## 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

Tiziano De Angelis, Giorgio Ferrari, and John Moriarty

#### 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