Add best_response_dynamics.py for implementing best response dynamics in game theory

Author: isatyamks

game_theory/best_response_dynamics.py

@@ -0,0 +1,26 @@
+def best_response_dynamics(payoff_matrix_a, payoff_matrix_b, iterations=10):
+    n = payoff_matrix_a.shape[0]
+    m = payoff_matrix_a.shape[1]
+
+    # Initialize strategies
+    strategy_a = np.ones(n) / n
+    strategy_b = np.ones(m) / m
+
+    for _ in range(iterations):
+        # Update strategy A
+        response_a = np.argmax(payoff_matrix_a @ strategy_b)
+        strategy_a = np.zeros(n)
+        strategy_a[response_a] = 1
+
+        # Update strategy B
+        response_b = np.argmax(payoff_matrix_b.T @ strategy_a)
+        strategy_b = np.zeros(m)
+        strategy_b[response_b] = 1
+
+    return strategy_a, strategy_b
+
+# Example usage
+payoff_a = np.array([[3, 0], [5, 1]])
+payoff_b = np.array([[2, 4], [0, 2]])
+strategies = best_response_dynamics(payoff_a, payoff_b)
+print("Final strategies:", strategies)