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New Algorithms for Solving Zero-Sum Stochastic Games

Author

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  • Miquel Oliu-Barton

    (Université Paris-Dauphine, Paris Sciences et Lettres Research University, Centre de Recherche en Mathématiques de la Décision, 75016 Paris, France)

Abstract

Zero-sum stochastic games, henceforth stochastic games, are a classical model in game theory in which two opponents interact and the environment changes in response to the players’ behavior. The central solution concepts for these games are the discounted values and the value, which represent what playing the game is worth to the players for different levels of impatience. In the present manuscript, we provide algorithms for computing exact expressions for the discounted values and for the value, which are polynomial in the number of pure stationary strategies of the players. This result considerably improves all the existing algorithms.

Suggested Citation

  • Miquel Oliu-Barton, 2021. "New Algorithms for Solving Zero-Sum Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 255-267, February.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:1:p:255-267
    DOI: 10.1287/moor.2020.1055
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    References listed on IDEAS

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    1. Krishnendu Chatterjee & Rupak Majumdar & Thomas Henzinger, 2008. "Stochastic limit-average games are in EXPTIME," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 219-234, June.
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    3. Eilon Solan & Nicolas Vieille, 2010. "Computing uniformly optimal strategies in two-player stochastic games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 237-253, January.
    4. Truman Bewley & Elon Kohlberg, 1976. "The Asymptotic Theory of Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 197-208, August.
    5. Luc Attia & Miquel Oliu-Barton, 2019. "A formula for the value of a stochastic game," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 116(52), pages 26435-26443, December.
    6. Miquel Oliu-Barton, 2014. "The Asymptotic Value in Finite Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 712-721, August.
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    Citations

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    Cited by:

    1. Guillaume Garnier & Bruno Ziliotto, 2023. "Percolation Games," Mathematics of Operations Research, INFORMS, vol. 48(4), pages 2156-2166, November.
    2. Luc Attia & Miquel Oliu-Barton & Raimundo Saona, 2025. "Marginal Values of a Stochastic Game," Mathematics of Operations Research, INFORMS, vol. 50(1), pages 482-505, February.
    3. Krishnendu Chatterjee & Miquel Oliu-Barton & Raimundo Saona, 2025. "Value-Positivity for Matrix Games," Mathematics of Operations Research, INFORMS, vol. 50(4), pages 2502-2525, November.
    4. Constantin Ickstadt & Thorsten Theobald & Elias Tsigaridas, 2024. "Semidefinite games," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(3), pages 827-857, September.

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