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$$\varepsilon $$ ε -Nash Equilibria of a Multi-player Nonzero-Sum Dynkin Game in Discrete Time

Author

Listed:
  • Said Hamadène

    (Le Mans Université, LMM)

  • Mohammed Hassani

    (Université Cadi Ayyad)

  • Marie-Amélie Morlais

    (Le Mans Université, LMM)

Abstract

We study the infinite horizon discrete time N-player nonzero-sum Dynkin game ( $$N\ge 2$$ N ≥ 2 ) with stopping times as strategies (or pure strategies). We prove existence of an $$\varepsilon $$ ε -Nash equilibrium point for the game by presenting a constructive algorithm. One of the main features is that the payoffs of the players depend on the set of players that stop at the termination stage which is the minimal stage in which at least one player stops. The existence result is extended to the case of a nonzero-sum game with finite horizon. Finally, the algorithm is illustrated by two explicit examples in the specific case of finite horizon.

Suggested Citation

  • Said Hamadène & Mohammed Hassani & Marie-Amélie Morlais, 2024. "$$\varepsilon $$ ε -Nash Equilibria of a Multi-player Nonzero-Sum Dynkin Game in Discrete Time," Dynamic Games and Applications, Springer, vol. 14(3), pages 642-664, July.
    • Handle: RePEc:spr:dyngam:v:14:y:2024:i:3:d:10.1007_s13235-023-00500-3
    DOI: 10.1007/s13235-023-00500-3
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