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Stationary Markov Perfect Equilibria in Discounted Stochastic Games

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  • He, Wei
  • Sun, Yeneng

Abstract

The existence of stationary Markov perfect equilibria in stochastic games is shown in several contexts under a general condition called "coarser transition kernels". These results include various earlier existence results on correlated equilibria, noisy stochastic games, stochastic games with mixtures of constant transition kernels as special cases. The minimality of the condition is illustrated. The results here also shed some new light on a recent example on the nonexistence of stationary equilibrium. The proofs are remarkably simple via establishing a new connection between stochastic games and conditional expectations of correspondences.

Suggested Citation

  • He, Wei & Sun, Yeneng, 2013. "Stationary Markov Perfect Equilibria in Discounted Stochastic Games," MPRA Paper 51274, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:51274
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    File URL: https://mpra.ub.uni-muenchen.de/51274/1/MPRA_paper_51274.pdf
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    References listed on IDEAS

    as
    1. Yehuda (John) Levy, 2012. "A Discounted Stochastic Game with No Stationary Nash Equilibrium," Discussion Paper Series dp596r, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem, revised May 2012.
    2. 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.
    3. John Duggan, 2012. "Noisy Stochastic Games," Econometrica, Econometric Society, vol. 80(5), pages 2017-2045, September.
    4. John Duggan, 2012. "Noisy Stochastic Games," RCER Working Papers 570, University of Rochester - Center for Economic Research (RCER).
    5. Yehuda Levy, 2013. "Discounted Stochastic Games With No Stationary Nash Equilibrium: Two Examples," Econometrica, Econometric Society, vol. 81(5), pages 1973-2007, September.
    6. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
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    Cited by:

    1. Page, Frank, 2016. "On K-Class discounted stochastic games," LSE Research Online Documents on Economics 67809, London School of Economics and Political Science, LSE Library.
    2. Page, Frank, 2015. "Stationary Markov equilibria for K-class discounted stochastic games," LSE Research Online Documents on Economics 65103, London School of Economics and Political Science, LSE Library.
    3. Anna Jaśkiewicz & Andrzej S. Nowak, 2016. "Stationary Almost Markov Perfect Equilibria in Discounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 430-441, May.

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    More about this item

    Keywords

    Stochastic game; stationary Markov perfect equilibrium; equilibrium existence; coarser transition kernel;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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