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A formula for the value of a stochastic game

Author

Listed:
  • Luc Attia

    (Centre de Mathématiques Appliquées, École Polytechnique, 91128 Palaiseau, France)

  • Miquel Oliu-Barton

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

Abstract

In 1953, Lloyd Shapley defined the model of stochastic games, which were the first general dynamic model of a game to be defined, and proved that competitive stochastic games have a discounted value. In 1982, Jean-François Mertens and Abraham Neyman proved that competitive stochastic games admit a robust solution concept, the value, which is equal to the limit of the discounted values as the discount rate goes to 0. Both contributions were published in PNAS. In the present paper, we provide a tractable formula for the value of competitive stochastic games.

Suggested Citation

  • 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.
    • Handle: RePEc:nas:journl:v:116:y:2019:p:26435-26443
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    Citations

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    Cited by:

    1. Miquel Oliu-Barton, 2022. "Weighted-average stochastic games with constant payoff," Operational Research, Springer, vol. 22(3), pages 1675-1696, July.
    2. Levy, Yehuda John, 2022. "Uniformly supported approximate equilibria in families of games," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    3. Miquel Oliu-Barton, 2021. "New Algorithms for Solving Zero-Sum Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 255-267, February.

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