def test_qre_exploitability_of_nash(self, payoff_tensor, nash,
temperature):
# assumes symmetric games
exp = exploitability.qre_exploitability(nash, payoff_tensor,
temperature)
self.assertGreaterEqual(
1e-10, exp, 'uniform nash should have zero exploitability')
def test_qre_exploitability_of_non_nash(self, payoff_tensor, temperature,
dist, exp):
# assumes symmetric games
exp_pred = exploitability.qre_exploitability(dist, payoff_tensor,
temperature)
self.assertAlmostEqual(exp_pred,
exp,
msg='dist should have the given exploitability')
def exploitability(self, params, payoff_matrices):
"""Compute and return shannon entropy regularized exploitability.
Args:
params: tuple of params (dist, y), see qre.gradients
payoff_matrices: (>=2 x A x A) np.array, payoffs for each joint action
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.shape[-1]
dists = random.rand(trials, num_strategies)
dists /= np.sum(dists, axis=1, keepdims=True)
exploitable = []
for dist in dists:
exp = exploitability.qre_exploitability(dist, payoff_tensor,
temperature)
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')