New maximal numbers of equilibria in bimatrix games

32Citations
Citations of this article
4Readers
Mendeley users who have this article in their library.

This article is free to access.

Abstract

This paper presents a new lower bound of 2.414d/√d on the maximal number of Nash equilibria in d × d bimatrix games, a central concept in game theory. The proof uses an equivalent formulation of the problem in terms of pairs of polytopes with 2d facets in d-space. It refutes a recent conjecture that 2d - 1 is an upper bound, which was proved for d ≤ 4. The first counterexample is a 6 × 6 game with 75 equilibria. The case d = 5 remains open. The result carries the lower bound closer to the previously known upper bound of 2.6d/√d.

Cite

CITATION STYLE

APA

Von Stengel, B. (1999). New maximal numbers of equilibria in bimatrix games. Discrete and Computational Geometry, 21(4), 557–568. https://doi.org/10.1007/PL00009438

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free