Add shapley_value.py for calculating Shapley values in game theory

Author: isatyamks

game_theory/shapley_value.py

@@ -0,0 +1,27 @@
+import numpy as np
+
+def shapley_value(payoff_matrix):
+    n = payoff_matrix.shape[0]  # Number of players
+    shapley_values = np.zeros(n)  # Initialize Shapley values
+
+    # Iterate over each player
+    for i in range(n):
+        # Iterate over all subsets of players (from 0 to 2^n - 1)
+        for s in range(1 << n):  # All subsets of players
+            if (s & (1 << i)) == 0:  # If player i is not in subset S
+                continue
+
+            # Calculate the value of the subset S without player i
+            s_without_i = s & ~(1 << i)  # Remove player i from the subset
+            marginal_contribution = payoff_matrix[s][i] - (payoff_matrix[s_without_i][i] if s_without_i else 0)
+            
+            # Count the size of the subset S
+            size_of_s = bin(s).count('1')  # Number of players in subset S
+            shapley_values[i] += marginal_contribution / (size_of_s * (n - size_of_s))  # 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)