Abstract：

 

Under non-exponential discounting, we develop a dynamic theory for stopping problems in continuous time. Our framework particularly covers discount functions that induce decreasing impatience. Due to the inherent time inconsistency, the stopping problem is presented as an inter-temporal game among a continuum of non-cooperative players. We look for equilibrium stopping policies, which are formulated as fixed points of an operator. Under appropriate conditions, we show that fixed-point iterations converge to equilibrium stopping policies. This in particular provides an explicit connection between optimal stopping times in classical stopping literature and equilibrium stopping policies under current game-theoretic setting. This connection is new in the literature of time-inconsistent problems, and it corresponds to increasing levels of strategic reasoning. Our theory is illustrated in a real option pricing model.