def test_random_matrix(self): seed = 12345 rng = np.random.default_rng(seed) size = (10, 15) A = rng.normal(size=size) v, x, y = minmax(A) for z in [x, y]: assert_((z >= 0).all()) assert_allclose(z.sum(), 1) g = NormalFormGame((Player(A), Player(-A.T))) NE = lemke_howson(g) assert_allclose(v, NE[0] @ A @ NE[1]) assert_(g.is_nash((x, y)))
def test_player_corner_cases(): n, m = 3, 4 player = Player(np.zeros((n, m))) for action in range(n): eq_(player.is_best_response(action, [1 / m] * m), True) for method in [None, 'simplex']: eq_(player.is_dominated(action, method=method), False) e = 1e-8 player = Player([[-e, -e], [1, -1], [-1, 1]]) action = 0 eq_(player.is_best_response(action, [1 / 2, 1 / 2], tol=e), True) eq_(player.is_best_response(action, [1 / 2, 1 / 2], tol=e / 2), False) for method in [None, 'simplex']: eq_(player.is_dominated(action, tol=e, method=method), False) eq_(player.is_dominated(action, tol=e / 2, method=method), True)
def anti_coordination(N, v): payoff_array = np.empty((2, ) * N) payoff_array[0, :] = 1 payoff_array[1, :] = 0 payoff_array[1].flat[0] = v g = NormalFormGame((Player(payoff_array), ) * N) return g
def setUp(self): """Setup a Player instance""" payoffs_2opponents = [[[3, 6], [4, 2]], [[1, 0], [5, 7]]] self.player = Player(payoffs_2opponents)
def setUp(self): """Setup a NormalFormGame instance""" payoffs_2opponents = [[[3, 6], [4, 2]], [[1, 0], [5, 7]]] player = Player(payoffs_2opponents) self.g = NormalFormGame([player for i in range(3)])
def test_random_choice(): n, m = 5, 4 payoff_matrix = np.zeros((n, m)) player = Player(payoff_matrix) eq_(player.random_choice([0]), 0) actions = list(range(player.num_actions)) ok_(player.random_choice() in actions)
def test_player_corner_cases(): n, m = 3, 4 player = Player(np.zeros((n, m))) for action in range(n): eq_(player.is_best_response(action, [1 / m] * m), True) for method in LP_METHODS: eq_(player.is_dominated(action, method=method), False) e = 1e-8 * 2 player = Player([[-e, -e], [1, -1], [-1, 1]]) action = 0 eq_(player.is_best_response(action, [1 / 2, 1 / 2], tol=e), True) eq_(player.is_best_response(action, [1 / 2, 1 / 2], tol=e / 2), False) for method in LP_METHODS: eq_(player.is_dominated(action, tol=2 * e, method=method), False) eq_(player.dominated_actions(tol=2 * e, method=method), []) eq_(player.is_dominated(action, tol=e / 2, method=method), True) eq_(player.dominated_actions(tol=e / 2, method=method), [action])
def test_player_corner_cases(): n, m = 3, 4 player = Player(np.zeros((n, m))) for action in range(n): assert_(player.is_best_response(action, [1 / m] * m)) for method in LP_METHODS: assert_(not player.is_dominated(action, method=method)) e = 1e-8 * 2 player = Player([[-e, -e], [1, -1], [-1, 1]]) action = 0 assert_(player.is_best_response(action, [1 / 2, 1 / 2], tol=e)) assert_(not player.is_best_response(action, [1 / 2, 1 / 2], tol=e / 2)) for method in LP_METHODS: assert_(not player.is_dominated(action, tol=2 * e, method=method)) assert_(player.dominated_actions(tol=2 * e, method=method) == []) assert_(player.is_dominated(action, tol=e / 2, method=method)) assert_(player.dominated_actions(tol=e / 2, method=method) == [action])
def test_player_repr(): nums_actions = (2, 3, 4) payoff_arrays = [ np.arange(np.prod(nums_actions[0:i])).reshape(nums_actions[0:i]) for i in range(1, len(nums_actions)+1) ] players = [Player(payoff_array) for payoff_array in payoff_arrays] for player in players: player_new = eval(repr(player)) assert_array_equal(player_new.payoff_array, player.payoff_array)
def setUp(self): self.game_dicts = [] # From von Stengel 2007 in Algorithmic Game Theory bimatrix = [[(3, 3), (3, 3)], [(2, 2), (5, 6)], [(0, 3), (6, 1)]] NEs_dict = {0: ([0, 1 / 3, 2 / 3], [1 / 3, 2 / 3])} d = { 'g': NormalFormGame(bimatrix), 'NEs_dict': NEs_dict, 'converged': True } self.game_dicts.append(d) # == Examples of cycles by "ad hoc" tie breaking rules == # # Example where tie breaking that picks the variable with # the smallest row index in the tableau leads to cycling A = np.array([[0, 0, 0], [0, 1, 1], [1, 1, 0]]) B = np.array([[1, 0, 1], [1, 1, 0], [0, 0, 2]]) NEs_dict = {0: ([0, 2 / 3, 1 / 3], [0, 1, 0])} d = { 'g': NormalFormGame((Player(A), Player(B))), 'NEs_dict': NEs_dict, 'converged': True } self.game_dicts.append(d) # Example where tie breaking that picks the variable with # the smallest variable index in the tableau leads to cycling perm = [2, 0, 1] C = A[:, perm] D = B[perm, :] NEs_dict = {0: ([0, 2 / 3, 1 / 3], [0, 0, 1])} d = { 'g': NormalFormGame((Player(C), Player(D))), 'NEs_dict': NEs_dict, 'converged': True } self.game_dicts.append(d)
def test_normalformgame_payoff_profile_array(): nums_actions = (2, 3, 4) for N in range(1, len(nums_actions) + 1): payoff_arrays = [ np.arange(np.prod(nums_actions[0:N])).reshape(nums_actions[i:N] + nums_actions[0:i]) for i in range(N) ] players = [Player(payoff_array) for payoff_array in payoff_arrays] g = NormalFormGame(players) g_new = NormalFormGame(g.payoff_profile_array) for player_new, payoff_array in zip(g_new.players, payoff_arrays): assert_array_equal(player_new.payoff_array, payoff_array)
def random_skew_sym(n, m=None, random_state=None): """ Generate a random skew symmetric zero-sum NormalFormGame of the form O B -B.T O where B is an n x m matrix. """ if m is None: m = n random_state = check_random_state(random_state) B = random_state.random_sample((n, m)) A = np.empty((n + m, n + m)) A[:n, :n] = 0 A[n:, n:] = 0 A[:n, n:] = B A[n:, :n] = -B.T return NormalFormGame([Player(A) for i in range(2)])
def test_normalformgame_invalid_input_players_dtype_inconsistent(): p0 = Player(np.zeros((2, 2), dtype=int)) p1 = Player(np.zeros((2, 2), dtype=float)) NormalFormGame([p0, p1])
def test_normalformgame_invalid_input_players_num_inconsistent(): p0 = Player(np.zeros((2, 2, 2))) p1 = Player(np.zeros((2, 2, 2))) NormalFormGame([p0, p1])
def test_player_zero_actions(): Player([[]])
def setUp(self): """Setup a Player instance""" self.payoffs = [[0, 1]] self.player = Player(self.payoffs)
def setUp(self): """Setup a Player instance""" self.payoffs = [0, 1, -1] self.player = Player(self.payoffs) self.best_response_action = 1 self.dominated_actions = [0, 2]
def setUp(self): """Setup a Player instance""" coordination_game_matrix = [[4, 0], [3, 2]] self.player = Player(coordination_game_matrix)
def test_normalformgame_invalid_input_players_shape_inconsistent(): p0 = Player(np.zeros((2, 3))) p1 = Player(np.zeros((2, 3))) assert_raises(ValueError, NormalFormGame, [p0, p1])
def test_normalformgame_invalid_input_players_dtype_inconsistent(): p0 = Player(np.zeros((2, 2), dtype=int)) p1 = Player(np.zeros((2, 2), dtype=float)) assert_raises(ValueError, NormalFormGame, [p0, p1])
def test_normalformgame_invalid_input_players_shape_inconsistent(): p0 = Player(np.zeros((2, 3))) p1 = Player(np.zeros((2, 3))) g = NormalFormGame([p0, p1])