The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 28, Number 1 (2018), 112-147.
Nash equilibria of threshold type for two-player nonzero-sum games of stopping
This paper analyses two-player nonzero-sum games of optimal stopping on a class of linear regular diffusions with not nonsingular boundary behaviour [in the sense of Itô and McKean (Diffusion Processes and Their Sample Paths (1974) Springer, page 108)]. We provide sufficient conditions under which Nash equilibria are realised by each player stopping the diffusion at one of the two boundary points of an interval. The boundaries of this interval solve a system of algebraic equations. We also provide conditions sufficient for the uniqueness of the equilibrium in this class.
Ann. Appl. Probab., Volume 28, Number 1 (2018), 112-147.
Received: August 2015
Revised: November 2016
First available in Project Euclid: 3 March 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 91A05: 2-person games 91A15: Stochastic games 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60J60: Diffusion processes [See also 58J65] 35R35: Free boundary problems
De Angelis, Tiziano; Ferrari, Giorgio; Moriarty, John. Nash equilibria of threshold type for two-player nonzero-sum games of stopping. Ann. Appl. Probab. 28 (2018), no. 1, 112--147. doi:10.1214/17-AAP1301. https://projecteuclid.org/euclid.aoap/1520046085