semivalues 0.0.13

A package for computing semivalues.

This package offers tools for computing semivalues, with the Shapley value being the most prominent example. It places special emphasis on graph-based games, without being restricted to it.

Broad Functionality:

• Compute Shapley/Banzhaf value exact or approximately
• Compute decomposition matrices

Detailed Functionality:

• Compute Shapley/Banzhaf value (exact and approximately)
• Compute Shapley/Banzhaf value decomposition by size (exact and approximately) (n x n matrix where each entry is aggregated over the respective subset size)
• Compute Shapley value of a player to another player (exact and approximately) (Hausken, Kjell, and Matthias Mohr. "The value of a player in n-person games." Social Choice and Welfare 18 (2001): 465-483.)

For the approximation methods of the Shapley value we refer to https://arxiv.org/pdf/1306.4265

How To Use

You need to have a utility function mapping an arbitrary set of players to a real number. Players names should be {0, ..., n-1}, i.e. the utility function should return values for all subsets of {0, ..., n-1}. We will use the example introduced here

def utility_game_function(S):
    GAME_VALUES = {
        frozenset(): 0,
        frozenset({0}): 180,
        frozenset({1}): 0,
        frozenset({2}): 0,
        frozenset({1, 2}): 0,
        frozenset({0, 1}): 360,
        frozenset({0, 2}): 540,
        frozenset({0, 1, 2}): 540,
    }

    def game_utility(coalition: set) -> int:
        return GAME_VALUES.get(frozenset(coalition), 0)

    return game_utility(S)


num_players = 3

from semivalues import shapley, banzhaf
# (n-vector)
shapley.exact(utility_game_function=utility_game_function, num_players=num_players)
shapley.strata_sampling(utility_game_function=utility_game_function, num_players=num_players, num_samples=100000)

banzhaf.exact(utility_game_function=utility_game_function, num_players=num_players)
banzhaf.sampling(utility_game_function=utility_game_function, num_players=num_players, num_samples=100000)


from semivalues.decompositions.shapley import by_size
# (n x n matrix)
by_size.exact(utility_game_function=utility_game_function, num_players=num_players)
by_size.strata_sampling(utility_game_function=utility_game_function, num_players=num_players, num_samples=100000)

from semivalues.decompositions.banzhaf import by_size
# (n x n matrix)
by_size.exact(utility_game_function=utility_game_function, num_players=num_players)
by_size.monte_carlo_sampling(utility_game_function=utility_game_function, num_players=num_players, num_samples=100000)


from semivalues.decompositions.shapley import player_to_player
# (n x n matrix)
player_to_player.exact(utility_game_function=utility_game_function, num_players=num_players)
player_to_player.monte_carlo_sampling(utility_game_function=utility_game_function, num_players=num_players, num_samples=100000)