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

TL;DR

This paper studies Nash equilibria in two-player nonzero-sum stopping games for diffusions, showing conditions for boundary-based equilibria and their uniqueness, with implications for strategic stopping in stochastic processes.

Contribution

It introduces conditions under which Nash equilibria are of threshold type and characterizes their uniqueness for certain diffusion processes.

Findings

Nash equilibria occur at boundary points of an interval.

Equilibrium boundaries satisfy a specific algebraic system.

Conditions for the uniqueness of these equilibria are established.

Abstract

This paper analyses two-player nonzero-sum games of optimal stopping on a class of linear regular diffusions with not non-singular boundary behaviour (in the sense of It\^o and McKean (1974), p.\ 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.