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Computing uniformly optimal strategies in two-player stochastic games

Author

Listed:
  • Nicolas Vieille

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • Eilon Solan

    (TAU - School of Mathematical Sciences [Tel Aviv] - TAU - Raymond and Beverly Sackler Faculty of Exact Sciences [Tel Aviv] - TAU - Tel Aviv University)

Abstract

We provide a computable algorithm to calculate uniform ε-optimal strategies in two-player zero-sum stochastic games. Our approach can be used to construct algorithms that calculate uniform ε-equilibria and uniform correlated ε-equilibria in various classes of multi-player non-zero-sum stochastic games.

Suggested Citation

  • Nicolas Vieille & Eilon Solan, 2009. "Computing uniformly optimal strategies in two-player stochastic games," Post-Print hal-00528413, HAL.
    • Handle: RePEc:hal:journl:hal-00528413
    DOI: 10.1007/s00199-009-0437-1
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    References listed on IDEAS

    as
    1. Herings, P. Jean-Jacques & Peeters, Ronald J. A. P., 2004. "Stationary equilibria in stochastic games: structure, selection, and computation," Journal of Economic Theory, Elsevier, vol. 118(1), pages 32-60, September.
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    4. 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.
    5. Solan, Eilon & Vieille, Nicolas, 2002. "Correlated Equilibrium in Stochastic Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 362-399, February.
    6. Mertens, Jean-Francois, 2002. "Stochastic games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 47, pages 1809-1832, Elsevier.
    7. Eilon Solan & Nicolas Vieille, 1998. "Quitting Games," Discussion Papers 1227, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Eilon Solan & Nicolas Vieille, 2002. "Perturbed Markov Chains," Discussion Papers 1342, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    Cited by:

    1. Bernhard Stengel, 2010. "Computation of Nash equilibria in finite games: introduction to the symposium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 1-7, January.
    2. Miquel Oliu-Barton, 2014. "The Asymptotic Value in Finite Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 712-721, August.
    3. Miquel Oliu-Barton, 2012. "The asymptotic value in finite stochastic games," Working Papers halshs-00772631, HAL.
    4. Cheng, Jianqiang & Leung, Janny & Lisser, Abdel, 2016. "Random-payoff two-person zero-sum game with joint chance constraints," European Journal of Operational Research, Elsevier, vol. 252(1), pages 213-219.
    5. Jérôme Bolte & Stéphane Gaubert & Guillaume Vigeral, 2015. "Definable Zero-Sum Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 171-191, February.
    6. Miquel Oliu-Barton, 2021. "New Algorithms for Solving Zero-Sum Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 255-267, February.
    7. ,, 2015. "Unraveling in a repeated moral hazard model with multiple agents," Theoretical Economics, Econometric Society, vol. 10(1), January.

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    More about this item

    Keywords

    Optimal strategies; Stochastic games; Computation;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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