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Another Set of Optimality Conditions for Zero-Sum Stochastic Games with Sample-Path Average Payoffs

Jie Yang

Abstract


This paper deals with noncooperative, discrete-time, two-person zero-sum stochastic games with the long-run sample-path average payoff (SPAP) criterion in Borel spaces. The payoff function may have neither upper nor lower bounds. We propose new conditions for the existence of a pair of SPAP optimal stationary strategies. Our conditions are slightly weaker than those in the previous literature. Moreover, some sufficient conditions for the verifications of our hypotheses are imposed on the primitive data of the model. Also, under our conditions, we also ensure the existence of a pair of SPAP optimal stationary strategies by a so-called two-optimality inequality approach. Finally, we use controlled population processes to illustrate applications of the main results in this paper.

Keywords


Zero-sum stochastic games, Borel spaces, sample-path average payoff, optimal stationary strategies, new conditions.

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