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Stochastic games with non-absorbing states. (English) Zbl 1050.91013

The author considers stochastic two-person non-zero-sum games with finite state space, finite action spaces and the average-per-unit-of-time problem position. The main result is: Every such a stochastic game with at most two non-absorbing states admits an equilibrium payoff. The author proves this result for positive recursive games with the absorbing property of N. Vieille [Isr. J. Math. 119, 55–91 (2000; Zbl 0974.91005)] and two non-absorbing states. The proof is troublesome. O. J. Vrieze and F. Thuijsman [Int. J. Game Theory 18, No. 3, 293–310 (1989; Zbl 0678.90107)] solved the problem for one non-absorbing state. Finally, a counterexample with four non-absorbing states is given where the author’s approach fails to succeed.

MSC:

91A15 Stochastic games, stochastic differential games
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References:

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