class TestNormalFormGame_Asym2p:
"""Test the methods of NormalFormGame with asymmetric two players"""
def setUp(self):
"""Setup a NormalFormGame instance"""
self.BoS_bimatrix = np.array([[(3, 2), (1, 1)], [(0, 0), (2, 3)]])
self.g = NormalFormGame(self.BoS_bimatrix)
def test_getitem(self):
action_profile = (1, 0)
assert_array_equal(self.g[action_profile],
self.BoS_bimatrix[action_profile])
def test_delete_action(self):
action_to_delete = 0
for i, player in enumerate(self.g.players):
g_new = self.g.delete_action(i, action_to_delete)
actions_to_remain = \
np.setdiff1d(np.arange(player.num_actions), action_to_delete)
assert_array_equal(
g_new.payoff_profile_array,
self.g.payoff_profile_array.take(actions_to_remain, axis=i))
def test_is_nash_pure(self):
ok_(not self.g.is_nash((1, 0)))
def test_is_nash_mixed(self):
ok_(self.g.is_nash(([3 / 4, 1 / 4], [1 / 4, 3 / 4])))
def test_payoff_arrays(self):
assert_array_equal(self.g.payoff_arrays[0], self.BoS_bimatrix[:, :, 0])
assert_array_equal(self.g.payoff_arrays[1], self.BoS_bimatrix[:, :,
1].T)
class TestNormalFormGame_1p:
"""Test for trivial NormalFormGame with a single player"""
def setUp(self):
"""Setup a NormalFormGame instance"""
data = [[0], [1], [1]]
self.g = NormalFormGame(data)
def test_construction(self):
"""Trivial game: construction"""
ok_(self.g.N == 1)
assert_array_equal(self.g.players[0].payoff_array, [0, 1, 1])
def test_getitem(self):
"""Trivial game: __getitem__"""
eq_(self.g[0], 0)
def test_is_nash_pure(self):
"""Trivial game: is_nash with pure action"""
ok_(self.g.is_nash((1,)))
ok_(not self.g.is_nash((0,)))
def test_is_nash_mixed(self):
"""Trivial game: is_nash with mixed action"""
ok_(self.g.is_nash(([0, 1 / 2, 1 / 2],)))
def test_normalformgame_constant_payoffs():
g = NormalFormGame((2, 2))
ok_(g.is_nash((0, 0)))
ok_(g.is_nash((0, 1)))
ok_(g.is_nash((1, 0)))
ok_(g.is_nash((1, 1)))
def test_normalformgame_constant_payoffs():
g = NormalFormGame((2, 2))
ok_(g.is_nash((0, 0)))
ok_(g.is_nash((0, 1)))
ok_(g.is_nash((1, 0)))
ok_(g.is_nash((1, 1)))
class TestNormalFormGame_1p:
"""Test for trivial NormalFormGame with a single player"""
def setUp(self):
"""Setup a NormalFormGame instance"""
data = [[0], [1], [1]]
self.g = NormalFormGame(data)
def test_construction(self):
"""Trivial game: construction"""
ok_(self.g.N == 1)
assert_array_equal(self.g.players[0].payoff_array, [0, 1, 1])
def test_getitem(self):
"""Trivial game: __getitem__"""
eq_(self.g[0], 0)
def test_delete_action(self):
actions_to_delete = [1, 2]
for i, player in enumerate(self.g.players):
g_new = self.g.delete_action(i, actions_to_delete)
actions_to_remain = \
np.setdiff1d(np.arange(player.num_actions), actions_to_delete)
assert_array_equal(
g_new.payoff_profile_array,
self.g.payoff_profile_array.take(actions_to_remain, axis=i))
def test_is_nash_pure(self):
"""Trivial game: is_nash with pure action"""
ok_(self.g.is_nash((1, )))
ok_(not self.g.is_nash((0, )))
def test_is_nash_mixed(self):
"""Trivial game: is_nash with mixed action"""
ok_(self.g.is_nash(([0, 1 / 2, 1 / 2], )))
class TestNormalFormGame_3p:
"""Test the methods of NormalFormGame with three players"""
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_getitem(self):
assert_array_equal(self.g[0, 0, 1], [6, 4, 1])
def test_delete_action(self):
action_to_delete = 0
for i, player in enumerate(self.g.players):
g_new = self.g.delete_action(i, action_to_delete)
actions_to_remain = \
np.setdiff1d(np.arange(player.num_actions), action_to_delete)
assert_array_equal(
g_new.payoff_profile_array,
self.g.payoff_profile_array.take(actions_to_remain, axis=i)
)
def test_is_nash_pure(self):
ok_(self.g.is_nash((0, 0, 0)))
ok_(not self.g.is_nash((0, 0, 1)))
def test_is_nash_mixed(self):
p = (1 + np.sqrt(65)) / 16
ok_(self.g.is_nash(([1 - p, p], [1 - p, p], [1 - p, p])))
class TestNormalFormGame_3p:
"""Test the methods of NormalFormGame with three players"""
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_getitem(self):
assert_array_equal(self.g[0, 0, 1], [6, 4, 1])
def test_delete_action(self):
action_to_delete = 0
for i, player in enumerate(self.g.players):
g_new = self.g.delete_action(i, action_to_delete)
actions_to_remain = \
np.setdiff1d(np.arange(player.num_actions), action_to_delete)
assert_array_equal(
g_new.payoff_profile_array,
self.g.payoff_profile_array.take(actions_to_remain, axis=i))
def test_is_nash_pure(self):
ok_(self.g.is_nash((0, 0, 0)))
ok_(not self.g.is_nash((0, 0, 1)))
def test_is_nash_mixed(self):
p = (1 + np.sqrt(65)) / 16
ok_(self.g.is_nash(([1 - p, p], [1 - p, p], [1 - p, p])))
class TestNormalFormGame_1p:
"""Test for trivial NormalFormGame with a single player"""
def setUp(self):
"""Setup a NormalFormGame instance"""
data = [[0], [1], [1]]
self.g = NormalFormGame(data)
def test_construction(self):
"""Trivial game: construction"""
ok_(self.g.N == 1)
assert_array_equal(self.g.players[0].payoff_array, [0, 1, 1])
def test_getitem(self):
"""Trivial game: __getitem__"""
eq_(self.g[0], 0)
def test_is_nash_pure(self):
"""Trivial game: is_nash with pure action"""
ok_(self.g.is_nash((1,)))
ok_(not self.g.is_nash((0,)))
def test_is_nash_mixed(self):
"""Trivial game: is_nash with mixed action"""
ok_(self.g.is_nash(([0, 1/2, 1/2],)))
class TestNormalFormGame_Asym2p:
"""Test the methods of NormalFormGame with asymmetric two players"""
def setUp(self):
"""Setup a NormalFormGame instance"""
self.BoS_bimatrix = np.array([[(3, 2), (1, 1)],
[(0, 0), (2, 3)]])
self.g = NormalFormGame(self.BoS_bimatrix)
def test_getitem(self):
action_profile = (1, 0)
assert_array_equal(self.g[action_profile],
self.BoS_bimatrix[action_profile])
def test_is_nash_pure(self):
ok_(not self.g.is_nash((1, 0)))
def test_is_nash_mixed(self):
ok_(self.g.is_nash(([3/4, 1/4], [1/4, 3/4])))
def test_payoff_arrays(self):
assert_array_equal(
self.g.payoff_arrays[0], self.BoS_bimatrix[:, :, 0]
)
assert_array_equal(
self.g.payoff_arrays[1], self.BoS_bimatrix[:, :, 1].T
)
class TestNormalFormGame_Sym2p:
"""Test the methods of NormalFormGame with symmetric two players"""
def setUp(self):
"""Setup a NormalFormGame instance"""
coordination_game_matrix = [[4, 0], [3, 2]]
self.g = NormalFormGame(coordination_game_matrix)
def test_getitem(self):
assert_array_equal(self.g[0, 1], [0, 3])
def test_is_nash_pure(self):
ok_(self.g.is_nash((0, 0)))
def test_is_nash_mixed(self):
ok_(self.g.is_nash(([2 / 3, 1 / 3], [2 / 3, 1 / 3])))
class TestNormalFormGame_Asym2p:
"""Test the methods of NormalFormGame with asymmetric two players"""
def setUp(self):
"""Setup a NormalFormGame instance"""
matching_pennies_bimatrix = [[(1, -1), (-1, 1)], [(-1, 1), (1, -1)]]
self.g = NormalFormGame(matching_pennies_bimatrix)
def test_getitem(self):
assert_array_equal(self.g[1, 0], [-1, 1])
def test_is_nash_against_pure(self):
ok_(not self.g.is_nash((0, 0)))
def test_is_nash_against_mixed(self):
ok_(self.g.is_nash(([1 / 2, 1 / 2], [1 / 2, 1 / 2])))
class TestNormalFormGame_Asym2p:
"""Test the methods of NormalFormGame with asymmetric two players"""
def setUp(self):
"""Setup a NormalFormGame instance"""
matching_pennies_bimatrix = [[(1, -1), (-1, 1)], [(-1, 1), (1, -1)]]
self.g = NormalFormGame(matching_pennies_bimatrix)
def test_getitem(self):
assert_array_equal(self.g[1, 0], [-1, 1])
def test_is_nash_against_pure(self):
ok_(not self.g.is_nash((0, 0)))
def test_is_nash_against_mixed(self):
ok_(self.g.is_nash(([1 / 2, 1 / 2], [1 / 2, 1 / 2])))
class TestNormalFormGame_Sym2p:
"""Test the methods of NormalFormGame with symmetric two players"""
def setUp(self):
"""Setup a NormalFormGame instance"""
coordination_game_matrix = [[4, 0], [3, 2]]
self.g = NormalFormGame(coordination_game_matrix)
def test_getitem(self):
assert_array_equal(self.g[0, 1], [0, 3])
def test_is_nash_pure(self):
ok_(self.g.is_nash((0, 0)))
def test_is_nash_mixed(self):
ok_(self.g.is_nash(([2 / 3, 1 / 3], [2 / 3, 1 / 3])))
class TestNormalFormGame_3p:
"""Test the methods of NormalFormGame with three players"""
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_getitem(self):
assert_array_equal(self.g[0, 0, 1], [6, 4, 1])
def test_is_nash_pure(self):
ok_(self.g.is_nash((0, 0, 0)))
ok_(not self.g.is_nash((0, 0, 1)))
def test_is_nash_mixed(self):
p = (1 + np.sqrt(65)) / 16
ok_(self.g.is_nash(([1 - p, p], [1 - p, p], [1 - p, p])))
class TestNormalFormGame_3p:
"""Test the methods of NormalFormGame with three players"""
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_getitem(self):
assert_array_equal(self.g[0, 0, 1], [6, 4, 1])
def test_is_nash_pure(self):
ok_(self.g.is_nash((0, 0, 0)))
ok_(not self.g.is_nash((0, 0, 1)))
def test_is_nash_mixed(self):
p = (1 + np.sqrt(65)) / 16
ok_(self.g.is_nash(([1 - p, p], [1 - p, p], [1 - p, p])))
class TestNormalFormGame_Asym2p:
"""Test the methods of NormalFormGame with asymmetric two players"""
def setUp(self):
"""Setup a NormalFormGame instance"""
self.BoS_bimatrix = np.array([[(3, 2), (1, 1)],
[(0, 0), (2, 3)]])
self.g = NormalFormGame(self.BoS_bimatrix)
def test_getitem(self):
action_profile = (1, 0)
assert_array_equal(self.g[action_profile],
self.BoS_bimatrix[action_profile])
def test_delete_action(self):
action_to_delete = 0
for i, player in enumerate(self.g.players):
g_new = self.g.delete_action(i, action_to_delete)
actions_to_remain = \
np.setdiff1d(np.arange(player.num_actions), action_to_delete)
assert_array_equal(
g_new.payoff_profile_array,
self.g.payoff_profile_array.take(actions_to_remain, axis=i)
)
def test_is_nash_pure(self):
ok_(not self.g.is_nash((1, 0)))
def test_is_nash_mixed(self):
ok_(self.g.is_nash(([3/4, 1/4], [1/4, 3/4])))
def test_payoff_arrays(self):
assert_array_equal(
self.g.payoff_arrays[0], self.BoS_bimatrix[:, :, 0]
)
assert_array_equal(
self.g.payoff_arrays[1], self.BoS_bimatrix[:, :, 1].T
)
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)))
class TestNormalFormGame_1p:
"""Test for trivial NormalFormGame with a single player"""
def setUp(self):
"""Setup a NormalFormGame instance"""
data = [[0], [1], [1]]
self.g = NormalFormGame(data)
def test_construction(self):
"""Trivial game: construction"""
ok_(self.g.N == 1)
assert_array_equal(self.g.players[0].payoff_array, [0, 1, 1])
def test_getitem(self):
"""Trivial game: __getitem__"""
eq_(self.g[0], 0)
def test_delete_action(self):
actions_to_delete = [1, 2]
for i, player in enumerate(self.g.players):
g_new = self.g.delete_action(i, actions_to_delete)
actions_to_remain = \
np.setdiff1d(np.arange(player.num_actions), actions_to_delete)
assert_array_equal(
g_new.payoff_profile_array,
self.g.payoff_profile_array.take(actions_to_remain, axis=i)
)
def test_is_nash_pure(self):
"""Trivial game: is_nash with pure action"""
ok_(self.g.is_nash((1,)))
ok_(not self.g.is_nash((0,)))
def test_is_nash_mixed(self):
"""Trivial game: is_nash with mixed action"""
ok_(self.g.is_nash(([0, 1/2, 1/2],)))
