Long Lemke-Howson Paths

The Lemke-Howson algorithm is the classical algorithm for find- ing 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 d-space.

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