pygambit.nash.enumpoly_solve#

pygambit.nash.enumpoly_solve(game: Game, use_strategic: bool = False, stop_after: int | None = None, maxregret: float = 0.0001, phcpack_path: Path | str | None = None) → NashComputationResult#

Compute Nash equilibria by enumerating all support profiles of strategies or actions, and for each support finding all totally-mixed equilibria of the game over that support.

Parameters:

  • game (Game) – The game to compute equilibria in.

  • use_strategic (bool, default False) – Whether to use the strategic form. If True, always uses the strategic representation even if the game’s native representation is extensive.

  • stop_after (int, optional) – Maximum number of equilibria to compute. If not specified, examines all support profiles of the game.

  • maxregret (float, default 1e-4) – The acceptance criterion for approximate Nash equilibrium; the maximum regret of any player must be no more than maxregret times the difference of the maximum and minimum payoffs of the game

  • phcpack_path (str or pathlib.Path, optional) – If specified, use PHCpack to solve the systems of equations. This argument specifies the path to the PHCpack executable. With this method, only enumeration on the strategic game is supported.

Returns:

res – The result represented as a NashComputationResult object.

Return type:

NashComputationResult

Notes

PHCpack is available at https://homepages.math.uic.edu/~jan/PHCpack/phcpack.html

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