We consider three equilibrium concepts proposed in the literature for time-inconsistent stop- ping problems, including mild equilibria, weak equilibria (introduced in [4]) and strong equilibria. The discount function is assumed to be log sub- additive and the underlying process is a one-dimension diffusion. We first provide necessary and sufficient conditions for weak equilibria, and the smooth-fit condition is obtained as a by-product. Next, based on the characterization of weak equilibrium, we show that an optimal mild equilibrium is also weak. Then we provide conditions under which a weak equilibrium is strong. We further show that an optimal mild equilibrium is also strong under a certain condition. Examples are provided at last, including one that shows a weak equilibrium may not be strong, and another one shows a strong equilibrium may not be optimal mild.

This talk is based on joint work with Erhan Bayraktar and Zhou Zhou

Speaker(s): Zhenhua Wang (UM)