def test_constant_sum_transition_matrix(self):
"""Tests closed-form transition matrix computation for constant-sum case."""
game = pyspiel.load_matrix_game("matrix_rps")
payoff_tables = utils.nfg_to_ndarray(game)
# Checks if the game is symmetric and runs single-population analysis if so
_, payoff_tables = utils.is_symmetric_matrix_game(payoff_tables)
payoffs_are_hpt_format = utils.check_payoffs_are_hpt(payoff_tables)
m = 20
alpha = 0.1
# Case 1) General-sum game computation (slower)
game_is_constant_sum = False
use_local_selection_model = False
payoff_sum = None
c1, rhos1 = alpharank._get_singlepop_transition_matrix(
payoff_tables[0], payoffs_are_hpt_format, m, alpha,
game_is_constant_sum, use_local_selection_model, payoff_sum)
# Case 2) Constant-sum closed-form computation (faster)
game_is_constant_sum, payoff_sum = utils.check_is_constant_sum(
payoff_tables[0], payoffs_are_hpt_format)
c2, rhos2 = alpharank._get_singlepop_transition_matrix(
payoff_tables[0], payoffs_are_hpt_format, m, alpha,
game_is_constant_sum, use_local_selection_model, payoff_sum)
# Ensure both cases match
np.testing.assert_array_almost_equal(c1, c2)
np.testing.assert_array_almost_equal(rhos1, rhos2)
def test_constant_sum_checker(self):
"""Tests if verification of constant-sum game is correct."""
game = pyspiel.load_matrix_game("matrix_rps")
payoff_tables = utils.nfg_to_ndarray(game)
payoffs_are_hpt_format = utils.check_payoffs_are_hpt(payoff_tables)
game_is_constant_sum, payoff_sum = utils.check_is_constant_sum(
payoff_tables[0], payoffs_are_hpt_format)
self.assertTrue(game_is_constant_sum)
self.assertEqual(payoff_sum, 0.)
def compute(payoff_tables,
m=50,
alpha=100,
use_local_selection_model=True,
verbose=False,
use_inf_alpha=False,
inf_alpha_eps=0.01):
"""Computes the finite population stationary statistics.
Args:
payoff_tables: List of game payoff tables, one for each agent identity. Each
payoff_table may be either a numpy array, or a _PayoffTableInterface
object.
m: Finite population size.
alpha: Fermi distribution temperature parameter.
use_local_selection_model: Enable local evolutionary selection model, which
considers fitness against the current opponent only, rather than the
global population state.
verbose: Set to True to print intermediate results.
use_inf_alpha: Use infinite-alpha alpharank model.
inf_alpha_eps: Noise term to use in infinite-alpha alpharank model.
Returns:
rhos: Matrix of strategy-to-strategy fixation probabilities.
rho_m: Neutral fixation probability.
pi: Finite population stationary distribution.
num_strats: Number of available strategies.
"""
payoffs_are_hpt_format = utils.check_payoffs_are_hpt(payoff_tables)
num_populations = len(payoff_tables)
num_strats_per_population = utils.get_num_strats_per_population(
payoff_tables, payoffs_are_hpt_format)
# Handles the trivial case of Markov chain with one state
if np.array_equal(num_strats_per_population,
np.ones(len(num_strats_per_population))):
rhos = np.asarray([[1]])
rho_m = 1. / m if not use_inf_alpha else 1
num_profiles = 1
pi = np.asarray([1.])
return rhos, rho_m, pi, num_profiles, num_strats_per_population
if verbose:
print('Constructing c matrix')
print('num_strats_per_population:', num_strats_per_population)
if num_populations == 1:
# User fast closed-form analysis for constant-sum single-population games
game_is_constant_sum, payoff_sum = utils.check_is_constant_sum(
payoff_tables[0], payoffs_are_hpt_format)
if verbose:
print('game_is_constant_sum:', game_is_constant_sum,
'payoff sum: ', payoff_sum)
# Single-population/symmetric game just uses the first player's payoffs
c, rhos = _get_singlepop_transition_matrix(payoff_tables[0],
payoffs_are_hpt_format,
m,
alpha,
game_is_constant_sum,
use_local_selection_model,
payoff_sum,
use_inf_alpha=use_inf_alpha,
inf_alpha_eps=inf_alpha_eps)
num_profiles = num_strats_per_population[0]
else:
c, rhos = _get_multipop_transition_matrix(payoff_tables,
payoffs_are_hpt_format,
m,
alpha,
use_inf_alpha=use_inf_alpha,
inf_alpha_eps=inf_alpha_eps)
num_profiles = utils.get_num_profiles(num_strats_per_population)
pi = _get_stationary_distr(c)
rho_m = 1. / m if not use_inf_alpha else 1 # Neutral fixation probability
if verbose:
print_results(payoff_tables, payoffs_are_hpt_format, rhos, rho_m, c,
pi)
return rhos, rho_m, pi, num_profiles, num_strats_per_population
