def test_lemke_howson_capping():
bimatrix = [[(3, 3), (3, 2)], [(2, 2), (5, 6)], [(0, 3), (6, 1)]]
g = NormalFormGame(bimatrix)
m, n = g.nums_actions
max_iter = 10**6 # big number
for k in range(m + n):
NE0, res0 = lemke_howson(g,
init_pivot=k,
max_iter=max_iter,
capping=None,
full_output=True)
NE1, res1 = lemke_howson(g,
init_pivot=k,
max_iter=max_iter,
capping=max_iter,
full_output=True)
for action0, action1 in zip(NE0, NE1):
assert_allclose(action0, action1)
eq_(res0.init, res1.init)
init_pivot = 1
max_iter = m + n
NE, res = lemke_howson(g,
init_pivot=init_pivot,
max_iter=max_iter,
capping=1,
full_output=True)
eq_(res.num_iter, max_iter)
eq_(res.init, init_pivot - 1)
def test_lemke_howson(self):
for d in self.game_dicts:
for k in d['NEs_dict'].keys():
NE_computed = lemke_howson(d['g'], init_pivot=k)
for action_computed, action in zip(NE_computed,
d['NEs_dict'][k]):
assert_allclose(action_computed, action)
def test_lemke_howson(self):
for d in self.game_dicts:
for k in d['NEs_dict'].keys():
NE_computed = lemke_howson(d['g'], init_pivot=k)
for action_computed, action in zip(NE_computed,
d['NEs_dict'][k]):
assert_allclose(action_computed, action)
def test_lemke_howson_degenerate(self):
for d in self.game_dicts:
for k in d['NEs_dict'].keys():
NE_computed, res = lemke_howson(d['g'], init_pivot=k,
full_output=True)
for action_computed, action in zip(NE_computed,
d['NEs_dict'][k]):
assert_allclose(action_computed, action)
eq_(res.converged, d['converged'])
def test_lemke_howson_degenerate(self):
for d in self.game_dicts:
for k in d['NEs_dict'].keys():
NE_computed, res = lemke_howson(d['g'], init_pivot=k,
full_output=True)
for action_computed, action in zip(NE_computed,
d['NEs_dict'][k]):
assert_allclose(action_computed, action)
eq_(res.converged, d['converged'])
def test_lemke_howson_capping():
bimatrix = [[(3, 3), (3, 2)],
[(2, 2), (5, 6)],
[(0, 3), (6, 1)]]
g = NormalFormGame(bimatrix)
m, n = g.nums_actions
max_iter = 10**6 # big number
for k in range(m+n):
NE0, res0 = lemke_howson(g, init_pivot=k, max_iter=max_iter,
capping=None, full_output=True)
NE1, res1 = lemke_howson(g, init_pivot=k, max_iter=max_iter,
capping=max_iter, full_output=True)
for action0, action1 in zip(NE0, NE1):
assert_allclose(action0, action1)
eq_(res0.init, res1.init)
init_pivot = 1
max_iter = m+n
NE, res = lemke_howson(g, init_pivot=init_pivot, max_iter=max_iter,
capping=1, full_output=True)
eq_(res.num_iter, max_iter)
eq_(res.init, init_pivot-1)
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_lemke_howson_invalid_init_pivot_float():
bimatrix = [[(3, 3), (3, 2)],
[(2, 2), (5, 6)],
[(0, 3), (6, 1)]]
g = NormalFormGame(bimatrix)
lemke_howson(g, 1.0)
def test_lemke_howson_invalid_g():
bimatrix = [[(3, 3), (3, 2)],
[(2, 2), (5, 6)],
[(0, 3), (6, 1)]]
lemke_howson(bimatrix)
def test_lemke_howson_invalid_init_pivot_float():
bimatrix = [[(3, 3), (3, 2)], [(2, 2), (5, 6)], [(0, 3), (6, 1)]]
g = NormalFormGame(bimatrix)
lemke_howson(g, 1.0)
def test_lemke_howson_invalid_g():
bimatrix = [[(3, 3), (3, 2)], [(2, 2), (5, 6)], [(0, 3), (6, 1)]]
lemke_howson(bimatrix)
