Fast algorithms for rank-1 bimatrix games

Adsul, Bharat, Garg, Jugal, Mehta, Ruta, Sohoni, Milind and Von Stengel, Bernhard ORCID: 0000-0002-3488-8322 (2020) Fast algorithms for rank-1 bimatrix games. Operations Research. 0-0. ISSN 0030-364X

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Abstract

The rank of a bimatrix game is the matrix rank of the sum of the two payoff matrices. This paper comprehensively analyzes games of rank one, and shows the following: (1) For a game of rank r, the set of its Nash equilibria is the intersection of a generically one-dimensional set of equilibria of parameterized games of rank r − 1 with a hyperplane. (2) One equilibrium of a rank-1 game can be found in polynomial time. (3) All equilibria of a rank-1 game can be found by following a piecewise linear path. In contrast, such a path-following method finds only one equilibrium of a bimatrix game. (4) The number of equilibria of a rank-1 game may be exponential. (5) There is a homeomorphism between the space of bimatrix games and their equilibrium correspondence that preserves rank. It is a variation of the homeomorphism used for the concept of strategic stability of an equilibrium component.

Item Type:	Article
Official URL:	https://pubsonline.informs.org/journal/opre
Additional Information:	© 2020 INFORMS
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	02 Jan 2020 11:24
Last Modified:	12 Dec 2024 02:01
URI:	http://eprints.lse.ac.uk/id/eprint/102978

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