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

Luc Attia () and Miquel Oliu-Barton ()
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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

Mathematics of Operations Research, 2021, vol. 46, issue 3, 1181-1202

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.

Keywords: Primary: 91A15; secondary: 15A22; 15A30; Primary: games/group decisions/stochastic; secondary: mathematics/matrices; stochastic game; multiparameter eigenvalue problems; matrix pencil; Shapley–Snow kernel; discounted value; limit value (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:46:y:2021:i:3:p:1181-1202

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