chore: nash.py added to game theory

Author: isatyamks

game_theory/nash_equilibrium.py

@@ -0,0 +1,30 @@
+import numpy as np
+from scipy.optimize import linprog
+
+def find_nash_equilibrium(payoff_matrix_A, payoff_matrix_B):
+    n = payoff_matrix_A.shape[0]
+    m = payoff_matrix_A.shape[1]
+
+    # Solve for player A
+    c = [-1] * n  # Objective: maximize A's payoff
+    A_ub = -payoff_matrix_A  # A's constraints
+    b_ub = [-1] * m
+
+    result_A = linprog(c, A_ub=A_ub, b_ub=b_ub, bounds=(0, None))
+    p_A = result_A.x
+
+    # Solve for player B
+    c = [-1] * m  # Objective: maximize B's payoff
+    A_ub = -payoff_matrix_B.T  # B's constraints
+    b_ub = [-1] * n
+
+    result_B = linprog(c, A_ub=A_ub, b_ub=b_ub, bounds=(0, None))
+    p_B = result_B.x
+
+    return p_A, p_B
+
+# Example usage
+payoff_A = np.array([[3, 0], [5, 1]])
+payoff_B = np.array([[2, 4], [0, 2]])
+equilibrium = find_nash_equilibrium(payoff_A, payoff_B)
+print("Nash Equilibrium strategies:", equilibrium)