An experimental analysis of Lemke-Howson algorithm

We present an experimental investigation of the performance of the Lemke-Howson algorithm, which is the most widely used algorithm for the computation of a Nash equilibrium for bimatrix games. Lemke-Howson algorithm is based upon a simple pivoting strategy, which corresponds to following a path whose endpoint is a Nash equilibrium. We analyze both the basic Lemke-Howson algorithm and a heuristic modification of it, which we designed to cope with the effects of a `bad' initial choice of the pivot. Our experimental findings show that, on uniformly random games, the heuristics achieves a linear running time, while the basic Lemke-Howson algorithm runs in time roughly proportional to a polynomial of degree seven. To conduct the experiments, we have developed our own implementation of LemkeHowson algorithm, which turns out to be significantly faster than state-of-the-art software. This allowed us to run the algorithm on a much larger set of data, and on instances of much larger size, ...

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Bruno Codenotti, Stefano De Rossi, Marino Pagan
• Keywords: Basic Lemke-howson Algorithm, CORR 2008, Education, Lemke-Howson Algorithm, Nash Equilibrium