hisss.calculate_nash_equilibrium

hisss.calculate_nash_equilibrium(available_actions, joint_action_list, joint_action_value_arr)

Calculates the Nash equilibrium for a given game formulation using a C++ backend. The algorithm used here is from Porter et al. (“Simple search methods for finding a Nash equilibrium”). It works for both 2-player as well as N-player games.

Parameters:

• available_actions (list[list[int]]) – A list where the index represents the player and the value is a list of integer IDs representing their available actions.

• joint_action_list (list[tuple[int, ...]]) – A list of all possible joint actions, where each tuple represents a combination of actions chosen by all players.

• joint_action_value_arr (ndarray) – A 2D numpy array of shape (num_joint_actions, num_players) representing the payoffs. Rows correspond to the joint actions (aligned with joint_action_list) and columns correspond to each player’s payout.

Returns:

A tuple containing two elements:

• value_list (list[float]): The expected payoff/value for each player at the calculated Nash equilibrium.

• policy_list (list[np.ndarray]): The equilibrium strategy for each player, represented as a list of numpy arrays. Each array contains the probability distribution over that player’s available actions.

Return type:

tuple[list[float], list[ndarray]]

Raises:

ValueError – If the number of columns in joint_action_value_arr does not match the number of players inferred from available_actions.