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OpenGame.ipynb
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‎Examples/OpenGame.ipynb‎

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "4a2a11de",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Outcome: ('Cooperate', 'Cooperate')\n",
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"Payoff: 3\n",
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"Feedback: Strategy always_cooperate resulted in a reward of 3\n",
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"Best Response Strategy against always cooperate: my_strategy\n",
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"Best response outcome: ('Defect', 'Defect')\n",
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"Best response payoff: 1\n"
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]
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}
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],
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"source": [
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"from typing import TypeVar, Generic, Callable, Tuple\n",
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"\n",
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"# Define generic type variables for the OpenGame class\n",
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"Input = TypeVar('Input')\n",
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"Output = TypeVar('Output')\n",
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"Payoff = TypeVar('Payoff')\n",
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"Feedback = TypeVar('Feedback')\n",
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"\n",
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"class BaseStrategy(Generic[Input, Output]):\n",
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" \"\"\"\n",
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" Base class for all strategies.\n",
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" A strategy is a class that can decide an output given an input.\n",
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" It can store its own internal state (e.g., weights, memory).\n",
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" \"\"\"\n",
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" def select_action(self, input_val: Input) -> Output:\n",
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" \"\"\"\n",
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" Selects an action (output) based on the given input.\n",
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" This method must be implemented by concrete strategy classes.\n",
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" \"\"\"\n",
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" raise NotImplementedError\n",
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"\n",
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"Strategy = TypeVar('Strategy', bound=BaseStrategy[Input, Output])\n",
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"\n",
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"\n",
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"class OpenGame(Generic[Input, Output, Payoff, Feedback, Strategy]):\n",
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" \"\"\"\n",
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" A generic class representing an open game.\n",
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" \"\"\"\n",
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"\n",
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" def play(\n",
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" self,\n",
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" strategy: Strategy,\n",
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" input_val: Input,\n",
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" ) -> Output:\n",
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" \"\"\"\n",
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" Plays the game given a strategy and an input, and returns the output.\n",
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"\n",
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" Args:\n",
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" strategy: The strategy to use.\n",
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" input_val: The input to the game.\n",
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"\n",
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" Returns:\n",
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" The output of the game.\n",
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" \"\"\"\n",
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" raise NotImplementedError\n",
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"\n",
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" def coplay(\n",
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" self,\n",
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" strategy: Strategy,\n",
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" input_val: Input,\n",
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" reward: Payoff,\n",
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" ) -> Feedback:\n",
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" \"\"\"\n",
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" Co-plays the game, providing feedback based on the strategy, input, and reward.\n",
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"\n",
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" Args:\n",
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" strategy: The strategy to use.\n",
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" input_val: The input to the game.\n",
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" reward: The reward received.\n",
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"\n",
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" Returns:\n",
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" Feedback on the game play.\n",
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" \"\"\"\n",
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" raise NotImplementedError\n",
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"\n",
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" def best_response(\n",
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" self,\n",
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" input_val: Input,\n",
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" payoff_function: Callable[[Output], Payoff],\n",
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" ) -> Callable[[Strategy, Strategy], Strategy]:\n",
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" \"\"\"\n",
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" Finds the best response strategy given an input and a reward function that\n",
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" maps outputs to payoffs. Returns a function that takes two strategies\n",
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" and returns the best response strategy. The intent is that the two input\n",
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" strategies are the other players strategies, and the function determines\n",
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" how to best play in response to those.\n",
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"\n",
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" Args:\n",
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" input_val: The input to the game.\n",
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" payoff_function: A function that maps outputs to payoffs.\n",
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"\n",
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" Returns:\n",
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" A function that takes two strategies and returns the best response strategy.\n",
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" \"\"\"\n",
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" raise NotImplementedError\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "248784ae",
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"metadata": {},
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"outputs": [],
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"source": [
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"from typing import TypeAlias\n",
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"\n",
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"# Example Implementation: Prisoner's Dilemma\n",
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"\n",
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"# Define type aliases for the Prisoner's Dilemma\n",
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"PDAction: TypeAlias = str # \"Cooperate\" or \"Defect\"\n",
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"PDPayoff: TypeAlias = int # Numerical representation of reward/penalty\n",
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"PDFeedback: TypeAlias = str # Can be some string indicating what happened\n",
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"PDStrategy: TypeAlias = Callable[[PDAction], PDAction] # Function to choose action\n",
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"PDInput: TypeAlias = None # No real input, can make it a turn number if needed\n",
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"\n",
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"\n",
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"class PrisonerDilemma(OpenGame[\n",
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" PDInput,\n",
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" Tuple[PDAction, PDAction],\n",
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" PDPayoff,\n",
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" PDFeedback, PDStrategy]\n",
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"):\n",
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" \"\"\"\n",
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" An implementation of the Prisoner's Dilemma as an OpenGame.\n",
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" \"\"\"\n",
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"\n",
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" def play(self, strategy: PDStrategy, input_val: PDInput) -> Tuple[PDAction, PDAction]:\n",
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" \"\"\"\n",
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" Simulates a single round of the Prisoner's Dilemma.\n",
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"\n",
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" Args:\n",
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" strategy: A strategy to use (takes their own action and returns action).\n",
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" input_val: Unused in this simple implementation.\n",
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"\n",
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" Returns:\n",
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" A tuple containing the actions of both players (player1, player2) assuming they use the same strategy. In a more complex setup,\n",
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" we'd take two strategies as arguments to play against each other.\n",
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" \"\"\"\n",
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" action1 = strategy(None) # Choose action based on empty input (no history)\n",
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" action2 = strategy(None) # Same for the other player.\n",
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" return (action1, action2)\n",
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"\n",
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" def coplay(self, strategy: PDStrategy, input_val: PDInput, reward: PDPayoff) -> PDFeedback:\n",
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" \"\"\"\n",
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" Provides feedback based on the strategy, input, and reward.\n",
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"\n",
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" Args:\n",
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" strategy: The strategy used.\n",
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" input_val: The input to the game.\n",
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" reward: The reward received.\n",
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"\n",
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" Returns:\n",
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" Feedback on the game play.\n",
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" \"\"\"\n",
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" return f\"Strategy {strategy.__name__} resulted in a reward of {reward}\"\n",
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"\n",
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" def best_response(self, input_val: PDInput, reward_function: Callable[[Tuple[PDAction, PDAction]], Payoff]) -> Callable[[PDStrategy, PDStrategy], PDStrategy]:\n",
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" \"\"\"\n",
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" Finds the best response strategy, given the other player's strategy. This is a simplified example and doesn't account for repeated games.\n",
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"\n",
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" Args:\n",
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" input_val: The input to the game.\n",
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" reward_function: A function that maps outputs to rewards.\n",
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"\n",
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" Returns:\n",
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" A function that takes two strategies (other players) and returns the best response strategy.\n",
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" \"\"\"\n",
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"\n",
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" def best_response_strategy(\n",
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" opponent_strategy: PDStrategy,\n",
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" self_strategy: PDStrategy\n",
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" ) -> PDStrategy: # added self_strategy to match signature\n",
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"\n",
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" def my_strategy(previous_action: PDAction = None) -> PDAction: # \"previous_action\" argument removed as it's not used\n",
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" \"\"\"\n",
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" A simple strategy that defects if the opponent defects, otherwise cooperates. This is a kind of \"tit-for-tat\"\n",
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" but only for one round, so not very good.\n",
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" \"\"\"\n",
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" opponent_action = opponent_strategy(None)\n",
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"\n",
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" if opponent_action == \"Defect\":\n",
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" return \"Defect\"\n",
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" else:\n",
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" return \"Defect\" # Always defect for the best response in a single round\n",
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" return my_strategy\n",
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"\n",
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" return best_response_strategy\n",
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"\n",
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"\n",
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"# Example Usage\n",
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"if __name__ == '__main__':\n",
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" pd = PrisonerDilemma()\n",
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"\n",
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" # Example Strategy: Always Cooperate\n",
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" def always_cooperate(previous_action: PDAction = None) -> PDAction:\n",
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" return \"Cooperate\"\n",
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"\n",
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" # Example Strategy: Always Defect\n",
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" def always_defect(previous_action: PDAction = None) -> PDAction:\n",
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" return \"Defect\"\n",
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"\n",
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" # Example Payoff function\n",
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" def prisoner_dilemma_payoff(actions: Tuple[PDAction, PDAction]) -> Payoff:\n",
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" \"\"\"\n",
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" Defines the payoff matrix for the Prisoner's Dilemma.\n",
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" \"\"\"\n",
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" action1, action2 = actions\n",
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" if action1 == \"Cooperate\" and action2 == \"Cooperate\":\n",
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" return 3 # Both cooperate\n",
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" elif action1 == \"Cooperate\" and action2 == \"Defect\":\n",
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" return 0 # Player 1 gets suckered\n",
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" elif action1 == \"Defect\" and action2 == \"Cooperate\":\n",
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" return 5 # Player 1 defects\n",
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" else: # Both defect\n",
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" return 1\n",
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"\n",
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" # Play the game\n",
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" outcome = pd.play(always_cooperate, None) # Input is None in this case\n",
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" print(f\"Outcome: {outcome}\")\n",
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"\n",
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" # Calculate payoff\n",
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" payoff = prisoner_dilemma_payoff(outcome)\n",
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" print(f\"Payoff: {payoff}\")\n",
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"\n",
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" # Get feedback\n",
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" feedback = pd.coplay(always_cooperate, None, payoff)\n",
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" print(f\"Feedback: {feedback}\")\n",
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"\n",
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" # Find the best response strategy\n",
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" best_response_func = pd.best_response(None, prisoner_dilemma_payoff)\n",
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" best_response_strategy = best_response_func(always_cooperate, always_cooperate)\n",
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"\n",
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" print(f\"Best Response Strategy against always cooperate: {best_response_strategy.__name__}\") # the best response strategy *IS* a strategy to play against the always cooperate strategy\n",
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"\n",
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" best_response_outcome = pd.play(best_response_strategy, None)\n",
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"\n",
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" print(f\"Best response outcome: {best_response_outcome}\")\n",
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" print(f\"Best response payoff: {prisoner_dilemma_payoff(best_response_outcome)}\")"
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]
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