def get_replicator_dynamics(game_name,
iterations,
learning_rate=0.01,
verbose=False):
game = pyspiel.load_game(game_name)
if not isinstance(game, pyspiel.MatrixGame):
print(
"Game " + game_name +
"is not a matrix game, construction of payoff matrix will take a long time..."
)
payoff_matrix = game_payoffs_array(game)
dyn = dynamics.SinglePopulationDynamics(payoff_matrix, dynamics.replicator)
legal_actions = game.num_distinct_actions()
x = [np.random.rand() for _ in range(legal_actions)]
s = sum(x)
x = [v / s for v in x]
actions = np.zeros((iterations, legal_actions))
for i in range(0, iterations):
x += learning_rate * dyn(x)
actions[i] = x
if verbose:
util.pretty_print_strategies(game, actions)
return actions
def test_rd_rps_pure_fixed_points(self):
game = pyspiel.load_matrix_game('matrix_rps')
payoff_matrix = game_payoffs_array(game)
rd = dynamics.replicator
dyn = dynamics.SinglePopulationDynamics(payoff_matrix, rd)
x = np.eye(3)
np.testing.assert_allclose(dyn(x[0]), np.zeros((3, )))
np.testing.assert_allclose(dyn(x[1]), np.zeros((3, )))
np.testing.assert_allclose(dyn(x[2]), np.zeros((3, )))
def rps_phaseplot_boltzmann(fig):
size = 111
game = pyspiel.load_game("matrix_rps")
payoff_tensor = game_payoffs_array(game)
print(payoff_tensor[0])
dyn = dynamics.SinglePopulationDynamics(payoff_tensor, lenient_boltzmannq)
sub = fig.add_subplot(size, projection="3x3")
sub.quiver(dyn)
sub.set_title("Phaseplot Rock Paper Scissors")
return sub
def matrix_rps_biased_phaseplot(size=None, fig=None):
fig = plt.figure(figsize=(10, 10)) if fig is None else fig
size = 111 if size is None else size
assert isinstance(fig, plt.Figure)
payoff_tensor = np.array([[[0, -1, 2], [1, 0, -1], [-2, 1, 0]],
[[0, 1, -2], [-1, 0, 1], [2, -1, 0]]])
dyn = dynamics.SinglePopulationDynamics(payoff_tensor, dynamics.replicator)
sub = fig.add_subplot(size, projection="3x3")
sub.quiver(dyn)
sub.set_title("Phaseplot Rock Paper Scissors")
return sub, pyspiel.create_matrix_game(payoff_tensor[0], payoff_tensor[1])
def matrix_rps_phaseplot(size=None, fig=None):
fig = plt.figure(figsize=(10, 10)) if fig is None else fig
size = 111 if size is None else size
assert isinstance(fig, plt.Figure)
game = pyspiel.load_game("matrix_rps")
payoff_tensor = game_payoffs_array(game)
dyn = dynamics.SinglePopulationDynamics(payoff_tensor, dynamics.replicator)
sub = fig.add_subplot(size, projection="3x3")
sub.quiver(dyn)
sub.set_title("Phaseplot Rock Paper Scissors")
return sub
def test_dynamics_rps_mixed_fixed_point(self, func):
game = pyspiel.load_matrix_game('matrix_rps')
payoff_matrix = game_payoffs_array(game)
dyn = dynamics.SinglePopulationDynamics(payoff_matrix, func)
x = np.ones(shape=(3, )) / 3.
np.testing.assert_allclose(dyn(x), np.zeros((3, )), atol=1e-15)
def _build_dynamics3x3():
"""Build single-population dynamics."""
game = pyspiel.load_game("matrix_rps")
payoff_tensor = utils.nfg_to_ndarray(game)
return dynamics.SinglePopulationDynamics(payoff_tensor,
dynamics.replicator)
def _build_dynamics3x3_beta():
"""Build single-population dynamics."""
game = pyspiel.load_game("matrix_rps")
payoff_tensor = utils.game_payoffs_array(game)
return dynamics.SinglePopulationDynamics(payoff_tensor,
dynamics_beta.replicator_beta)