Enumeration of Nash Equilibria for Two-Player Games
McGill University - School of Computer Sciences
Gabriel D. Rosenberg
Davis Polk & Wardwell LLP
University of Liverpool
Bernhard von Stengel
London School of Economics & Political Science (LSE) - Department of Mathematics
March, 20 2009
Economic Theory, Forthcoming
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.
Date posted: March 21, 2009
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