Source code for quantecon.game_theory.pure_nash
"""
Methods for computing pure Nash equilibria of a normal form game.
(For now, only brute force method is supported)
"""
import numpy as np
[docs]def pure_nash_brute(g, tol=None):
"""
Find all pure Nash equilibria of a normal form game by brute force.
Parameters
----------
g : NormalFormGame
tol : scalar(float), optional(default=None)
Tolerance level used in determining best responses. If None,
default to the value of the `tol` attribute of `g`.
Returns
-------
NEs : list(tuple(int))
List of tuples of Nash equilibrium pure actions.
If no pure Nash equilibrium is found, return empty list.
Examples
--------
Consider the "Prisoners' Dilemma" game:
>>> PD_bimatrix = [[(1, 1), (-2, 3)],
... [(3, -2), (0, 0)]]
>>> g_PD = NormalFormGame(PD_bimatrix)
>>> pure_nash_brute(g_PD)
[(1, 1)]
If we consider the "Matching Pennies" game, which has no pure nash
equilibrium:
>>> MP_bimatrix = [[(1, -1), (-1, 1)],
... [(-1, 1), (1, -1)]]
>>> g_MP = NormalFormGame(MP_bimatrix)
>>> pure_nash_brute(g_MP)
[]
"""
return list(pure_nash_brute_gen(g, tol=tol))
[docs]def pure_nash_brute_gen(g, tol=None):
"""
Generator version of `pure_nash_brute`.
Parameters
----------
g : NormalFormGame
tol : scalar(float), optional(default=None)
Tolerance level used in determining best responses. If None,
default to the value of the `tol` attribute of `g`.
Yields
------
out : tuple(int)
Tuple of Nash equilibrium pure actions.
"""
for a in np.ndindex(*g.nums_actions):
if g.is_nash(a, tol=tol):
yield a