Optimal Values of Multidimensional Mean-Payoff Games
Résumé
We study multidimensional mean-payoff games. More precisely, we want to compute all the values that can be ensured by the first player. Because weights are given in multiple dimensions, there can be incomparable such values, and even an infinite number of incomparable ones. We show that the set the values can be represented by a finite union of convex sets. From the computational point of view, we show that deciding if the intersection of the set of values with points satisfying a set of linear inequations can be done in Sigma2P. The problem is both NP-hard and coNP-hard.
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