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This paper revisits the well-studied \emph{optimal stopping} problem butwithin the \emph{large-population} framework. In particular, two classes ofoptimal stopping problems are formulated by taking into account the\emph{relative performance criteria}. It is remarkable the relative performancecriteria, also understood by the \emph{Joneses preference}, \emph{habitformation utility}, or \emph{relative wealth concern} in economics and finance,plays an important role in explaining various decision behaviors such as pricebubbles. By introducing such criteria in large-population setting, a givenagent can compare his individual stopping rule with the average behaviors ofits cohort. The associated mean-field games are formulated in order to derivethe decentralized stopping rules. The related consistency conditions arecharacterized via some coupled equation system and the asymptotic Nashequilibrium properties are also verified. In addition, some \emph{inverse}mean-field optimal stopping problem is also introduced and discussed.

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