Том 69
№ 9

All Issues

Markov Games with Several Ergodic Classes

Ibragimov G. I.

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We consider Markov games of the general form characterized by the property that, for all stationary strategies of players, the set of game states is partitioned into several ergodic sets and a transient set, which may vary depending on the strategies of players. As a criterion, we choose the mean payoff of the first player per unit time. It is proved that the general Markov game with a finite set of states and decisions of both players has a value, and both players have ε-optimal stationary strategies. The correctness of this statement is demonstrated on the well-known Blackwell's example (“Big Match”).

English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 6, pp 921-941.

Citation Example: Ibragimov G. I. Markov Games with Several Ergodic Classes // Ukr. Mat. Zh. - 2003. - 55, № 6. - pp. 762-778.

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