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

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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.

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Acknowledgments

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

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Authors and Affiliations

  1. Université du Maine, LMM, Avenue Olivier Messiaen, 72085 , Le Mans Cedex 9, France

    Said Hamadène

  2. Département de Mathématiques et Informatique, Faculté poly-disciplinaire de Safi, Université Cadi Ayyad, B.P. 4162, Safi, Maroc

    Mohammed Hassani

Authors
  1. Said Hamadène
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  2. Mohammed Hassani
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Correspondence to Said Hamadène.

Additional information

This work has been carried out while the second author was visiting Université du Maine, Le Mans (Fr.).

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Hamadène, S., Hassani, M. The multi-player nonzero-sum Dynkin game in discrete time. Math Meth Oper Res 79, 179–194 (2014). https://doi.org/10.1007/s00186-013-0458-1

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  • DOI: https://doi.org/10.1007/s00186-013-0458-1

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