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Continuous stochastic games: Value and optimal strategies. (Spanish. English summary) Zbl 0762.90097

Summary: The aim of this paper is to analyse stochastic games with state and action spaces which are metric and compact and with suitable continuity conditions about the payoff and transition functions. After the description of the model and the introduction of the continuity assumptions, the finite horizon problem is analyzed, in order to prove that a value exists and both players have optimal strategies, that can be recursively determined. The discounted infinite horizon case is also considered. The final result in this case was obtained A. Maitra and T. Parthasarathy [J. Optimization Theory Appl. 5, No. 4, 289- 300 (1970; Zbl 0181.232); and ibid. 8, No. 1, 154-160 (1971; Zbl 0206.492)] with a considerably more cumbersome proof. The simplification is based in the introduction of a terminal payoff, that can be suitably choosed in order to get the desired conclusions.

MSC:

91A15 Stochastic games, stochastic differential games
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References:

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