metadata": {}, "source": [ "We can use OpenSpiel's dynamics module to demonstrate evolutionary game theory dynamics, or \"replicator dynamics\", which models how a mixed strategy profile evolves over time based on how the strategies (e.g., choice of actions A, B, C with probabilities X, Y, Z) perform against one another.\n", "\n", "Let's start with an initial profile that is not at equilibrium, but weighted towards scissors with proportions: 30% Rock, 30% Paper, 40% Scissors:" ] }, { "cell_type": "code", "execution_count": 10, "id": "cf1acdeb", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0.03, -0.03, 0. ])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "matrix_rps_payoffs = game_payoffs_array(ops_matrix_rps_game)\n", "dyn = dynamics.SinglePopulationDynamics(matrix_rps_payoffs, dynamics.replicator)\n", "x = np.array([0.3, 0.3, 0.4])\n", "dyn(x)" ] }, { "cell_type": "markdown", "id": "fa382753", "metadata": {}, "source": [ "`dyn(x)` calculates the rate of change (derivative) for each strategy in the current profile and returns how fast each strategy's frequency is changing.\n", "\n", "In replicator dynamics, a strategy that performs well against others will increase in frequency, while strategies performing worse will decrease.\n", "In our rock-paper-scissors example, the performance of each strategy depends on the probability it is assigned in the mixed strategy profile. At the start, whilst there are more players choosing scissors as their action, then rock will perform well and increase in frequency (be more likely to get played in subsequent rounds), while paper will perform poorly and decrease in frequency. We can plot how the frequency of each strategy changes over time:" ] }, { "cell_type": "code", "execution_count": 11, "id": "b9a352c5", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_rps_dynamics(proportions, steps=100, alpha=0.1, plot_average_strategy=False):\n", " x = np.array(proportions)\n", " rock_proportions = [x[0]]\n", " paper_proportions = [x[1]]\n", " scissors_proportions = [x[2]]\n", " y = []\n", " for _ in range(steps):\n", " x += alpha * dyn(x)\n", " rock_proportions.append(x[0])\n", " paper_proportions.append(x[1])\n", " scissors_proportions.append(x[2])\n", " if plot_average_strategy:\n", " y.append([np.mean(rock_proportions), np.mean(paper_proportions), np.mean(scissors_proportions)])\n", " else:\n", " y.append(x.copy())\n", " y = np.array(y)\n", "\n", " plt.plot(y[:, 0], label=\"Rock\")\n", " plt.plot(y[:, 1], label=\"Paper\")\n", " plt.plot(y[:, 2], label=\"Scissors\")\n", " plt.xlabel(\"Time step\")\n", " if plot_average_strategy:\n", " plt.ylabel(\"Strategy frequency average up to time step\")\n", " else:\n", " plt.ylabel(\"Strategy frequency\")\n", " plt.legend()\n", " plt.show()\n", "\n", "plot_rps_dynamics([0.3, 0.3, 0.4])" ] }, { "cell_type": "markdown", "id": "8569aef4", "metadata": {}, "source": [ "Through the dynamics, we can see that the population proportions oscillate around the equilibrium point (1/3, 1/3, 1/3) without converging to it, because the best strategy depends on the likelihood of the opponents' actions, as defined by the current action probabilities.\n", "\n", "However, if we start with the initial population already at the equilibrium mixed strategy profile computed by Gambit (each action is chosen exactly 1/3 of the time), the strategy frequencies will remain constant over time (at the equilibrium point):" ] }, { "cell_type": "code", "execution_count": 12, "id": "86c6aa52", "metadata": {}, "outputs": [ { "data": { "image/png": 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y5YocPXrUs0277KJr3bq1/P333xa2NOTNnz/fq1suMdCCBADAXXZ1aWuOP97XV9qV1aBBA1sGDRpkIUdDzGuvvebTeYYOHSrPPvustex8//33dg7t/nryySftnFo3pPt++OEHCQsLkzFjxkjPnj3jfH7tmotOW5327t1rLV1Lly6Vbt26ybvvvmv1TO6uvYRGCxIAAHdBW0O0q+teL3GtP7qdUqVKydWrV62bTVtwfBnK/9BDD8krr7xiIahly5by6aefegWarl27yrx58+TVV1+VadOm2faSJUvKunXrrG7LTeuMtNhbW7BuR0fRafH3+PHjrfVLz/Prr79KYkkSAWnSpEkSGhpqybZ69erWDxobvdlVqlSxanpNmBUqVJCZM2fGerz+gvQ/onHjxnlt1/fT7dEXbSYEACC50aH8jz76qBVga5fXgQMH5Msvv7Q6nyeeeMLqkWrVqmXdcNpCc+DAAWsZWrx48S3n0q4uHWWmIUVHrGnA2bRpk4UfpaPPlixZYufYunWrrFy50rNPW36OHDlirUlaoP3NN99Y65N22bnrj2Ki3YAff/yx/Pbbb7J//377OTQw6Wi8ZNvFNnfuXLsxWjSm4UiDjDbNaVNarly5bjk+e/bsMnDgQCvs0nkRdAhix44d7Vh9XXTaR7l+/XobDhiT4cOHW1+mmyZYAACSGx1Fpp+xOhJM64UiIiKslUc/A998803PSDHtanvmmWesValYsWIxNhzoqDUNXO3bt7e5lHQovrYgDRs2zPZHRkbaSDZtkdIpALTeSd9X5c+f34b8a4F3+fLl7TO9U6dO8tZbb932+rVRRK9F84KeXwvAv/32W8mRI4ckliBX9HYuP9BfWNWqVa2i3T3UUH9pmi51boS40CKzZs2ayYgRIzzbdCihnltTrO7TRKtL9BYk57bbuXHjhi1uly5dsuu8ePGi/QcAAEj+rl+/bi0jhQsXtl4PBN7vST+/s2TJcsfPb792sek8CVu2bLEqeM8FpUpl69q3eCea7XQWUG1t0qZBNw1Zzz//vCVUnS8hNppGNX3qXA5a7HW7ingtMtMb6l40HAEAgOTJr11sZ8+etaYynbUzOl3XvsnYaOrTZjpt0dGmPp1XQSvy3XSmUJ3z4XazbOo+bXnS5r2ff/7ZZhM9ceKEjB07Nsbjdb827TlbkAAAQPLj9xqk+NBaIZ2zQedN0BYkDS46N4JOT64tUh988IEVht2uwj962NHqfa1n0inWtaXIOcOo0m0xbQcAAMmPX7vYtLBLW4C0yCs6XdcZM2Oj3XBaPKYj2HT44FNPPWXBRumzZk6fPm2zbGorki5aZa/Had1RbLReSbvYDh48mIA/IQAACER+DUjaaqOzZWorUPT6IV3XmTbjSl/jLqDW2iMdwqgtTO5FR7FpPZIWbMdGj9PgFdPIOQAAovPz+Cbcg9+P37vYtKurQ4cONreRPldFh/nr8EIduq90GKHWG7lbiPSrHqsP0tNQpMMFdR4kfWCe0qJr57A/nWVTW6SKFy9u61oAvmHDBs+TiHVdJ7t67rnn7OnDAADExD1r87Vr12weHiRN+vtRdzPLtt8DUps2beTMmTP2kDp9Oq92m+nEVO7CbX3oXfTJozQ86URTOr+C/sep8yHphFF6nrjSWiKdEl2nSteQpcMANSBFr0sCAMBJy0J0Th4t5VAZMybMjNZIuJYjDUf6+9Hfk/6+AnYepEAV13kUAADJi35s6h/0Fy5c8PelIBYajrTnKKbwGtfPb7+3IAEAEEj0Qzdv3rxWs6ozUiNp0W61u2k5ciMgAQAQD/ohnBAfxEiaksTDagEAAJISAhIAAIADAQkAAMCBgAQAAOBAQAIAAHAgIAEAADgQkAAAABwISAAAAA4EJAAAAAcCEgAAgAMBCQAAwIGABAAA4EBAAgAAcCAgAQAAOBCQAAAAHAhIAAAADgQkAAAABwISAACAAwEJAADAgYAEAADgQEACAABwICABAAA4EJAAAAAcCEgAAAAOBCQAAAAHAhIAAIADAQkAAMCBgAQAAOBAQAIAAHAgIAEAADgQkAAAABwISAAAAA4EJAAAAAcCEgAAgAMBCQAAwIGABAAA4EBAAgAASIoBadKkSRIaGirp06eX6tWry8aNG2M9dt68eVKlShXJmjWrhISESIUKFWTmzJmxHt+1a1cJCgqScePGeW0/f/68tGvXTu677z47V6dOneTKlSsJ+nMBAIDA5PeANHfuXOnbt68MGTJEtm7dKuXLl5dGjRrJ6dOnYzw+e/bsMnDgQFm3bp3s2LFDOnbsaMuSJUtuOXb+/Pmyfv16yZcv3y37NBzt3LlTli5dKgsXLpTVq1dLly5dEuVnBAAAgSXI5XK5/HkB2mJUtWpVmThxoq1HRUVJgQIFpGfPntK/f/84naNSpUrSrFkzGTFihGfbsWPH7NwanHRfnz59bFG7d++WUqVKyaZNm6w1Si1evFiaNm0qR48ejTFQOV26dEmyZMkiFy9etFYoAACQ9MX189uvLUjh4eGyZcsWqV+//v8uKFUqW9cWojvRbLd8+XLZu3ev1KpVy7NdQ9bzzz8vr7/+upQuXfqW1+m5tVvNHY6Uvqe+94YNG2J8rxs3bthNjb4AAIDkya8B6ezZsxIZGSm5c+f22q7rJ0+ejPV1mvoyZcokadOmtdahCRMmSIMGDTz7R48eLcHBwdKrV68YX6/nzpUrl9c2PV6772J737CwMEuc7kVbuQAAQPIULAEoc+bMsm3bNiuq1hYkrWEqUqSI1KlTx1qkPvjgA6tn0uLshDJgwAB7HzdtQSIkAQCQPPkckFauXCl169ZNkDfPmTOnpE6dWk6dOuW1Xdfz5MkT6+u0K6xYsWL2vY5i05oibeHRgLRmzRor8C5YsKDneG2levXVV20k28GDB+3cziLwmzdv2si22N43Xbp0tgAAgOTP5y62xo0bS9GiReXtt9+WI0eO3NWbaxdZ5cqVrRUoev2QrteoUSPO59HXaI2Q0tojHd2mLUzuRYuutR7JPdJNz33hwgVrbXJbsWKFnUcLuwEAQMrmcwuSjg7TeYemT58uw4YNk0cffdTmEGrRooUFHl9pt1WHDh2sYLpatWrWynP16lUbuq/at28v+fPntxYipV/1WA1pGooWLVpk1zNlyhTbnyNHDluiS5MmjbUMFS9e3NZLlixpQa9z584ydepUiYiIkB49ekjbtm3jNIINAAAkb6ni0y32yiuvWMuMjvh66KGHpFu3bhYstCh6+/btPp2vTZs28t5778ngwYOtu0zPq0Pu3YXbhw8flhMnTniO1/Ck76ej0x555BH56quvZNasWfLiiy/69L6zZ8+WEiVKSL169Wx4f82aNeWjjz7y6RwAACB5uut5kI4fP27BYtSoUTYS7Pr169aFpS0zMQ2xTy6YBwkAgMCTqPMgaZfUf//7X2t5KVSokNX26ESPWly9b98+29a6deu7uX4AAIDAaUHSGa6/+OILm6RRC6K1a6tMmTJex+hcQtrlpkXPyRUtSAAAJN/Pb5+LtHft2mUTM7Zs2TLWYe9ap6TTAQAAAAQivz+LLVDRggQAQOBJtBokHWb/ySef3LJdt+kjPgAAAAKdzwHpww8/tOHxTjpiTUeuAQAApLiApAXYefPmvWX7/fff7zVfEQAAQIoJSPqA1p9++umW7bqNWagBAEBy4PMoNn08R58+fWwuJH3MiNJnp73xxhv2QFgAAIAUF5D0oa/nzp2zx32Eh4fbtvTp00u/fv1kwIABiXGNAAAAgTHM/8qVK7J7927JkCGDPPjgg7HOiZRcMcwfAIDAk2gTRbplypRJqlatGt+XAwAAJFk+B6SrV6/ag2m17uj06dO3PE5k//79CXl9AAAAST8g6bPXVq1aZc9h0+H+QUFBiXNlAAAAgRKQvv/+e/nuu+/kkUceSZwrAgAACLR5kLJlyybZs2dPnKsBAAAIxIA0YsQIGTx4sFy7di1xrggAACDQutjGjBkjf/75p+TOnVtCQ0MlTZo0Xvu3bt2akNcHAACQ9ANSixYtEudKAAAAAn2iyJSOiSIBAEi+n98+1yCpCxcuyL///W97tMj58+c9XWvHjh2L/xUDAAAEahfbjh07pH79+pa+Dh48aA+v1VFt8+bNk8OHD8uMGTMS50oBAADuEZ9bkPr27SsvvPCC/PHHH/aQWremTZvK6tWrE/r6AAAAkn5A2rRpk7z00ku3bM+fP7+cPHkyoa4LAAAgcAJSunTprMDJ6ffff5f7778/oa4LAAAgcAJS8+bNZfjw4RIREWHr+iw2rT3q16+ftGrVKjGuEQAAIGkHJJ0o8sqVK5IrVy75+++/pXbt2lKsWDHJnDmzjBw5MnGuEgAAICmPYtPRa0uXLpW1a9faiDYNS5UqVbKRbQAAAMkBE0XGExNFAgCQfD+/fW5B0vqj29EH2QIAAAQynwPS/Pnzvda1WPvAgQMSHBwsRYsWJSABAICUF5B++eWXGJurdPLIJ598MqGuCwAAwG/i9Sw2J+3DGzZsmAwaNCghTgcAABD4AUlpsZMuAAAAKa6Lbfz48V7rOgjuxIkTMnPmTGnSpElCXhsAAEBgBKT333/faz1VqlT2iJEOHTrIgAEDEvLaAAAAAiMg6Yg1AACA5CzBapAAAABSbAuSDuXXB9TGxbx58+JzTQAAAIHVgqTTcy9fvlw2b97s2bZlyxZZsWKFDffX/e4FAAAgRQSk3Llzy9NPP221SNpCpMv+/fulTZs2Vqz96aefepa4mjRpkoSGhkr69OmlevXqsnHjxliP1ferUqWKZM2aVUJCQqRChQo2gi66oUOHSokSJWx/tmzZ7EG6GzZs8DpG309bwqIvo0aN8vV2AACAZMjnh9VqCFq7dq0UL17ca/vevXvlH//4h5w7d86nC5g7d660b99epk6dauFo3Lhx8uWXX9r5cuXKdcvxP/74o/z1118WgNKmTSsLFy6UV199Vb777jtp1KiRHfP555/ba4sUKSJ///23jbzTc+7bt8+u3x2QOnXqJJ07d/acO3PmzBaq4oKH1QIAEHji+vntcwvSzZs3Zc+ePbds121RUVE+X+jYsWMtpHTs2FFKlSplQSljxozyySefxHh8nTp1rA6qZMmS9uy33r17S7ly5Sy0uT377LPWaqQBqXTp0vYeekN27NjhdS4NRHny5PEstwtHN27csHNEXwAAQPLkc0DSIKMtLxo6NJToMmbMGHnxxRdtny/Cw8OtfknDjOeCUqWy9XXr1t3x9dr4pfVQ2tpUq1atWN/jo48+srRYvnx5r33apZYjRw6pWLGivPvuuxb+YhMWFuZVX1WgQAGfflYAAJCMR7G999571tqioUhn0FZ58+aV119/3bq6fHH27FmJjIy0uqbodD2mVio3bRbLnz+/teqkTp1aJk+eLA0aNPA6Rrve2rZtK9euXbPrW7p0qeTMmdOzv1evXlKpUiXJnj27/PzzzzbJpf48Gvxiovv79u3rWdcWJEISAADJk88BSVt43njjDVvc3Uz3ugZHu8a2bdsmV65csRYkDS7anabdb25169a1YzSETZs2zQrLtVDbXdcUPexoF53WM7300kvWUpQuXbpb3lO3xbQdAAAkP/GaKFK7opYtWyZffPGFZ06k48ePW2DxhbboaAvQqVOnvLbrurZSxXrRqVJJsWLFbASbtlo99dRTFmyi03oiPebhhx+Wjz/+WIKDg+1rbLRAXH+ugwcP+vQzAACA5MfngHTo0CEpW7asPPHEE9K9e3c5c+aMbR89erS89tprPp1LW20qV65srUBuWuit6zVq1IjzefQ12t12N8doa5MGr5hGzgEAgJTF5y42HTWm8xBt377dCpzddGRZ9CHzcaVdXfqgWz1ntWrVbJj/1atXPQXfOgWA1hu5W4j0qx6rI9g08CxatMjmQZoyZYrt19eOHDlSmjdvbrVH2sWm8ywdO3ZMWrdubcdoAbh2t2k3nHbX6forr7wizz33nM2bBAAAUjafA9KaNWusqFlbf6LTeYU0hPhKJ5jUVqjBgwfLyZMnrdts8eLFnsLtw4cPW8uOmwagbt26ydGjRyVDhgw2H9KsWbPsPEq77LTAe/r06RaONMRVrVrVrluH/CutJZozZ45NKKkhq3DhwhaQotclAQCAlMvniSK1heWnn36yOYu09UVbkrRAWof7t2rV6pZ6ouSKiSIBAAg8iTZRZMOGDa0bzE2LtLU4e8iQIdK0adP4XzEAAECgtiAdOXJEGjdubJM0/vHHH1YPpF91RNrq1atTTJEzLUgAACTfz2+fA5LS4fD6DDXtXtPWI51wsV27dlYTlFIQkAAACDyJEpAiIiKsKFpnqdZnoaVkBCQAAAJPotQgpUmTRq5fv54Q1wcAAJBk+VykrZND6qSQt3uwKwAAQIqaB2nTpk020/UPP/xgM2rrIz2imzdvXkJeHwAAQNIPSFmzZrX5jpDwoiIj5a/L///RLQAApHTZMt8vqVKnTroBacGCBdKkSROrQfr0008T/6pSKA1Hdb5p4O/LAAAgSfjxiaWSI2vsD6/3ew2SPmftwoULnkd5nD59OrGvCwAAwG/i1IJ0//33y/r16+Xxxx+3CSJ19mwkTlOipmUAACD2uZikA1LXrl3liSeesGCkS548sTd3RUZGJuT1pSjaz+qvpkQAAOBjQNKn3rdt21b27dsnzZs3tzokLdYGAABI0aPYdAZtXfShtK1bt5aMGTMm7pUBAAD4SbyexQYeNQIAQCBKlEeNAAAApAQEJAAAAAcCEgAAwN0GpP379/v6EgAAgOQdkIoVKyZ169aVWbNmyfXr1xPnqgAAAAIpIG3dulXKlSsnffv2tQkjX3rpJdm4cWPiXB0AAEAgBKQKFSrIBx98IMePH5dPPvlETpw4ITVr1pQyZcrI2LFj5cwZnkYPAABSaJF2cHCwtGzZUr788ksZPXq0zbL92muvSYECBaR9+/YWnAAAAFJUQNq8ebN069ZN8ubNay1HGo7+/PNPWbp0qbUu6bPbAAAAkvWjRtw0DOmz2Pbu3StNmzaVGTNm2NdUqf5/1ipcuLB89tlnEhoamhjXCwAAkPQC0pQpU+Rf//qXvPDCC9Z6FJNcuXLJxx9/nBDXBwAAcM/xLLZ44llsAAAk389vn1uQduzYEeP2oKAgSZ8+vRQsWFDSpUvn62kBAACSjOD4DPPXMBSbNGnSSJs2beTDDz+0wAQAAJDsR7HNnz9fHnzwQfnoo49k27Zttuj3xYsXl88//9xqj1asWCFvvfVW4lwxAABAUmtBGjlypE0U2ahRI8+2smXLygMPPCCDBg2yWbVDQkLk1Vdflffeey+hrxcAACDptSD9+uuvUqhQoVu26zbd5+6GY6JIAACQYgJSiRIlZNSoURIeHu7ZFhERYdt0nzp27Jjkzp07Ya8UAAAgqXaxTZo0SZo3b25davrQWqUtR5GRkbJw4UJb379/v82yDQAAkGLmQbp8+bLMnj1bfv/9d1vXAu1nn31WMmfOLCkF8yABABB4Em0eJKVBqGvXrndzfQAAAMnrYbUzZ86UmjVrSr58+eTQoUO27f3335dvvvkmoa8PAAAg6QckfRZb3759pUmTJvLXX39Z7ZHKli2bjBs3LjGuEQAAIGkHpAkTJsi0adNk4MCBEhz8vx66KlWqeIb5AwAApKiAdODAAalYseIt2/X5a1evXo3XRejIuNDQUHs0SfXq1W2yydjMmzfPwljWrFltQkqdc0m7/KIbOnSoTTmg+7Vlq379+rJhwwavY86fPy/t2rWzAi09V6dOneTKlSvxun4AAJDCA1LhwoXt8SJOixcvlpIlS/p8AXPnzrUuuyFDhsjWrVulfPnyNkv36dOnYzw+e/bs1nq1bt06e3Bux44dbVmyZInnmIceekgmTpxoLVpr16618NWwYUM5c+aM5xgNRzt37pSlS5fa9ASrV6+WLl26+Hz9AAAgGXL5aNq0aa78+fO75syZ4woJCXF98cUXrrffftvzva+qVavm6t69u2c9MjLSlS9fPldYWFicz1GxYkXXW2+9Fev+ixcv6lQGrmXLltn6rl27bH3Tpk2eY77//ntXUFCQ69ixY3F6T/c59SsAAAgMcf389nmY/4svvigZMmSwh9Feu3bN5j/S0Wz6fLa2bdv6dC6djXvLli0yYMAAz7ZUqVJZl5i2EMUh3NmDcffu3SujR4+O9T30Ybo654G2Tik9t3araVedm76nvrd2xT355JO3nOfGjRu2RJ9HAQAAJE/xmgdJu6d00YCkdTu5cuWK15ufPXvWRsE5H0ui63v27In1dTq5U/78+S2wpE6dWiZPniwNGjTwOka7zTSw6TXmzZvXutJy5sxp+06ePHnLNWvBuXbf6b6YhIWFybBhw+L1cwIAgGReg/Too4/KhQsX7PuMGTN6goa2qOi+e0EnqtQ6qE2bNsnIkSOthunHH3/0OqZu3bp2zM8//yyNGzeWp59+Ota6prjQVi4NZu7lyJEjCfCTAACAZNGCpEEk+oNq3a5fvy5r1qzx6VzaoqMtQKdOnfLarut58uSJ9XXaFVasWDH7Xkex7d6921p46tSp4zlGR7DpMbo8/PDD8uCDD8rHH39sQUfP7QxLN2/etJFtsb2vjtLTBQAAJH9xDkg6Ysxt165dXl1R2k2mo9i028sXadOmlcqVK8vy5culRYsWti0qKsrWe/ToEefz6Gui1wfd6ZgaNWpYK5jWP+n7K61l0mN0mgEAAJCyxTkgaUtNUFCQLTF1pWnhtk4i6SvtHuvQoYMVTFerVs1m49b5lHTovmrfvr0FL20hUvpVjy1atKgFnkWLFtk8SDrDt9LXardb8+bNrfZI65x0nqVjx45J69at7RidjkC73Tp37ixTp06ViIgIC2Ras6QF5wAAIGUL9mWCSB01VqRIEZvI8f777/dqCdJaJO0u81WbNm1sfqLBgwdbq5QGMW2NchduHz582LrU3DQAdevWTY4ePWqhTCeEnDVrlp1H6TVogff06dMtHOXIkUOqVq1q3X+lS5f2nGf27NkWiurVq2fnb9WqlYwfP97n6wcAAMlPkI719/dFBCItStepA7RgW2fjBgAAyefzO17D/N11SNq64yzY1q4tAACAQOZzQNq/f79NpKiP8dB6JHcDlH7vLtgGAABIUfMg9e7d257HpsPkdR4kfZ6ZPsdMC6edcxEBAACkiBYkfUyHDonXOYy0uFmXmjVr2uiyXr16yS+//JI4VwoAAJBUW5C0C01nslYako4fP27fFypUyJ6JBgAAkOJakMqUKSPbt2+3bjadVPGdd96xYf76QFidAgAAACDFBaS33nrL5iJSw4cPl8cee0z++c9/2nxDc+fOTYxrBAAACLx5kPQZZtmyZfOMZEsJmAcJAIDk+/ntUw2SPpIjODhYfvvtN6/t2bNnT1HhCAAAJG8+BaQ0adJIwYIFmesIAAAkaz6PYhs4cKC8+eab1q0GAACQHPlcpD1x4kTZt2+fPfVeh/aHhIR47d+6dWtCXh8AAEDSD0hPPPEE9UYAACBZS5BRbCkRo9gAAAg8iTKKTelkkOfOnbtl+4ULF5goEgAAJAs+B6SDBw/GOIrtxo0bcvTo0YS6LgAAgKRfg7RgwQLP90uWLLHmKTcNTMuXL7fHjwAAAKSYgNSiRQv7qgXaHTp0uGV+pNDQUBkzZkzCXyEAAEBSDUhRUVH2VVuJNm3aJDlz5kzM6wIAAAicYf4HDhxInCsBAAAItCLtdevWycKFC722zZgxw1qUcuXKJV26dLFCbQAAgBQTkIYPHy47d+70rP/666/SqVMnqV+/vvTv31++/fZbCQsLS6zrBAAASHoBadu2bVKvXj3P+pw5c6R69eoybdo06du3r4wfP17+85//JNZ1AgAAJL2A9Ndff0nu3Lk966tWrZImTZp41qtWrSpHjhxJ+CsEAABIqgFJw5G7QDs8PNweSvvwww979l++fNmG+wMAAKSYgNS0aVOrNVqzZo0MGDBAMmbMKP/85z89+3fs2CFFixZNrOsEAABIesP8R4wYIS1btpTatWtLpkyZZPr06ZI2bVrP/k8++UQaNmyYWNcJAABwzwS5XC6XLy/Qp99qQEqdOrXX9vPnz9v26KEpOYvr04ABAEDgfX77PFFk9GewRZc9e3ZfTwUAABDYNUgAAAApBQEJAADAgYAEAADgQEACAABwICABAAA4EJAAAAAcCEgAAAAOBCQAAAAHAhIAAIADAQkAACApBqRJkyZJaGiopE+fXqpXry4bN26M9dh58+ZJlSpVJGvWrBISEiIVKlSQmTNnevZHRERIv379pGzZsrY/X7580r59ezl+/LjXefT9goKCvJZRo0Yl6s8JAAACg98D0ty5c6Vv374yZMgQ2bp1q5QvX14aNWokp0+fjvWZbwMHDpR169bJjh07pGPHjrYsWbLE9l+7ds3OM2jQIPuqgWrv3r3SvHnzW841fPhwOXHihGfp2bNnov+8AAAg6QtyuVwuf16AthhVrVpVJk6caOtRUVFSoEABCyv9+/eP0zkqVaokzZo1kxEjRsS4f9OmTVKtWjU5dOiQFCxY0NOC1KdPH1sS82nAAAAg6Yjr57dfW5DCw8Nly5YtUr9+/f9dUKpUtq4tRHei2W758uXWQlSrVq1Yj9OboF1o2i0XnXap5ciRQypWrCjvvvuu3Lx5M9Zz3Lhxw25q9AUAACRPwf5887Nnz0pkZKTkzp3ba7uu79mz57aBJ3/+/BZaUqdOLZMnT5YGDRrEeOz169etJumZZ57xSoq9evWyliftsvv5559lwIAB1s02duzYGM8TFhYmw4YNi/fPCgAAAodfA1J8Zc6cWbZt2yZXrlyxFiStYSpSpIjUqVPH6zgt2H766aetpWnKlCle+/Q1buXKlZO0adPKSy+9ZEEoXbp0t7ynBqjor9EWJO0KBAAAyY9fA1LOnDmtBejUqVNe23U9T548sb5Ou+GKFStm3+sott27d1uwiR6Q3OFI645WrFhxxzohrYXSLraDBw9K8eLFb9mvoSmm4AQAAJIfv9YgaatN5cqVrRXITYu0db1GjRpxPo++RrvbnOHojz/+kGXLllmd0Z1oi5QGr1y5csXjJwEAAMmJ37vYtNuqQ4cONreRjjQbN26cXL161YbuK53DSOuNtIVI6Vc9tmjRohaKFi1aZPMgubvQNBw99dRTNsR/4cKFVuN08uRJ26f1RhrKtAB8w4YNUrduXeuu0/VXXnlFnnvuOcmWLZsf7wYAAEgK/B6Q2rRpI2fOnJHBgwdbkNEus8WLF3sKtw8fPmwtO24anrp16yZHjx6VDBkySIkSJWTWrFl2HnXs2DFZsGCBfa/nim7lypXWDaddZXPmzJGhQ4dayCpcuLAFpOg1RgAAIOXy+zxIgYp5kAAACDwBMQ8SAABAUkRAAgAAcCAgAQAAOBCQAAAAHAhIAAAADgQkAAAABwISAACAAwEJAADAgYAEAADgQEACAABwICABAAA4EJAAAAAcCEgAAAAOBCQAAAAHAhIAAIADAQkAAMCBgAQAAOBAQAIAAHAgIAEAADgQkAAAABwISAAAAA4EJAAAAAcCEgAAgAMBCQAAwIGABAAA4EBAAgAAcCAgAQAAOBCQAAAAHAhIAAAADgQkAAAABwISAACAAwEJAADAgYAEAADgQEACAABwICABAAA4EJAAAAAcCEgAAAAOBCQAAAAHAhIAAIADAQkAACApBqRJkyZJaGiopE+fXqpXry4bN26M9dh58+ZJlSpVJGvWrBISEiIVKlSQmTNnevZHRERIv379pGzZsrY/X7580r59ezl+/LjXec6fPy/t2rWT++67z87VqVMnuXLlSqL+nAAAIDD4PSDNnTtX+vbtK0OGDJGtW7dK+fLlpVGjRnL69OkYj8+ePbsMHDhQ1q1bJzt27JCOHTvasmTJEtt/7do1O8+gQYPsqwaqvXv3SvPmzb3Oo+Fo586dsnTpUlm4cKGsXr1aunTpck9+ZgAAkLQFuVwulz8vQFuMqlatKhMnTrT1qKgoKVCggPTs2VP69+8fp3NUqlRJmjVrJiNGjIhx/6ZNm6RatWpy6NAhKViwoOzevVtKlSpl27U1Si1evFiaNm0qR48etVYnpxs3btjidunSJbvOixcvWisUAABI+vTzO0uWLHf8/PZrC1J4eLhs2bJF6tev/78LSpXK1rWF6E402y1fvtxaiGrVqhXrcXoTgoKCrCtN6bn1e3c4Uvqe+t4bNmyI8RxhYWF2Q92LhiMAAJA8+TUgnT17ViIjIyV37txe23X95MmTtw08mTJlkrRp01rL0YQJE6RBgwYxHnv9+nWrSXrmmWc8SVHPnStXLq/jgoODrfsutvcdMGCAva97OXLkSDx+YgAAEAiCJQBlzpxZtm3bZkXV2oKkNUxFihSROnXqeB2nBdtPP/20tTRNmTLlrt4zXbp0tgAAgOTPrwEpZ86ckjp1ajl16pTXdl3PkydPrK/TrrBixYrZ9zqKTWuKtAssekByhyOtO1qxYoVXP6Oe21kEfvPmTRvZdrv3BQAAKYNfu9i0i6xy5crWCuSmRdq6XqNGjTifR18TvYDaHY7++OMPWbZsmeTIkcPreD33hQsXrP7JTUOUnkeLxgEAQMrm9y427R7r0KGDFUzrSLNx48bJ1atXbei+0jmM8ufPby1ESr/qsUWLFrVQtGjRIpsHyd2FpuHoqaeesiH+Onxfa5zcdUVaY6ShrGTJktK4cWPp3LmzTJ061V7To0cPadu2bYwj2AAAQMri94DUpk0bOXPmjAwePNiCjHaZ6ZB7d+H24cOHrUvNTcNTt27dbDh+hgwZpESJEjJr1iw7jzp27JgsWLDAvtdzRbdy5UpPN9zs2bMtFNWrV8/O36pVKxk/fvw9/MkBAEBS5fd5kJL7PAoAACDpCIh5kAAAAJIiAhIAAIADAQkAAMCBgAQAAOBAQAIAAHAgIAEAADgQkAAAABwISAAAAA4EJAAAAAcCEgAAgAMBCQAAwIGABAAA4EBAAgAAcCAgAQAAOBCQAAAAHAhIAAAADgQkAAAABwISAACAAwEJAADAgYAEAADgQEACAABwICABAAA4EJAAAAAcCEgAAAAOBCQAAAAHAhIAAIADAQkAAMCBgAQAAOBAQAIAAHAgIAEAADgQkAAAABwISAAAAA4EJAAAAAcCEgAAgAMBCQAAwIGABAAA4EBAAgAAcCAgAQAAOBCQAAAAklpAmjRpkoSGhkr69OmlevXqsnHjxliPnTdvnlSpUkWyZs0qISEhUqFCBZk5c+YtxzRs2FBy5MghQUFBsm3btlvOU6dOHdsXfenatWui/HwAACDw+DUgzZ07V/r27StDhgyRrVu3Svny5aVRo0Zy+vTpGI/Pnj27DBw4UNatWyc7duyQjh072rJkyRLPMVevXpWaNWvK6NGjb/venTt3lhMnTniWd955J8F/PgAAEJiCXC6Xy19vri1GVatWlYkTJ9p6VFSUFChQQHr27Cn9+/eP0zkqVaokzZo1kxEjRnhtP3jwoBQuXFh++eUXa2lytiDptnHjxsX72i9duiRZsmSRixcvyn333Rfv8wAAgHsnrp/fweIn4eHhsmXLFhkwYIBnW6pUqaR+/frWQnQnmutWrFghe/fuvWNrUUxmz54ts2bNkjx58sjjjz8ugwYNkowZM8Z6/I0bN2xx0xvrvtEAACAwuD+379Q+5LeAdPbsWYmMjJTcuXN7bdf1PXv2xPo6DSb58+e3sJI6dWqZPHmyNGjQwKf3fvbZZ6VQoUKSL18+66rr16+fBS2tX4pNWFiYDBs27Jbt2uIFAAACy+XLl60lKckFpPjKnDmzFV5fuXJFli9fbjVMRYoUsW6zuOrSpYvn+7Jly0revHmlXr168ueff0rRokVjfI22dOl7uWl34Pnz5z3F4AmZbDV0HTlyhK67RMa9vre43/cO9/re4V4H3r3WliMNR9pIcjt+C0g5c+a0FqBTp055bdd17faKjXbDFStWzL7XOqLdu3db644vASmmWii1b9++WANSunTpbIlOR9MlFv3l83+2e4N7fW9xv+8d7vW9w70OrHt9u5Yjv49iS5s2rVSuXNlagaK3yuh6jRo14nwefU302qD4cE8FoC1JAAAAfu1i0y6rDh062NxG1apVs1FlOkxfh+6r9u3bW72RthAp/arHaiuPhqJFixbZPEhTpkzxnFO7vQ4fPizHjx+3da0tUtoqpYt2o33++efStGlT6x7TGqRXXnlFatWqJeXKlfPLfQAAAEmLXwNSmzZt5MyZMzJ48GA5efKkdZktXrzYU7itQUe71Nw0PHXr1k2OHj0qGTJkkBIlSthIND2P24IFCzwBS7Vt29a+6lxLQ4cOtZarZcuWecKY9me2atVK3nrrLUkKtBtPr9XZnYeEx72+t7jf9w73+t7hXiffe+3XeZAAAACSIr8/agQAACCpISABAAA4EJAAAAAcCEgAAAAOBKQkZtKkSRIaGirp06e3CSw3btzo70sKeDo9hD4UWWdhz5Url7Ro0cIz/YPb9evXpXv37jb1Q6ZMmWxko3MSU/hm1KhRNst8nz59PNu4zwnr2LFj8txzz9n91JG9+mSAzZs3e/brGBwdJaxzvOl+fdblH3/84ddrDkT6WCx9Xqc+AF3vo041ow9Ijz7GiXsdP6tXr7bnoeqs1vrvxddff+21Py73Vaf3adeunU0eqRM4d+rUyZ62cbcISEnI3LlzbW4oHca4detWKV++vDRq1EhOnz7t70sLaKtWrbIP5fXr18vSpUslIiJCGjZsaNM8uOlcWN9++618+eWXdrzOo9WyZUu/Xncg27Rpk3z44Ye3zC3GfU44f/31lzzyyCOSJk0a+f7772XXrl0yZswYyZYtm+eYd955R8aPHy9Tp06VDRs2SEhIiP2bokEVcacPRNf59iZOnGhPb9B1vbcTJkzwHMO9jh/9d1g/67RxICZxua8ajnbu3Gn/vi9cuNBCV/RHisWbDvNH0lCtWjVX9+7dPeuRkZGufPnyucLCwvx6XcnN6dOn9c8+16pVq2z9woULrjRp0ri+/PJLzzG7d++2Y9atW+fHKw1Mly9fdj344IOupUuXumrXru3q3bu3bec+J6x+/fq5atasGev+qKgoV548eVzvvvuuZ5v+DtKlS+f64osv7tFVJg/NmjVz/etf//La1rJlS1e7du3se+51wtB/C+bPn+9Zj8t93bVrl71u06ZNnmO+//57V1BQkOvYsWN3dT20ICUR4eHhsmXLFms+dNNJMnV93bp1fr225ObixYv2NXv27PZV77u2KkW/9zoJacGCBbn38aCtdc2aNfO6n4r7nLB0Ulx9skDr1q2t67hixYoybdo0z/4DBw7YBLzR77c+f0q77rnfvvnHP/5hj8H6/fffbX379u2ydu1aadKkia1zrxNHXO6rftVuNf3/gpser5+f2uIUsDNp43/Onj1r/dzuWcTddH3Pnj1+u67kRp/dpzUx2jVRpkwZ26b/B9QZ1p0PH9Z7r/sQd3PmzLHuYe1ic+I+J6z9+/dbt492y7/55pt2z3v16mX3WB/h5L6nMf2bwv32Tf/+/e1J8hro9SHr+m/1yJEjrWtHca8TR1zuq37VPxCiCw4Otj+A7/beE5CQ4lo3fvvtN/vrDwnryJEj0rt3b6sD0EEGSPywr381/9///Z+tawuS/rettRoakJBw/vOf/8js2bPtOZ6lS5e2B5zrH1paWMy9Tr7oYksicubMaX+ZOEf06Lo+ZBd3r0ePHlbAt3LlSnnggQc82/X+ahfnhQsXvI7n3vtGu9B0QEGlSpXsLzhdtBBbCyz1e/2rj/uccHRUT6lSpby2lSxZ0p5hqdz3lH9T7t7rr79urUj6bE8dKfj888/bgAP3g9S514kjLvdVvzoHMt28edNGtt3tvScgJRHaLF65cmXr547+F6Ku16hRw6/XFui09k/D0fz582XFihU2VDc6ve86Eij6vddpAPSDhnsfd/Xq1ZNff/3V/rp2L9rCod0Q7u+5zwlHu4md01VojUyhQoXse/3vXD8got9v7SbSugzut2+uXbvm9eB0pX/Q6r/RinudOOJyX/Wr/tGlf6C56b/z+rvRWqW7clcl3khQc+bMser8zz77zCrzu3Tp4sqaNavr5MmT/r60gPbyyy+7smTJ4vrxxx9dJ06c8CzXrl3zHNO1a1dXwYIFXStWrHBt3rzZVaNGDVtwd6KPYlPc54SzceNGV3BwsGvkyJGuP/74wzV79mxXxowZXbNmzfIcM2rUKPs35JtvvnHt2LHD9cQTT7gKFy7s+vvvv/167YGmQ4cOrvz587sWLlzoOnDggGvevHmunDlzut544w3PMdzr+I96/eWXX2zRSDJ27Fj7/tChQ3G+r40bN3ZVrFjRtWHDBtfatWttFO0zzzzjulsEpCRmwoQJ9gGSNm1aG/a/fv16f19SwNP/08W0fPrpp55j9P9s3bp1c2XLls0+ZJ588kkLUUjYgMR9Tljffvutq0yZMvaHVYkSJVwfffSR134dJj1o0CBX7ty57Zh69eq59u7d67frDVSXLl2y/4713+b06dO7ihQp4ho4cKDrxo0bnmO41/GzcuXKGP991lAa1/t67tw5C0SZMmVy3Xfffa6OHTta8LpbQfo/d9cGBQAAkLxQgwQAAOBAQAIAAHAgIAEAADgQkAAAABwISAAAAA4EJAAAAAcCEgAAgAMBCQAAwIGABCDgvPDCC9KiRQt/XwaAZCzY3xcAANEFBQXddv+QIUPkgw8+sIcQJyU//vij1K1bV/766y/JmjWrvy8HwF0iIAFIUk6cOOH5fu7cuTJ48GCvp9ZnypTJFgBITHSxAUhS8uTJ41myZMliLUrRt2k4cnax1alTR3r27Cl9+vSRbNmySe7cuWXatGly9epV6dixo2TOnFmKFSsm33//vdd7/fbbb9KkSRM7p77m+eefl7Nnz8Z6bYcOHZLHH3/c3iMkJERKly4tixYtkoMHD1rrkdJ9es16jSoqKkrCwsKkcOHCkiFDBilfvrz897//9Wp50uO/++47KVeunKRPn14efvhhuzYA/kNAApAsTJ8+XXLmzCkbN260sPTyyy9L69at5R//+Ids3bpVGjZsaAHo2rVrdvyFCxfk0UcflYoVK8rmzZtl8eLFcurUKXn66adjfY/u3bvLjRs3ZPXq1fLrr7/K6NGjLVwVKFBAvvrqKztGW7u0FUy7AZWGoxkzZsjUqVNl586d8sorr8hzzz0nq1at8jr366+/LmPGjJFNmzbJ/fffb0EsIiIiUe8ZgNtwAUAS9emnn7qyZMlyy/YOHTq4nnjiCc967dq1XTVr1vSs37x50xUSEuJ6/vnnPdtOnDihRUuudevW2fqIESNcDRs29DrvkSNH7Ji9e/fGeD1ly5Z1DR06NMZ9K1eutNf+9ddfnm3Xr193ZcyY0fXzzz97HdupUyfXM8884/W6OXPmePafO3fOlSFDBtfcuXNvc3cAJCZqkAAkC9o95ZY6dWrJkSOHlC1b1rNNu9DU6dOn7ev27dtl5cqVMdYz/fnnn/LQQw/dsr1Xr17WMvXDDz9I/fr1pVWrVl7v67Rv3z5rsWrQoIHX9vDwcGu5iq5GjRqe77Nnzy7FixeX3bt3x/GnB5DQCEgAkoU0adJ4rWtdT/Rt7tFxWhOkrly5Yt1Y2k3mlDdv3hjf48UXX5RGjRpZvZCGJO0+024x7dKLib6H0uPz58/vtS9dunQ+/4wA7h0CEoAUqVKlSlY3FBoaKsHBcf+nUOuNunbtasuAAQOsGFwDUtq0aW1/ZGSk59hSpUpZEDp8+LDUrl37tuddv369FCxY0L7XqQJ+//13KVmyZLx/PgB3hyJtACmSFlyfP39ennnmGSuM1m61JUuW2Ki36CEnOh0lp8ccOHDACr+1i84dYgoVKmStVAsXLpQzZ85Y65GOnnvttdesMFuLyPU99HUTJkyw9eiGDx8uy5cvt9FrOgJOC86ZDBPwHwISgBQpX7588tNPP1kY0hFuWq+kAUgneUyVKuZ/GvVYDVYaiho3bmx1SpMnT7Z92oU2bNgw6d+/v9U79ejRw7aPGDFCBg0aZN1x7tdpl5sO+49u1KhR0rt3b6lcubKcPHlSvv32W0+rFIB7L0grtf3wvgAAZuAGkixakAAAABwISAAAAA50sQEAADjQggQAAOBAQAIAAHAgIAEAADgQkAAAABwISAAAAA4EJAAAAAcCEgAAgAMBCQAAQLz9P8/d4fC5ZmL0AAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_rps_dynamics([1/3, 1/3, 1/3])" ] }, { "cell_type": "markdown", "id": "a1f6662e", "metadata": {}, "source": [ "When starting from an unbalanced initial mixed strategy profile, the strategy frequencies will oscillate around the equilibrium point without converging to it. However, if we plot the average strategy frequencies over time, we can see that this begins to converge to the equilibrium point:" ] }, { "cell_type": "code", "execution_count": 13, "id": "189f898f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_rps_dynamics([0.3, 0.3, 0.4], plot_average_strategy=True)" ] }, { "cell_type": "markdown", "id": "078a21e0", "metadata": {}, "source": [ "## Normal form games created with Gambit\n", "\n", "You can also set up a normal form game in Gambit and export it to OpenSpiel. Here we demonstrate this with the Prisoner's Dilemma game from tutorial 1." ] }, { "cell_type": "code", "execution_count": 14, "id": "cdd0bfe0", "metadata": {}, "outputs": [ { "data": { "text/html": [ "

Prisoner's Dilemma

\n", "
CooperateDefect
Cooperate-1,-1-3,0
Defect0,-3-2,-2
\n" ], "text/plain": [ "Game(title='Prisoner's Dilemma')" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gbt_prisoners_dilemma_game = gbt.read_nfg(\"games/prisoners_dilemma.nfg\")\n", "gbt_prisoners_dilemma_game" ] }, { "cell_type": "code", "execution_count": 15, "id": "d42e6545", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\left[\\left[0,1\\right],\\left[0,1\\right]\\right]$" ], "text/plain": [ "[[Rational(0, 1), Rational(1, 1)], [Rational(0, 1), Rational(1, 1)]]" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gbt.nash.lcp_solve(gbt_prisoners_dilemma_game).equilibria[0]" ] }, { "cell_type": "markdown", "id": "15dd432d", "metadata": {}, "source": [ "As expected, Gambit computes the equilibrium strategy for both players as choosing cooperate with probability 0 and defect with probability 1.\n", "\n", "To re-create the game in OpenSpiel we extract the player payoffs to NumPy arrays, which are then used to create a matrix game in OpenSpiel:" ] }, { "cell_type": "code", "execution_count": 16, "id": "fcd42af0", "metadata": {}, "outputs": [], "source": [ "p1_payoffs, p2_payoffs = gbt_prisoners_dilemma_game.to_arrays(dtype=float)\n", "ops_prisoners_dilemma_game = pyspiel.create_matrix_game(\n", " gbt_prisoners_dilemma_game.title,\n", " \"Classic Prisoner's Dilemma\", # description\n", " [strategy.label for strategy in gbt_prisoners_dilemma_game.players[0].strategies],\n", " [strategy.label for strategy in gbt_prisoners_dilemma_game.players[1].strategies],\n", " p1_payoffs,\n", " p2_payoffs\n", ")" ] }, { "cell_type": "markdown", "id": "625a35a4", "metadata": {}, "source": [ "Like rock-paper-scissors, the Prisoner's Dilemma is a 1-step simultaneous-move normal form game; we'll apply a list of player actions in one step to reach the terminal state. Let's have both player choose to defect (1):" ] }, { "cell_type": "code", "execution_count": 17, "id": "7ce6f2e2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Terminal? true\n", "History: 1, 1\n", "Returns: -2,-2\n", "Row actions: \n", "Col actions: \n", "Utility matrix:\n", "-1,-1 -3,0 \n", "0,-3 -2,-2 " ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "state = ops_prisoners_dilemma_game.new_initial_state()\n", "state.apply_actions([1, 1])\n", "state" ] }, { "cell_type": "markdown", "id": "1fea0224", "metadata": {}, "source": [ "Unlike in rock-paper-scissors, the Prisoner's Dilemma has a dominant strategy equilibrium, in which both players defect.\n", "Using evolutionary dynamics, we can see that a population starting with a mix of cooperators and defectors will evolve towards all defectors over time:" ] }, { "cell_type": "code", "execution_count": 18, "id": "d1495c7c", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "matrix_pd_payoffs = game_payoffs_array(ops_prisoners_dilemma_game)\n", "pd_dyn = dynamics.SinglePopulationDynamics(matrix_pd_payoffs, dynamics.replicator)\n", "\n", "def plot_pd_dynamics(proportions, steps=100, alpha=0.1):\n", " x = np.array(proportions)\n", " y = []\n", " for _ in range(steps):\n", " x += alpha * pd_dyn(x)\n", " y.append(x.copy())\n", " y = np.array(y)\n", " plt.plot(y[:, 0], label=\"Cooperate\")\n", " plt.plot(y[:, 1], label=\"Defect\")\n", " plt.xlabel(\"Time step\")\n", " plt.ylabel(\"Frequency\")\n", " plt.legend()\n", " plt.show()\n", "\n", "plot_pd_dynamics([0.8, 0.2])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "" ] }, { "cell_type": "markdown", "id": "b12f6330", "metadata": {}, "source": [ "## Extensive form games from the OpenSpiel library\n", "\n", "For extensive form games, OpenSpiel can export to the EFG format used by Gambit. Here we demonstrate this with **Tiny Hanabi**, loaded from the OpenSpiel [game library](https://openspiel.readthedocs.io/en/latest/games.html)." ] }, { "cell_type": "code", "execution_count": 19, "id": "02a42600", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'EFG 2 R \"tiny_hanabi()\" { \"Pl0\" \"Pl1\" } \\nc \"\" 1 \"\" { \"d0\" 0.5000000000000000 \"d1\" 0.5000000000000000 } 0\\n c \"p0:d0\" 2 \"\" { \"d0\" 0.5000000000000000 \"d1\" 0.5000000000000000 } 0\\n p \"\" 1 1 \"\" { \"p0a0\" \"p0a1\" \"p0a2\" } 0\\n p \"\" 2 1 \"\" { \"p1a0\" \"p1a1\" \"p1a2\" } 0\\n t \"\" 1 \"\" { 10.0 10.0 }\\n t \"\" 2 \"\" { 0.0 0.0 }\\n t \"\" 3 \"\" { 0.0 0.0 }\\n p \"\" 2 2 \"\" { \"p1a0\" \"p1a1\" \"p1a2\" } 0\\n t \"\" 4 \"\" { 4.0 4.0 }\\n t \"\" 5 \"\" { 8.0 8.0 }\\n t \"\" 6 \"\" { 4.0 4.0 }\\n p \"\" 2 3 \"\" { \"p1a0\" \"p1a1\" \"p1a2\" } 0\\n t \"\" 7 \"\" { 10.0 10.0 }\\n t \"\" 8 \"\" { 0.0 0.0 }\\n t \"\" 9 \"\" { 0.0 0.0 }\\n p \"\" 1 1 \"\" { \"p0a0\" \"p0a1\" \"p0a2\" } 0\\n p \"\" 2 4 \"\" { \"p1a0\" \"p1a1\" \"p1a2\" } 0\\n t \"\" 10 \"\" { 0.0 0.0 }\\n t \"\" 11 \"\" { 0.0 0.0 }\\n t \"\" 12 \"\" { 10.0 10.0 }\\n p \"\" 2 5 \"\" { \"p1a0\" \"p1a1\" \"p1a2\" } 0\\n t \"\" 13 \"\" { 4.0 4.0 }\\n t \"\" 14 \"\" { 8.0 8.0 }\\n t \"\" 15 \"\" { 4.0 4.0 }\\n p \"\" 2 6 \"\" { \"p1a0\" \"p1a1\" \"p1a2\" } 0\\n t \"\" 16 \"\" { 0.0 0.0 }\\n t \"\" 17 \"\" { 0.0 0.0 }\\n t \"\" 18 \"\" { 10.0 10.0 }\\n c \"p0:d1\" 3 \"\" { \"d0\" 0.5000000000000000 \"d1\" 0.5000000000000000 } 0\\n p \"\" 1 2 \"\" { \"p0a0\" \"p0a1\" \"p0a2\" } 0\\n p \"\" 2 1 \"\" { \"p1a0\" \"p1a1\" \"p1a2\" } 0\\n t \"\" 19 \"\" { 0.0 0.0 }\\n t \"\" 20 \"\" { 0.0 0.0 }\\n t \"\" 21 \"\" { 10.0 10.0 }\\n p \"\" 2 2 \"\" { \"p1a0\" \"p1a1\" \"p1a2\" } 0\\n t \"\" 22 \"\" { 4.0 4.0 }\\n t \"\" 23 \"\" { 8.0 8.0 }\\n t \"\" 24 \"\" { 4.0 4.0 }\\n p \"\" 2 3 \"\" { \"p1a0\" \"p1a1\" \"p1a2\" } 0\\n t \"\" 25 \"\" { 0.0 0.0 }\\n t \"\" 26 \"\" { 0.0 0.0 }\\n t \"\" 27 \"\" { 0.0 0.0 }\\n p \"\" 1 2 \"\" { \"p0a0\" \"p0a1\" \"p0a2\" } 0\\n p \"\" 2 4 \"\" { \"p1a0\" \"p1a1\" \"p1a2\" } 0\\n t \"\" 28 \"\" { 10.0 10.0 }\\n t \"\" 29 \"\" { 0.0 0.0 }\\n t \"\" 30 \"\" { 0.0 0.0 }\\n p \"\" 2 5 \"\" { \"p1a0\" \"p1a1\" \"p1a2\" } 0\\n t \"\" 31 \"\" { 4.0 4.0 }\\n t \"\" 32 \"\" { 8.0 8.0 }\\n t \"\" 33 \"\" { 4.0 4.0 }\\n p \"\" 2 6 \"\" { \"p1a0\" \"p1a1\" \"p1a2\" } 0\\n t \"\" 34 \"\" { 10.0 10.0 }\\n t \"\" 35 \"\" { 0.0 0.0 }\\n t \"\" 36 \"\" { 0.0 0.0 }\\n'" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ops_hanabi_game = pyspiel.load_game(\"tiny_hanabi\")\n", "efg_hanabi_game = export_gambit(ops_hanabi_game)\n", "efg_hanabi_game" ] }, { "cell_type": "markdown", "id": "fa354c9f", "metadata": {}, "source": [ "Now let's load the EFG in Gambit.\n", "We can then compute equilibria strategies for the players as usual." ] }, { "cell_type": "code", "execution_count": 20, "id": "1a534e25", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Pl0\n", "Pl1\n" ] } ], "source": [ "gbt_hanabi_game = gbt.read_efg(StringIO(efg_hanabi_game))\n", "eqm = gbt.nash.lcp_solve(gbt_hanabi_game).equilibria[0]\n", "for player in gbt_hanabi_game.players:\n", " print(player.label)" ] }, { "cell_type": "markdown", "id": "cdfe924e", "metadata": {}, "source": [ "We can look at player 0's equilibrium strategy:" ] }, { "cell_type": "code", "execution_count": 21, "id": "1ec19b1c", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\left[\\left[0,0,1\\right],\\left[0,1,0\\right]\\right]$" ], "text/plain": [ "[[Rational(0, 1), Rational(0, 1), Rational(1, 1)], [Rational(0, 1), Rational(1, 1), Rational(0, 1)]]" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eqm['Pl0']" ] }, { "cell_type": "markdown", "id": "b54411c0", "metadata": {}, "source": [ "...and use Gambit to explore what those numbers actually mean for player 0:" ] }, { "cell_type": "code", "execution_count": 22, "id": "ae9fc7a7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "At information set 0, Player 0 plays action 0 with probability: 0 and action 1 with probability: 0 and action 2 with probability: 1\n", "At information set 1, Player 0 plays action 0 with probability: 0 and action 1 with probability: 1 and action 2 with probability: 0\n" ] } ], "source": [ "for infoset, mixed_action in eqm[\"Pl0\"].mixed_actions():\n", " print(\n", " f\"At information set {infoset.number}, \"\n", " f\"Player 0 plays action 0 with probability: {mixed_action['p0a0']}\"\n", " f\" and action 1 with probability: {mixed_action['p0a1']}\"\n", " f\" and action 2 with probability: {mixed_action['p0a2']}\"\n", " )" ] }, { "cell_type": "markdown", "id": "eac73a24", "metadata": {}, "source": [ "For player 1, we can do the same:" ] }, { "cell_type": "code", "execution_count": 23, "id": "8528e1bd", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\left[\\left[0,0,1\\right],\\left[0,1,0\\right],\\left[1,0,0\\right],\\left[0,0,1\\right],\\left[0,1,0\\right],\\left[0,0,1\\right]\\right]$" ], "text/plain": [ "[[Rational(0, 1), Rational(0, 1), Rational(1, 1)], [Rational(0, 1), Rational(1, 1), Rational(0, 1)], [Rational(1, 1), Rational(0, 1), Rational(0, 1)], [Rational(0, 1), Rational(0, 1), Rational(1, 1)], [Rational(0, 1), Rational(1, 1), Rational(0, 1)], [Rational(0, 1), Rational(0, 1), Rational(1, 1)]]" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eqm['Pl1']" ] }, { "cell_type": "code", "execution_count": 24, "id": "2965aed0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "At information set 0, Player 1 plays action 0 with probability: 0 and action 1 with probability: 0 and action 2 with probability: 1\n", "At information set 1, Player 1 plays action 0 with probability: 0 and action 1 with probability: 1 and action 2 with probability: 0\n", "At information set 2, Player 1 plays action 0 with probability: 1 and action 1 with probability: 0 and action 2 with probability: 0\n", "At information set 3, Player 1 plays action 0 with probability: 0 and action 1 with probability: 0 and action 2 with probability: 1\n", "At information set 4, Player 1 plays action 0 with probability: 0 and action 1 with probability: 1 and action 2 with probability: 0\n", "At information set 5, Player 1 plays action 0 with probability: 0 and action 1 with probability: 0 and action 2 with probability: 1\n" ] } ], "source": [ "for infoset, mixed_action in eqm[\"Pl1\"].mixed_actions():\n", " print(\n", " f\"At information set {infoset.number}, \"\n", " f\"Player 1 plays action 0 with probability: {mixed_action['p1a0']}\"\n", " f\" and action 1 with probability: {mixed_action['p1a1']}\"\n", " f\" and action 2 with probability: {mixed_action['p1a2']}\"\n", " )" ] }, { "cell_type": "markdown", "id": "d628c0d5", "metadata": {}, "source": [ "Let's now train 2 agents using independent Q-learning on Tiny Hanabi, and play them against eachother.\n", "\n", "We can compare the learned strategies played to the equilibrium strategies computed by Gambit.\n", "\n", "First let's open the RL environment for Tiny Hanabi and create the agents, one for each player (2 players in this case):" ] }, { "cell_type": "code", "execution_count": 25, "id": "4e72c924", "metadata": {}, "outputs": [], "source": [ "# Create the environment\n", "env = rl_environment.Environment(\"tiny_hanabi\")\n", "num_players = env.num_players\n", "num_actions = env.action_spec()[\"num_actions\"]\n", "\n", "# Create the agents\n", "agents = [\n", " tabular_qlearner.QLearner(player_id=idx, num_actions=num_actions)\n", " for idx in range(num_players)\n", "]" ] }, { "cell_type": "markdown", "id": "4bf9eea4", "metadata": {}, "source": [ "Now we can train the Q-learning agents in self-play." ] }, { "cell_type": "code", "execution_count": 26, "id": "53547263", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Episodes: 0\n", "Episodes: 10000\n", "Episodes: 20000\n", "Episodes: 30000\n" ] } ], "source": [ "for cur_episode in range(30000):\n", " if cur_episode % 10000 == 0:\n", " print(f\"Episodes: {cur_episode}\")\n", "\n", " time_step = env.reset()\n", " while not time_step.last():\n", " player_id = time_step.observations[\"current_player\"]\n", " agent_output = agents[player_id].step(time_step)\n", " time_step = env.step([agent_output.action])\n", "\n", " # Episode is over, step all agents with final info state.\n", " for agent in agents:\n", " agent.step(time_step)\n", "\n", "print(f\"Episodes: {cur_episode+1}\")" ] }, { "cell_type": "markdown", "id": "75cddd36", "metadata": {}, "source": [ "Let's check out the strategies our agents have learned by playing them against eachother again, this time in evaluation mode (setting `is_evaluation=True`):" ] }, { "cell_type": "code", "execution_count": 27, "id": "d71bc733", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "p0:d0 p1:d1\n", "Agent 0 chooses p0a2\n", "\n", "p0:d0 p1:d1 p0:a2\n", "Agent 1 chooses p1a2\n", "\n", "p0:d0 p1:d1 p0:a2 p1:a2\n", "Rewards: [10.0, 10.0]\n" ] } ], "source": [ "time_step = env.reset()\n", "\n", "while not time_step.last():\n", " print(\"\")\n", " print(env.get_state)\n", "\n", " player_id = time_step.observations[\"current_player\"]\n", " agent_output = agents[player_id].step(time_step, is_evaluation=True)\n", " print(f\"Agent {player_id} chooses {env.get_state.action_to_string(agent_output.action)}\")\n", " time_step = env.step([agent_output.action])\n", "\n", "print(\"\")\n", "print(env.get_state)\n", "print(f\"Rewards: {time_step.rewards}\")" ] }, { "cell_type": "markdown", "id": "f1e9b174", "metadata": {}, "source": [ "Are the learned strategies chosen by p0 and p1 consistent with an equilibrium computed by Gambit?\n", "\n", "When I ran the above I got the final game state `p0:d0 p1:d0 p0:a2 p1:a0` with payoffs `[10.0, 10.0]`. This is consistent with the equilibrium computed by Gambit:\n", "- The node `p0:d0 p1:d0` is part of player 0's information set 0.\n", "- p0 picks a2 which matches the first equilibrium strategy in `eqm['Pl0']` where action `p0a2` is played with probability 1.0.\n", "- This puts player 1 in their information set 2, and player 1 picks action 0, which is consistent with `eqm['Pl1']` where action `p1a0` is played with probability 1.0." ] }, { "cell_type": "markdown", "id": "6f356383", "metadata": {}, "source": [ "## Extensive form games created with Gambit\n", "\n", "It's also possible to create an extensive form game in Gambit and export it to OpenSpiel. Here we demonstrate this with the one-card poker game introduced in tutorial 3." ] }, { "cell_type": "code", "execution_count": 28, "id": "07340e32", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "efg_game()" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "with open(\"../poker.efg\", \"r\") as f:\n", " poker_efg_string = f.read()\n", " ops_one_card_poker = pyspiel.load_efg_game(poker_efg_string)\n", "ops_one_card_poker" ] }, { "cell_type": "markdown", "id": "ef6939f6", "metadata": {}, "source": [ "Games loaded from EFG in OpenSpiel do not take advantage of the full functionality of the package, for example, it is not possible to carry out training with RL algorithms on these games, as in the example above with Tiny Hanabi. The OpenSpiel documentation explains [how to submit new games to the library](https://openspiel.readthedocs.io/en/latest/developer_guide.html#adding-a-game) if you wish to add your own games.\n", "\n", "We can however use the state representation and play through the game step by step:" ] }, { "cell_type": "code", "execution_count": 29, "id": "c01c4d6f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ops_one_card_poker.num_distinct_actions()" ] }, { "cell_type": "markdown", "id": "9986860c", "metadata": {}, "source": [ "The one-card poker game has 4 distinct actions, 2 are for the first player (Alice in the example game): \"Raise\" and \"Fold\", and 2 for the second player (Bob): \"Meet\" and \"Pass\".\n", "\n", "Initialising the game state, we can see the current player at the start is the chance player, who deals the cards:" ] }, { "cell_type": "code", "execution_count": 30, "id": "3b9cc43b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0: Chance: 1 King 0.5 Queen 0.5" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "state = ops_one_card_poker.new_initial_state()\n", "state" ] }, { "cell_type": "markdown", "id": "7b0959f9", "metadata": {}, "source": [ "Let's make the chance player's action dealing a King (action 0):" ] }, { "cell_type": "code", "execution_count": 31, "id": "4dd5d504", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1: Player: 1 1 Raise Fold" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "state.apply_action(0)\n", "state" ] }, { "cell_type": "markdown", "id": "b4291f07", "metadata": {}, "source": [ "As expected, it's now the first player's (Alice's) turn.\n", "Let's have Alice choose to \"Raise\" (action 0):" ] }, { "cell_type": "code", "execution_count": 32, "id": "bd15369f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3: Player: 2 1 Meet Pass" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "state.apply_action(0)\n", "state" ] }, { "cell_type": "markdown", "id": "cd63f7d7", "metadata": {}, "source": [ "As expected, the current player is now player 2 (Bob), let's check the legal actions available to Bob:" ] }, { "cell_type": "code", "execution_count": 33, "id": "8d81ff6b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[2, 3]" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "state.legal_actions()" ] }, { "cell_type": "markdown", "id": "fdb5194f", "metadata": {}, "source": [ "Whereas player 1 (Alice) had the option to \"Raise\" (action 0) and \"Fold\" (action 1), player 2 (Bob) now has the option to \"Meet\" (action 2) or \"Pass\" (action 3).\n", "Let's have Bob choose to \"Pass\":" ] }, { "cell_type": "code", "execution_count": 34, "id": "97913fe5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "6: Terminal: Alice wins 1 -1" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "state.apply_action(3)\n", "state" ] }, { "cell_type": "markdown", "id": "1bf09576", "metadata": {}, "source": [ "Since Bob passed, Alice takes the small win and we reach a terminal state." ] } ], "metadata": { "kernelspec": { "display_name": "gbt_pygraphviz", "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": "3.11.13" } }, "nbformat": 4, "nbformat_minor": 5 }