Finding Nash Equilibria of Two-Player Games
Abstract
This paper is an exposition of algorithms for finding one or all equilibria of a bimatrix game (a two-player game in strategic form) in the style of a chapter in a graduate textbook. Using labeled "best-response polytopes", we present the Lemke-Howson algorithm that finds one equilibrium. We show that the path followed by this algorithm has a direction, and that the endpoints of the path have opposite index, in a canonical way using determinants. For reference, we prove that a number of notions of nondegeneracy of a bimatrix game are equivalent. The computation of all equilibria of a general bimatrix game, via a description of the maximal Nash subsets of the game, is canonically described using "complementary pairs" of faces of the best-response polytopes.
Keywords
Cite
@article{arxiv.2102.04580,
title = {Finding Nash Equilibria of Two-Player Games},
author = {Bernhard von Stengel},
journal= {arXiv preprint arXiv:2102.04580},
year = {2021}
}