Abstract

We study the complexity of finding the values and optimal strategies of mean payoff games on graphs, a family of perfect information games introduced by Ehrenfeucht and Mycielski and considered by Gurvich, Karzanov and Khachiyan. We describe a pseudo-polynomial time algorithm for the solution of such games, the decision problem for which is in NP " co-NP. Finally, we describe a polynomial reduction from mean payoff games to the simple stochastic games studied by Condon. These games are also known to be in NP " co-NP, but no polynomial or pseudo-polynomial time algorithm is known for them. 1 Introduction Let G = (V; E)be a finite directed graph in which each vertex has at least one edge going out of it. Let w : E ! f\GammaW; : : : ; 0; : : : ; Wg be a function that assigns an integral weight to each edge of G. Ehrenfeucht and Mycielski [EM79] studied the following infinite two-person game played on such a graph. The game starts at a vertex a 0 2 V . The first player chooses an edge e...

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