Abstract: We investigate time-inconsistency, or "regret over time", of optimal stopping problems under non-exponential discounting. This endeavor is important because numerous empirical studies indicate that people discount differently from an exponential discount function, contrary to classical formulations in Mathematical Finance. A game-theoretic perspective towards stopping problems is proposed: instead of maximizing expected discounted payoff locally at current time, one searches globally over time for an equilibrium among herself today and all her future selves at later dates. Such an equilibrium, which can be viewed as a stopping strategy agreed upon by current and future selves, is formulated as a fixed point of an operator acting on stopping strategies. An iterative procedure is devised to construct an equilibrium strategy. |