chore:shapley_value.py added to game theory

Author: isatyamks

game_theory/shapley_value.py

@@ -0,0 +1,19 @@
+def shapley_value(payoff_matrix):
+    n = payoff_matrix.shape[0]
+    shapley_values = np.zeros(n)
+
+    for i in range(n):
+        for S in range(1 << n):  # All subsets of players
+            if (S & (1 << i)) == 0:  # i not in S
+                continue
+
+            S_without_i = S & ~(1 << i)
+            marginal_contribution = payoff_matrix[S][i] - (payoff_matrix[S_without_i][i] if S_without_i else 0)
+            shapley_values[i] += marginal_contribution / (len(bin(S)) - 2)  # Normalize by size of S
+
+    return shapley_values
+
+# Example usage
+payoff_matrix = np.array([[1, 2], [3, 4]])
+shapley_vals = shapley_value(payoff_matrix)
+print("Shapley Values:", shapley_vals)