def test_qre_exploitability_of_non_nash(self, payoff_tensor, temperature,
dist, exp):
no_op = lambda x: x
exp_pred = exploitability.qre_exploitability(dist, payoff_tensor,
temperature, no_op)
close = np.allclose(exp_pred, exp)
msg = 'exploitability mismatch: pred={}, true={}'.format(exp_pred, exp)
self.assertTrue(close, msg=msg)
def exploitability(self, params, payoff_matrices):
"""Compute and return tsallis entropy regularized exploitability.
Args:
params: tuple of params (dist, y), see ate.gradients
payoff_matrices: dictionary with keys as tuples of agents (i, j) and
values of (2 x A x A) np.arrays, payoffs for each joint action. keys
are sorted and arrays should be indexed in the same order
Returns:
float, exploitability of current dist
"""
return exp.qre_exploitability(params, payoff_matrices, self.temperature)
def test_qre_exploitability_of_rand(self,
payoff_tensor,
temperature,
seed=None):
trials = 100
random = np.random.RandomState(seed)
num_strategies = payoff_tensor[0].shape
total_num_strategies = sum(num_strategies)
pseudo_dists = random.rand(trials, total_num_strategies)
exploitable = []
for pseudo_dist in pseudo_dists:
# first split and normalize pseudo_dist into strat for each player
pseudo_dist_i = np.split(pseudo_dist,
np.cumsum(num_strategies)[:-1])
dist = [pdi / pdi.sum() for pdi in pseudo_dist_i]
exp = exploitability.qre_exploitability(dist, payoff_tensor,
temperature, np.max)
exploitable.append(exp > 0.)
perc = 100 * np.mean(exploitable)
logging.info('rand strat exploitable rate out of %d is %f', trials,
perc)
self.assertEqual(perc, 100., 'found rand strat that was nash')
def test_qre_exploitability_of_nash(self, payoff_tensor, nash,
temperature):
exp = exploitability.qre_exploitability(nash, payoff_tensor,
temperature, np.max)
self.assertGreaterEqual(
1e-10, exp, 'uniform nash should have zero exploitability')