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Shapley–Snow Kernels, Multiparameter Eigenvalue Problems, and Stochastic Games

Author

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  • Luc Attia

    (Department of Mathematics, Research Center in the Mathematics of Decision (CEREMADE), National Center for Scientific Research, Paris Dauphine University, and Paris Sciences and Letters University, 75016 Paris, France)

  • Miquel Oliu-Barton

    (Department of Mathematics, Research Center in the Mathematics of Decision (CEREMADE), National Center for Scientific Research, Paris Dauphine University, and Paris Sciences and Letters University, 75016 Paris, France)

Abstract

We propose a connection between finite zero-sum stochastic games (henceforth stochastic games) and multiparameter eigenvalue problems. This connection, which relies on the theory developed by Shapley and Snow for matrix games, opens new possibilities in the study of stochastic games. In particular, we derive from this connection a handful of new results for stochastic games.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:3:p:1181-1202
    DOI: 10.1287/moor.2020.1104
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