lrsnash¶

lrsnash(g)[source]¶

Compute in exact arithmetic all extreme mixed-action Nash equilibria of a 2-player normal form game with integer payoffs. This function calls the Nash equilibrium computation routine in lrslib (through its Julia wrapper LRSLib.jl) which is based on the “lexicographic reverse search” vertex enumeration algorithm [1].

Parameters¶

gNormalFormGame: 2-player NormalFormGame instance with integer payoffs.

Returns¶

NEslist(tuple(ndarray(object, ndim=1))): List containing tuples of Nash equilibrium mixed actions, where the values are represented by fractions.Fraction.

Examples¶

A degenerate game example:

>>> import quantecon.game_theory as gt
>>> import jlgametheory as jgt
>>> from pprint import pprint
>>> bimatrix = [[(3, 3), (3, 3)],
...             [(2, 2), (5, 6)],
...             [(0, 3), (6, 1)]]
>>> g = gt.NormalFormGame(bimatrix)
>>> NEs = jgt.lrsnash(g)
>>> pprint(NEs)
[(array([Fraction(1, 1), Fraction(0, 1), Fraction(0, 1)], dtype=object),
  array([Fraction(1, 1), Fraction(0, 1)], dtype=object)),
 (array([Fraction(1, 1), Fraction(0, 1), Fraction(0, 1)], dtype=object),
  array([Fraction(2, 3), Fraction(1, 3)], dtype=object)),
 (array([Fraction(0, 1), Fraction(1, 3), Fraction(2, 3)], dtype=object),
  array([Fraction(1, 3), Fraction(2, 3)], dtype=object))]

The set of Nash equilibria of this degenerate game consists of an isolated equilibrium, the third output, and a non-singleton equilibrium component, the extreme points of which are given by the first two outputs.

References¶