Abstract
In this paper, we study a discounted noncooperative stochastic game with an abstract measurable state space, compact metric action spaces of players, and additive transition and reward structure in the sense of Himmelberget al. (Ref. 1) and Parthasarathy (Ref. 2). We also assume that the transition law of the game is absolutely continuous with respect to some probability distributionp of the initial state and together with the reward functions of players satisfies certain continuity conditions. We prove that such a game has an equilibrium stationary point, which extends a result of Parthasarathy from Ref. 2, where the action spaces of players are assumed to be finite sets. Moreover, we show that our game has a nonrandomized (ε-\(\bar p\))-equilibrium stationary point for each ε>0, provided that the probability distributionp is nonatomic. The latter result is a new existence theorem.
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Communicated by Y. C. Ho
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Nowak, A.S. Nonrandomized strategy equilibria in noncooperative stochastic games with additive transition and reward structure. J Optim Theory Appl 52, 429–441 (1987). https://doi.org/10.1007/BF00938215
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DOI: https://doi.org/10.1007/BF00938215