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Existence of SPE in Discounted Stochastic Games; Revisited and Simplified

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  • Yehuda Levy

Abstract

Mertens and Parthasarathy (1987) proved the existence of sub-game perfect equilibria in discounted stochastic games. Their method involved new techniques in dynamic programming, which were presented in a very general framework, with no expense spared in highlighting versatility and scope. This paper presents the fundamentals of their technique which are necessary, as well as identifies and elaborates on the components of their method, hence giving the core of the proof in a much more concise, direct, and illuminating manner.

Suggested Citation

  • Yehuda Levy, 2015. "Existence of SPE in Discounted Stochastic Games; Revisited and Simplified," Economics Series Working Papers 739, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:739
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    File URL: https://ora.ox.ac.uk/objects/uuid:8a8b75ed-baac-4d1c-8d83-4decba810079
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    References listed on IDEAS

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    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. Ashok P. Maitra & William D. Sudderth, 2007. "Subgame-Perfect Equilibria for Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 711-722, August.
    3. C. J. Himmelberg & T. Parthasarathy & F. S. VanVleck, 1976. "Optimal Plans for Dynamic Programming Problems," Mathematics of Operations Research, INFORMS, vol. 1(4), pages 390-394, November.
    4. Yehuda Levy, 2013. "Discounted Stochastic Games With No Stationary Nash Equilibrium: Two Examples," Econometrica, Econometric Society, vol. 81(5), pages 1973-2007, September.
    5. 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.
    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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    More about this item

    Keywords

    Stochastic Games; Equilibrium Existence; Subgame-Perfect Equilibrium;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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