The Annals of Applied Probability

Nash equilibria of threshold type for two-player nonzero-sum games of stopping

Tiziano De Angelis, Giorgio Ferrari, and John Moriarty

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 28, Number 1 (2018), 112-147.

Dates
Received: August 2015
Revised: November 2016
First available in Project Euclid: 3 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1520046085

Digital Object Identifier
doi:10.1214/17-AAP1301

Mathematical Reviews number (MathSciNet)
MR3770874

Zentralblatt MATH identifier
06873681

Subjects
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

Keywords
Nonzero-sum Dynkin games Nash equilibrium smooth-fit principle regular diffusions free boundary problems

Citation

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


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