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Remarks on sensitive equilibria in stochastic games with additive reward and transition structure

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  • Andrzej Nowak

Abstract

A class of stochastic games with additive reward and transition structure is studied. For zero-sum games under some ergodicity assumptions 1-equilibria are shown to exist. They correspond to so-called sensitive optimal policies in dynamic programming. For a class of nonzero-sum stochastic games with nonatomic transitions nonrandomized Nash equilibrium points with respect to the average payoff criterion are also obtained. Included examples show that the results of this paper can not be extented to more general payoff or transition structure. Copyright Springer-Verlag 2006

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  • 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.
    • Handle: RePEc:spr:mathme:v:64:y:2006:i:3:p:481-494
    DOI: 10.1007/s00186-006-0090-4
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    References listed on IDEAS

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    1. Andrzej S. Nowak & Anna Jaśkiewicz, 2005. "Nonzero-sum semi-Markov games with the expected average payoffs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(1), pages 23-40, September.
    2. 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.
    3. Andrzej S. Nowak, 1999. "Optimal strategies in a class of zero-sum ergodic stochastic games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(3), pages 399-419, December.
    4. repec:ebl:ecbull:v:17:y:2006:i:2:p:1-10 is not listed on IDEAS
    5. Raghavan, T.E.S. & Tijs, S.H. & Vrieze, O.J., 1985. "On stochastic games with additive reward and transition structure," Other publications TiSEM 28f85a14-9a6e-4ed8-9a4b-a, Tilburg University, School of Economics and Management.
    6. A. S. Nowak & T. E. S. Raghavan, 1992. "Existence of Stationary Correlated Equilibria with Symmetric Information for Discounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 519-526, August.
    7. Andrzej Nowak, 2006. "A note on an equilibrium in the great fish war game," Economics Bulletin, AccessEcon, vol. 17(2), pages 1-10.
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    Cited by:

    1. Wenzhao Zhang, 2019. "Discrete-Time Constrained Average Stochastic Games with Independent State Processes," Mathematics, MDPI, vol. 7(11), pages 1-18, November.
    2. Anna Jaśkiewicz & Andrzej Nowak, 2015. "On pure stationary almost Markov Nash equilibria in nonzero-sum ARAT stochastic games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(2), pages 169-179, April.

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