We study the complexity of finding the values and optimal strategies of mean payoff games, a family of perfect information games introduced by Ehrenfeucht and Mycielski. We describe a pseudopolynomial 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.
Polynomial Time Algorithm Stochastic Game Positional Strategy Average Vertex Polynomial Reduction
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