Cookies?
Library Header Image
LSE Research Online LSE Library Services

Fast algorithms for rank-1 Bimatrix games

Adsul, Bharat, Garg, Jugal, Mehta, Ruta, Sohoni, Milind and Von Stengel, Bernhard (2019) Fast algorithms for rank-1 Bimatrix games. Operations Research. ISSN 0030-364X (In Press)

[img] Text (Fast algorithms for rank 1 bimatrix games) - Accepted Version
Pending embargo until 1 January 2100.

Download (685kB) | Request a copy

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: 28 Jan 2020 00:16
URI: http://eprints.lse.ac.uk/id/eprint/102978

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics