mclennan_tourky¶

Author: Daisuke Oyama

Compute mixed Nash equilibria of an N-player normal form game by applying the imitation game algorithm by McLennan and Tourky to the best response correspondence.

quantecon.game_theory.mclennan_tourky.mclennan_tourky(g, init=None, epsilon=0.001, max_iter=200, full_output=False)[source]¶

Find one mixed-action epsilon-Nash equilibrium of an N-player normal form game by the fixed point computation algorithm by McLennan and Tourky [R4].

Parameters:

g : NormalFormGame

NormalFormGame instance.

init : array_like(int or array_like(float, ndim=1)),

optional(default=None)

Initial action profile, an array of N objects, where each object must be an iteger (pure action) or an array of floats (mixed action). If None, default to an array of zeros (the zero-th action for each player).

epsilon : scalar(float), optional(default=1e-3)

Value of epsilon-optimality.

max_iter : scalar(int), optional(default=100)

Maximum number of iterations.

full_output : bool, optional(default=False)

If False, only the computed Nash equilibrium is returned. If True, the return value is (NE, res), where NE is the Nash equilibrium and res is a NashResult object.

Returns:

NE : tuple(ndarray(float, ndim=1))

Tuple of computed Nash equilibrium mixed actions.

res : NashResult

Object containing information about the computation. Returned only when full_output is True. See NashResult for details.

‘)

[ 0.70710754 0.29289246] [ 0.70710754 0.29289246] [ 0.70710754 0.29289246] >>> g.is_nash(NE, tol=epsilon) True

Additional information is returned if full_output is set True:

>>> NE, res = mclennan_tourky(g, epsilon=epsilon, full_output=True)
>>> res.converged
True
>>> res.num_iter
18