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Summary: Economic Theory manuscript No.
(will be inserted by the editor)
Enumeration of Nash Equilibria for Two-Player Games
David Avis · Gabriel D. Rosenberg ·
Rahul Savani · Bernhard von Stengel
Received: date / Accepted: date
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 frame-
work using faces of best-response polyhedra. The first method is based on the known
vertex enumeration program lrs, for "lexicographic reverse search". It enumerates the
vertices of only one best-response polytope, which determine a complementary face
in the other polytope. The second method is a modification of the known EEE algo-
rithm, 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
the lrs-based and the EEE algorithm, and report on computational experiments that
compare the two algorithms, which show that both have their strengths and weak-
nesses.
Keywords Bimatrix game · Nash equilibrium · Linear programming · Complemen-
tarity
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