Implementing Best Responses in Python

The concept of a best response is one of the most fundamental ideas in game theory. Given what your opponent is doing, what's the best you can do? That's your best response. If both players are playing best responses to each other simultaneously, then its a Nash equilibrium. What Is a Best Response? In a two-player game with a payoff matrix,finding player 1's best response to a specific pure strategy of player 2. import numpy as np # Payoff matrix for Player 1 # Rows = Player 1's strategies, Columns = Player 2's strategies payoff_matrix = np.array([ [3, 0], [0, 3], [1, 1] ]) def best_response_to_pure(payoff_matrix, opponent_strategy_index): """Returns the best response to a pure strategy of the opponent.""" payoffs = payoff_matrix[:, opponent_strategy_index] return np.argmax(payoffs) print(best_response_to_pure(payoff_matrix, 0)) # Best response when opponent plays strategy 0 print(best_response_to_pure(payoff_matrix, 1)) # Best response when opponent plays strategy 1 Best responses to