Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2003-14

August 2003

Long Lemke-Howson Paths

Rahul Savani and Bernhard von Stengel


The Lemke-Howson algorithm is the classical algorithm for finding one equilibrium of a bimatrix game. In this paper we present a class of square bimatrix games for which the length of the shortest Lemke-Howson path grows exponentially in the dimension d of the game. We construct the games using pairs of dual cyclic polytopes with 2d facets in dspace.

This paper is obsolete and the improved version Exponentially Many Steps for Finding a Nash Equilibrium in a Bimatrix Game should be considered instead.

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