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])
