Utilities

Helper functions.

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Initial states

popgames.utilities.sample_initial_states(population_game, num, seed=None)[source]

Sample strategic distributions uniformly at random, e.g., as initial states of Simulator.run_ensemble.

The strategic distribution of each population is sampled uniformly on its simplex (scaled by the mass of the population), independently of the other populations.

Parameters:

  • population_game (PopulationGame) – The population game.

  • num (int) – The number of strategic distributions.

  • seed (Union[int, np.random.Generator], optional) – Seed or random number generator. Defaults to None, in which case NumPy’s global random state is used (see np.random.seed).

Returns:

The strategic distributions, of shape (num, n, 1).

Return type:

np.ndarray

Examples

>>> import numpy as np
>>> import popgames as pg
>>> from popgames.utilities import sample_initial_states
>>> game = pg.SinglePopulationGame(num_strategies=3, fitness_function=lambda x: -x)
>>> x0s = sample_initial_states(game, num=5, seed=0)
>>> x0s.shape
(5, 3, 1)
>>> bool(np.allclose(x0s.sum(axis=1), 1.0))
True