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Sensitive equilibria for ergodic stochastic games with countable state spaces

Author

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  • Andrzej S. Nowak

Abstract

We consider stochastic games with countable state spaces and unbounded immediate payoff functions. Our assumptions on the transition structure of the game are based on a recent work by Meyn and Tweedie [19] on computable bounds for geometric convergence rates of Markov chains. The main results in this paper concern the existence of sensitive optimal strategies in some classes of zero-sum stochastic games. By sensitive optimality we mean overtaking or 1-optimality. We also provide a new Nash equilibrium theorem for a class of ergodic nonzero-sum stochastic games with denumerable state spaces. Copyright Springer-Verlag Berlin Heidelberg 1999

Suggested Citation

  • Andrzej S. Nowak, 1999. "Sensitive equilibria for ergodic stochastic games with countable state spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(1), pages 65-76, August.
    • Handle: RePEc:spr:mathme:v:50:y:1999:i:1:p:65-76
    DOI: 10.1007/PL00020927
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    Cited by:

    1. Wenzhao Zhang & Yonghui Huang & Xianping Guo, 2014. "Nonzero-sum constrained discrete-time Markov games: the case of unbounded costs," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 1074-1102, October.
    2. Beatris Escobedo-Trujillo & Daniel López-Barrientos & Onésimo Hernández-Lerma, 2012. "Bias and Overtaking Equilibria for Zero-Sum Stochastic Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 662-687, June.
    3. Vassili Kolokoltsov & Wei Yang, 2012. "Turnpike Theorems for Markov Games," Dynamic Games and Applications, Springer, vol. 2(3), pages 294-312, September.
    4. Andrzej Nowak, 2006. "Remarks on sensitive equilibria in stochastic games with additive reward and transition structure," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 481-494, December.

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