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Nonzero-sum games for continuous-time Markov chains with unbounded transition and average payoff rates

Science China Mathematics 2012年第11期55卷 2405-2416页

作者： ZHANG WenZhao GUO XianPing School of Mathematics and Computational Science Sun Yat-Sen UniversityGuangzhou 510275China

This paper attempts to study two-person nonzero-sum games for denumerable continuous-time Markov chains determined by transition rates,with an expected average *** transition rates are allowed to be unbounded,and the payoff functions may be unbounded from above and from *** give suitable conditions under which the existence of a Nash equilibrium is *** precisely,using the socalled "vanishing discount" approach,a Nash equilibrium for the average criterion is obtained as a limit point of a sequence of equilibrium strategies for the discounted criterion as the discount factors tend to *** results are illustrated with a birth-and-death game.

关键词： nonzero-sum game expected average criterion Nash equilibrium unbounded transition rates unbounded payoff function

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New optimality conditions for average-payoff continuous-time Markov games in Polish spaces

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Science China Mathematics 2011年第4期54卷 793-816页

作者： GUO XianPing HERNNDEZ-LERMA Onsimo The School of Mathematics and Computational Science Zhongshan UniversityGuangzhou 510275China Department of Mathematics CINVESTAV-IPN A.Postal 14-740Mxico D.F.07000Mxico

This paper concerns two-person zero-sum games for a class of average-payoff continuous-time Markov processes in Polish *** underlying processes are determined by transition rates that are allowed to be unbounded,and the payoff function may have neither upper nor lower *** use two optimality inequalities to replace the so-called optimality equation in the previous *** more general conditions,these optimality inequalities yield the existence of the value of the game and of a pair of optimal stationary *** some additional conditions we further establish the optimality equation ***,we use several examples to illustrate our results,and also to show the difference between the conditions in this paper and those in the *** particular,one of these examples shows that our approach is more general than all of the existing ones because it allows nonergodic Markov processes.

关键词： zero-sum stochastic Markov games average payoffs optimality inequalities unbounded transition rates

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