The Complexity of Mean Payoff Games on Graphs

We study the complexity of nding the values and optimal strategies of mean payoo 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 payoo 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.