A Class of Mean-Field Games with Optimal Stopping and its Inverse Problem

TL;DR

This paper develops a mean-field game framework for optimal stopping problems incorporating relative performance criteria, analyzing equilibrium behavior and inverse problems in large populations with applications in economics and finance.

Contribution

It introduces a novel class of mean-field optimal stopping problems with relative performance criteria and explores their equilibrium and inverse problem formulations.

Findings

Characterized equilibrium conditions via coupled equations.

Verified asymptotic Nash equilibrium properties.

Discussed inverse mean-field optimal stopping problems.

Abstract

This paper revisits the well-studied \emph{optimal stopping} problem but within the \emph{large-population} framework. In particular, two classes of optimal stopping problems are formulated by taking into account the \emph{relative performance criteria}. It is remarkable the relative performance criteria, also understood by the \emph{Joneses preference}, \emph{habit formation utility}, or \emph{relative wealth concern} in economics and finance, plays an important role in explaining various decision behaviors such as price bubbles. By introducing such criteria in large-population setting, a given agent can compare his individual stopping rule with the average behaviors of its cohort. The associated mean-field games are formulated in order to derive the decentralized stopping rules. The related consistency conditions are characterized via some coupled equation system and the asymptotic Nash equilibrium properties are also verified. In addition, some \emph{inverse} mean-field optimal stopping problem is also introduced and discussed.