Enumeration of Nash Equilibria for Two-Player Games

Posted: 21 Mar 2009  

David Avis

McGill University - School of Computer Sciences

Gabriel D. Rosenberg

Davis Polk & Wardwell LLP

Rahul Savani

University of Liverpool

Bernhard von Stengel

London School of Economics & Political Science (LSE) - Department of Mathematics

Date Written: March, 20 2009

Abstract

This paper describes algorithms for finding all Nash equilibria of a two-player game in strategic form. We present two algorithms that extend earlier work. Our presentation is self-contained, and explains the two methods in a unified framework using faces of best-response polyhedra. The first method lrsnash is based on the known vertex enumeration program lrs, for lexicographic reverse search. It enumerates the vertices of only one best-response polytope, and the vertices of the complementary faces that correspond to these vertices (if they are not empty) in the other polytope. The second method is a modification of the known EEE algorithm, for enumeration of extreme equilibria. We also describe a second, as yet not implemented, variant that is space efficient. We discuss details of implementations of lrsnash and EEE, and report on computational experiments that compare the two algorithms, which show that both have their strengths and weaknesses.

Suggested Citation

Avis, David and Rosenberg, Gabriel D. and Savani, Rahul and von Stengel, Bernhard, Enumeration of Nash Equilibria for Two-Player Games (March, 20 2009). Economic Theory, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1365927

David Avis

McGill University - School of Computer Sciences ( email )

3480 University
Montreal, Quebec
Canada

Gabriel D. Rosenberg

Davis Polk & Wardwell LLP ( email )

450 Lexington Ave.
New York, NY 10017
United States

Rahul Savani

University of Liverpool ( email )

Department of Computer Science
Ashton Building
Liverpool, L69 3BX
United Kingdom

HOME PAGE: http://www.csc.liv.ac.uk/~rahul

Bernhard Von Stengel (Contact Author)

London School of Economics & Political Science (LSE) - Department of Mathematics ( email )

Houghton Street
GB-London WC2A 2AE
United Kingdom
+44-20-7955 6438 (Phone)
+44-20-7955 6877 (Fax)

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