  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.
