Game Theory | Sage Reference Manual

Sage Cell Server

integer_function = {(): 0,
                    (1,): 1,
                    (2,): 1,
                    (3,): 1,
                    (1, 2,): 3,
                    (1, 3,): 4,
                    (2, 3,): 5,
                    (1, 2, 3,): 5}
integer_game = CooperativeGame(integer_function)
integer_game.is_superadditive()

False

Sage Cell Server

integer_function = {(): 0,
                    (1,): 1,
                    (2,): 1,
                    (3,): 1,
                    (1, 2,): 3,
                    (1, 3,): 4,
                    (2, 3,): 5,
                    (1, 2, 3,): 7}
integer_game = CooperativeGame(integer_function)
integer_game.is_superadditive()

True

Sage Cell Server

integer_function = {(): 0,
                    (1,): 0,
                    (2,): 2,
                    (1, 2,): 2}
integer_game = CooperativeGame(integer_function)
integer_game.is_superadditive()

True

Sage Cell Server

integer_function = {(): 0,
                    (1,): 0,
                    (2,): 2,
                    (1, 2,): 2}
integer_game = CooperativeGame(integer_function)
integer_game.shapley_value()

{1: 0, 2: 2}

Sage Cell Server

letter_function = {(): 0,
                   ('C',): 0,
                   ('W1',): 0,
                   ('W2',): 0,
                   ('C', 'W1',): 3,
                   ('C', 'W2',): 3,
                   ('W1', 'W2',): 0,
                   ('C', 'W1', 'W2',): 4}
letter_game = CooperativeGame(letter_function)
letter_game.shapley_value()

{'C': 7/3, 'W1': 5/6, 'W2': 5/6}