[pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

Author: pre-commit-ci[bot]

game_theory/best_response_dynamics.py

@@ -19,6 +19,7 @@ def best_response_dynamics(payoff_matrix_a, payoff_matrix_b, iterations=10):
 
     return strategy_a, strategy_b
 
+
 # Example usage
 payoff_a = np.array([[3, 0], [5, 1]])
 payoff_b = np.array([[2, 4], [0, 2]])

game_theory/fictitious_play.py

@@ -25,6 +25,7 @@ def fictitious_play(payoff_matrix_a, payoff_matrix_b, iterations=100):
 
     return strategy_a, strategy_b
 
+
 # Example usage
 payoff_a = np.array([[3, 0], [5, 1]])
 payoff_b = np.array([[2, 4], [0, 2]])

game_theory/minimax_algorithm.py

@@ -3,7 +3,7 @@ def minimax(depth, node_index, is_maximizing_player, values, alpha, beta):
         return values[node_index]
 
     if is_maximizing_player:
-        best_value = float('-inf')
+        best_value = float("-inf")
         for i in range(2):  # Two children (0 and 1)
             value = minimax(depth - 1, node_index * 2 + i, False, values, alpha, beta)
             best_value = max(best_value, value)
@@ -12,7 +12,7 @@ def minimax(depth, node_index, is_maximizing_player, values, alpha, beta):
                 break  # Beta cut-off
         return best_value
     else:
-        best_value = float('inf')
+        best_value = float("inf")
         for i in range(2):  # Two children (0 and 1)
             value = minimax(depth - 1, node_index * 2 + i, True, values, alpha, beta)
             best_value = min(best_value, value)
@@ -21,8 +21,9 @@ def minimax(depth, node_index, is_maximizing_player, values, alpha, beta):
                 break  # Alpha cut-off
         return best_value
 
+
 # Example usage
 values = [3, 5, 2, 9, 0, 1, 8, 6]  # Leaf node values
 depth = 3  # Depth of the game tree
-result = minimax(depth, 0, True, values, float('-inf'), float('inf'))
+result = minimax(depth, 0, True, values, float("-inf"), float("inf"))
 print("The optimal value is:", result)

game_theory/nash_equlibrium.py

@@ -1,6 +1,7 @@
 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]
@@ -23,6 +24,7 @@ def find_nash_equilibrium(payoff_matrix_a, payoff_matrix_b):
 
     return p_a, p_b
 
+
 # Example usage
 payoff_a = np.array([[3, 0], [5, 1]])
 payoff_b = np.array([[2, 4], [0, 2]])

game_theory/shapley_value.py

@@ -1,5 +1,6 @@
 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
@@ -13,14 +14,19 @@ def shapley_value(payoff_matrix):
 
             # 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)
-            
+            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
+            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)