Equilibrium in two-player non-zero-sum Dynkin games in continuous time

Abstract

We prove that every two-player non-zero-sum Dynkin game in continuous time admits an ϵ-equilibrium in randomized stopping times. We provide a condition that ensures the existence of an ϵ-equilibrium in non-randomized stopping times.

Keywords:

• Dynkin games
• stopping games
• equilibrium
• stochastic analysis
• continuous time

2000 Mathematics Subject Classification::

• 91A05
• 91A10
• 91A55
• 60G40

Acknowledgements

We thank Said Hamadène for his assistance and for his helpful comments. The work of Solan was supported by the Israel Science Foundation, Grant 212/09.

Notes

^1. [email protected].

^†The results presented in this paper were proven while the authors attended the workshop on ‘Repeated Games and Differential Games’, organized by Marc Quincampoix and Sylvain Sorin in November 2008, Roscoff, France.

^2. Our results hold for the larger class of D payoff processes defined by Dellacherie and Meyer [7, §II-18]. This class contains in particular integrable processes.

^3. A statement holds on a measurable set A if and only if the set of points in A that do not satisfy the statement has probability 0.

^4. The additional ϵ arises because in Part 1 we had , whereas in Part 4 we have .

Additional information

Notes on contributors

Rida Laraki

1 1. [email protected].