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

Said Hamadène (), Mohammed Hassani () and Marie-Amélie Morlais ()
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Said Hamadène: Le Mans Université, LMM
Mohammed Hassani: Université Cadi Ayyad
Marie-Amélie Morlais: Le Mans Université, LMM

Dynamic Games and Applications, 2024, vol. 14, issue 3, No 5, 642-664

Abstract: 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.

Keywords: Nonzero-sum game; Dynkin game; Snell envelope; Stopping time; Nash equilibrium point; Pure strategy; 91A15; 91A10; 91A30; 60G40; 91A60 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13235-023-00500-3

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