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Stationary Equilibria in Discounted Stochastic Games

Author

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  • Luc Attia

    (Université Paris Dauphine - PSL)

  • Miquel Oliu-Barton

    (Université Paris Dauphine - PSL)

Abstract

We provide a new characterisation of the set of stationary equilibria for finite discounted N-player stochastic games, based on the definition of an auxiliary one-shot game with the same set of equilibria. This result is the extension, to the N-player case, of a similar characterisation for two-player zero-sum stochastic games (Attia and Oliu-Barton in Proc Natl Acad Sci USA 116:26435–26443, 2019) which led to a tractable formula for the limit value. Though the general case presents additional challenges, our characterisation may have further applications, notably in terms of the description and computation of stationary equilibria and of their limit as the discount rates vanish.

Suggested Citation

  • Luc Attia & Miquel Oliu-Barton, 2024. "Stationary Equilibria in Discounted Stochastic Games," Dynamic Games and Applications, Springer, vol. 14(2), pages 271-284, May.
    • Handle: RePEc:spr:dyngam:v:14:y:2024:i:2:d:10.1007_s13235-023-00495-x
    DOI: 10.1007/s13235-023-00495-x
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    References listed on IDEAS

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    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.
    2. Porter, Ryan & Nudelman, Eugene & Shoham, Yoav, 2008. "Simple search methods for finding a Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 63(2), pages 642-662, July.
    3. S. R. Mohan & S. K. Neogy & T. Parthasarathy, 2001. "Pivoting Algorithms For Some Classes Of Stochastic Games: A Survey," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 3(02n03), pages 253-281.
    4. Raghavan, T.E.S. & Tijs, S.H. & Vrieze, O.J., 1985. "On stochastic games with additive reward and transition structure," Other publications TiSEM 28f85a14-9a6e-4ed8-9a4b-a, Tilburg University, School of Economics and Management.
    5. Luc Attia & Miquel Oliu-Barton, 2021. "Shapley–Snow Kernels, Multiparameter Eigenvalue Problems, and Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 46(3), pages 1181-1202, August.
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