def get_projected_replicator_dynamics_pi(payoff_table):
# matrix must be symmetric
assert len(np.shape(payoff_table)) == 2
assert np.shape(payoff_table)[0] == np.shape(payoff_table)[1]
payoff_tables = [payoff_table, payoff_table.T]
# payoff_tables = [heuristic_payoff_table.from_matrix_game(payoff_tables[0]),
# heuristic_payoff_table.from_matrix_game(payoff_tables[1].T)]
# Check if the game is symmetric (i.e., players have identical strategy sets
# and payoff tables) and return only a single-player’s payoff table if so.
# This ensures Alpha-Rank automatically computes rankings based on the
# single-population dynamics.
is_symmetric, _ = utils.is_symmetric_matrix_game(payoff_tables)
assert is_symmetric
assert len(payoff_tables) == 2
pi = projected_replicator_dynamics(payoff_tensors=payoff_tables,
prd_initial_strategies=None,
prd_iterations=int(1e6),
prd_dt=1e-3,
prd_gamma=0.0,
average_over_last_n_strategies=None)
return pi
def _prd(meta_game, per_player_repeats, ignore_repeats=False):
"""Projected replicator dynamics."""
if not ignore_repeats:
meta_game = _expand_meta_game(meta_game, per_player_repeats)
meta_dist = projected_replicator_dynamics.projected_replicator_dynamics(
meta_game)
labels = string.ascii_lowercase[:len(meta_dist)]
comma_labels = ",".join(labels)
meta_dist = np.einsum("{}->{}".format(comma_labels, labels), *meta_dist)
meta_dist[meta_dist < DIST_TOL] = 0.0
meta_dist /= np.sum(meta_dist)
meta_dist = _unexpand_meta_dist(meta_dist, per_player_repeats)
return meta_dist, dict()
def prd_strategy(solver, return_joint=False, checkpoint_dir=None):
"""Computes Projected Replicator Dynamics strategies. Args: solver: GenPSROSolver instance. return_joint: If true, only returns marginals. Otherwise marginals as well as joint probabilities. Returns: PRD-computed strategies.
"""
meta_games = solver.get_meta_game()
if not isinstance(meta_games, list):
meta_games = [meta_games, -meta_games]
kwargs = solver.get_kwargs()
result = projected_replicator_dynamics.projected_replicator_dynamics(
meta_games, **kwargs)
if not return_joint:
return result
else:
joint_strategies = get_joint_strategy_from_marginals(result)
return result, joint_strategies
def prd_strategy(solver):
"""Computes Projected Replicator Dynamics strategies.
Args:
solver: GenPSROSolver instance.
Returns:
PRD-computed strategies.
"""
meta_games = solver.get_meta_game
if not isinstance(meta_games, list):
meta_games = [meta_games, -meta_games]
kwargs = solver.get_kwargs
return projected_replicator_dynamics.projected_replicator_dynamics(
meta_games, **kwargs)
def test_three_players(self):
test_a = np.array([[[2, 1, 0], [1, 0, -1]], [[1, 0, -1], [0, -1, -2]]])
test_b = np.array([[[2, 1, 0], [1, 0, -1]], [[1, 0, -1], [0, -1, -2]]])
test_c = np.array([[[2, 1, 0], [1, 0, -1]], [[1, 0, -1], [0, -1, -2]]])
strategies = projected_replicator_dynamics.projected_replicator_dynamics(
[test_a, test_b, test_c],
prd_initial_strategies=None,
prd_iterations=50000,
prd_dt=1e-3,
prd_gamma=1e-6,
average_over_last_n_strategies=10)
self.assertLen(strategies, 3, "Wrong strategy length.")
self.assertGreater(
strategies[0][0], 0.999,
"Projected Replicator Dynamics failed in trivial case.")
