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Two-player stochastic games I: A reduction

Author

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  • Nicolas Vieille

    (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, GREThA - Groupe de Recherche en Economie Théorique et Appliquée - UB - Université de Bordeaux - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper is the first step in the proof of existence of equilibrium payoffs for two-player stochastic games with finite state and action sets. It reduces the existence problem to the class of so-called positive absorbing recursive games. The existence problem for this class is solved in a subsequent paper.

Suggested Citation

  • Nicolas Vieille, 2000. "Two-player stochastic games I: A reduction," Post-Print hal-00481401, HAL.
    • Handle: RePEc:hal:journl:hal-00481401
    DOI: 10.1007/BF02810663
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    Citations

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    Cited by:

    1. Renault, Jérôme & Ziliotto, Bruno, 2020. "Hidden stochastic games and limit equilibrium payoffs," Games and Economic Behavior, Elsevier, vol. 124(C), pages 122-139.
    2. Venel, Xavier, 2021. "Regularity of dynamic opinion games," Games and Economic Behavior, Elsevier, vol. 126(C), pages 305-334.
    3. Solan, Eilon, 2018. "Acceptable strategy profiles in stochastic games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 523-540.
    4. Robert Samuel Simon, 2012. "A Topological Approach to Quitting Games," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 180-195, February.
    5. P. Jean-Jacques Herings & Harold Houba, 2022. "Costless delay in negotiations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(1), pages 69-93, July.
    6. Eilon Solan & Nicholas Vieille, 2001. "Quitting Games - An Example," Discussion Papers 1314, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Xavier Venel, 2015. "Commutative Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 403-428, February.
    8. Boros, E. & Gurvich, V., 2003. "On Nash-solvability in pure stationary strategies of finite games with perfect information which may have cycles," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 207-241, October.
    9. Rabah Amir & Igor V. Evstigneev & Valeriya Potapova, 2021. "Unbeatable Strategies," Economics Discussion Paper Series 2101, Economics, The University of Manchester, revised Jul 2023.
    10. Sam Ganzfried & Conner Laughlin & Charles Morefield, 2019. "Parallel Algorithm for Approximating Nash Equilibrium in Multiplayer Stochastic Games with Application to Naval Strategic Planning," Papers 1910.00193, arXiv.org, revised Mar 2020.
    11. Zerong Chen, 2024. "Evolutionary Finance: Models with Short-Lived Assets," Economics Discussion Paper Series 2402, Economics, The University of Manchester.
    12. Heller, Yuval & Solan, Eilon & Tomala, Tristan, 2012. "Communication, correlation and cheap-talk in games with public information," Games and Economic Behavior, Elsevier, vol. 74(1), pages 222-234.
    13. J. Flesch & G. Schoenmakers & O. Vrieze, 2011. "Loss of skills in coordination games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 769-789, November.
    14. Walker, Mark & Wooders, John & Amir, Rabah, 2011. "Equilibrium play in matches: Binary Markov games," Games and Economic Behavior, Elsevier, vol. 71(2), pages 487-502, March.
    15. Jérôme Renault & Bruno Ziliotto, 2020. "Limit Equilibrium Payoffs in Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 889-895, August.

    More about this item

    Keywords

    stochastic games;

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