Constrained Expected Average Stochastic Games for Continuous-Time Jump Processes
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In this paper we study the nonzero-sum constrained stochastic games for continuous-time jump processes with denumerable states and possibly unbounded transition rates. The optimality criterion under consideration is the expected average payoff criterion and the payoff functions of the players are allowed to be unbounded. Under the reasonable conditions, we introduce an approximating sequence of the auxiliary game models and show the existence of stationary constrained Nash equilibria for these approximating game models via employing the average occupation measures and constructing a suitable multifunction. Moreover, we obtain that any limit point of the stationary constrained Nash equilibria for the approximating sequence of the game models is a constrained Nash equilibrium for the original game model. Furthermore, we use a controlled birth and death system to illustrate our main results.
KeywordsNonzero-sum games Expected average payoff criterion Constrained Nash equilibrium Continuous-time jump process
Mathematics Subject Classification91A15 91A25
I am greatly indebted to the referees for the valuable comments and suggestions which have greatly improved the presentation. The research was supported by National Natural Science Foundation of China (Grant No. 11601166).
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Conflict of interest
I declare that no conflict of interest exists in this paper.