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On K-Class discounted stochastic games

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  • Page, Frank

Abstract

For a discounted stochastic game with an uncountable state space and compact metric action spaces, we show that if the measurable-selection-valued, Nash payoff selection correspondence of the underlying one-shot game contains a sub-correspondence having the K- limit property (i.e., if the Nash payoff selection sub-correspondence contains its K-limits and therefore is a K correspondence), then the discounted stochastic game has a stationary Markov equilibrium. Our key result is a new fixed point theorem for measurable-selection-valued correspondences having the K-limit property. We also show that if the discounted stochastic game is noisy (Duggan, 2012), or if the underlying probability space satisfies the G-nonatomic condition of Rokhlin (1949) and Dynkin and Evstigneev (1976) (and therefore satisfies the coaser transition kernel condition of He and Sun, 2014), then the Nash payoff selection correspondence contains a sub-correspondence having the K-limit property.

Suggested Citation

  • 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.
    • Handle: RePEc:ehl:lserod:67809
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    File URL: http://eprints.lse.ac.uk/67809/
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    References listed on IDEAS

    as
    1. John Duggan, 2012. "Noisy Stochastic Games," Econometrica, Econometric Society, vol. 80(5), pages 2017-2045, September.
    2. Forges, Francoise M, 1986. "An Approach to Communication Equilibria," Econometrica, Econometric Society, vol. 54(6), pages 1375-1385, November.
    3. He, Wei & Sun, Yeneng, 2013. "Stationary Markov Perfect Equilibria in Discounted Stochastic Games," MPRA Paper 51274, University Library of Munich, Germany.
    4. 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.
    5. Yehuda John Levy & Andrew McLennan, 2015. "Corrigendum to “Discounted Stochastic Games With No Stationary Nash Equilibrium: Two Examples”," Econometrica, Econometric Society, vol. 83(3), pages 1237-1252, May.
    6. Artstein, Zvi, 1979. "A note on fatou's lemma in several dimensions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 277-282, December.
    7. John Duggan, 2012. "Noisy Stochastic Games," RCER Working Papers 570, University of Rochester - Center for Economic Research (RCER).
    8. Yehuda Levy, 2013. "Discounted Stochastic Games With No Stationary Nash Equilibrium: Two Examples," Econometrica, Econometric Society, vol. 81(5), pages 1973-2007, September.
    9. Andrzej Nowak, 2007. "On stochastic games in economics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 513-530, December.
    10. 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.
    11. Andrzej Nowak, 2003. "On a new class of nonzero-sum discounted stochastic games having stationary Nash equilibrium points," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 121-132, December.
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    More about this item

    Keywords

    approximate Caratheodory selections; fixed points of nonconvex valuedcorrespondences; measurable selection valued correspondences; Komlos limits; Komlos’ Theorem; weak star convergence; discounted stochastic games; stationaryMarkov equilibria;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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