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Mathematical Methods of Operations Research

, Volume 79, Issue 2, pp 179–194 | Cite as

The multi-player nonzero-sum Dynkin game in discrete time

  • Said Hamadène
  • Mohammed Hassani
Article

Abstract

We study the infinite horizon discrete time N-player nonzero-sum Dynkin game (\(N \ge 2\)) with stopping times as strategies (or pure strategies). The payoff depends on the set of players that stop at the termination stage (where the termination stage is the minimal stage in which at least one player stops). We prove existence of a Nash equilibrium point for the game provided that, for each player \(\pi _i\) and each nonempty subset \(S\) of players that does not contain \(\pi _i\), the payoff if \(S\) stops at a given time is at least the payoff if \(S\) and \(\pi _i\) stop at that time.

Keywords

Nonzero-sum Game Dynkin game Snell envelope Stopping time Nash equilibrium point Pure strategies 

Mathematics Subject Classification

91A15 91A10 91A30 60G40 91A60 

Notes

Acknowledgments

The authors thank the anonymous referees for their comments and suggestions which led to the improvement the paper.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Université du Maine, LMMLe Mans Cedex 9France
  2. 2.Département de Mathématiques et Informatique, Faculté poly-disciplinaire de SafiUniversité Cadi AyyadSafiMaroc

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