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Nonzero-sum Stochastic Games

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  • Nowak, Andrzej S.
  • Szajowski, Krzysztof

Abstract

This paper treats of stochastic games. We focus on nonzero-sum games and provide a detailed survey of selected recent results. In Section 1, we consider stochastic Markov games. A correlation of strategies of the players, involving ``public signals'', is described, and a correlated equilibrium theorem proved recently by Nowak and Raghavan for discounted stochastic games with general state space is presented. We also report an extension of this result to a class of undiscounted stochastic games, satisfying some uniform ergodicity condition. Stopping games are related to stochastic Markov games. In Section 2, we describe a version of Dynkin's game related to observation of a Markov process with random assignment mechanism of states to the players. Some recent contributions of the second author in this area are reported. The paper also contains a brief overview of the theory of nonzero-sum stochastic games and stopping games which is very far from being complete.

Suggested Citation

  • Nowak, Andrzej S. & Szajowski, Krzysztof, 1998. "Nonzero-sum Stochastic Games," MPRA Paper 19995, University Library of Munich, Germany, revised 1999.
    • Handle: RePEc:pra:mprapa:19995
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    References listed on IDEAS

    as
    1. Mertens, J.-F. & Parthasarathy, T., 1987. "Equilibria for discounted stochastic games," LIDAM Discussion Papers CORE 1987050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Nowak Andrzej S., 1994. "Zero-Sum Average Payoff Stochastic Games with General State Space," Games and Economic Behavior, Elsevier, vol. 7(2), pages 221-232, September.
    3. Forges, Francoise M, 1986. "An Approach to Communication Equilibria," Econometrica, Econometric Society, vol. 54(6), pages 1375-1385, November.
    4. Parthasarathy, T & Sinha, S, 1989. "Existence of Stationary Equilibrium Strategies in Non-zero Sum Discounted Stochastic Games with Uncountable State Space and State-Independent Transitions," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 189-194.
    5. Manfred Schäl, 1993. "Average Optimality in Dynamic Programming with General State Space," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 163-172, February.
    6. Masami Kurano, 1986. "Markov Decision Processes with a Borel Measurable Cost Function---The Average Case," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 309-320, May.
    7. Dutta, P.K., 1991. "What Do Discounted Optima Converge To? A Theory of Discount Rate Asymptotics in Economic Models," RCER Working Papers 264, University of Rochester - Center for Economic Research (RCER).
    8. Christopher Harris, 1991. "The Existence of Subgame-Perfect Equilibrium in Games with Simultaneous Moves," Working papers 570, Massachusetts Institute of Technology (MIT), Department of Economics.
    9. Vrieze, O J & Thuijsman, F, 1989. "On Equilibria in Repeated Games with Absorbing States," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 293-310.
    10. Ioannis Karatzas & Martin Shubik & William D. Sudderth, 1992. "Construction of Stationary Markov Equilibria in a Strategic Market Game," Cowles Foundation Discussion Papers 1033, Cowles Foundation for Research in Economics, Yale University.
    11. Dutta, Prajit K., 1991. "What do discounted optima converge to?: A theory of discount rate asymptotics in economic models," Journal of Economic Theory, Elsevier, vol. 55(1), pages 64-94, October.
    12. Yoshio Ohtsubo, 1987. "A Nonzero-Sum Extension of Dynkin's Stopping Problem," Mathematics of Operations Research, INFORMS, vol. 12(2), pages 277-296, May.
    13. Yasuda, M., 1985. "On a randomized strategy in Neveu's stopping problem," Stochastic Processes and their Applications, Elsevier, vol. 21(1), pages 159-166, December.
    14. 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.
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    More about this item

    Keywords

    average payoff stochastic games; correlated stationary equilibria; nonzero-sum games; stopping time; stopping games;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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