Equilibria of time‐inconsistent stopping for one‐dimensional diffusion processes

We consider three equilibrium concepts proposed in the literature for time-inconsistent stopping problems, including mild equilibria (introduced Huang and Nguyen-Huu (2018)), weak Christensen Lindensjö strong Bayraktar et al. (2021)). The discount function is assumed to be log subadditive underlying process one-dimensional diffusion. first provide necessary sufficient conditions characterization of equilibria. smooth-fit condition obtained as a by-product. Next, based on equilibria, we show that an optimal also weak. Then under which strong. further certain condition. Finally, several examples one showing may not strong, another mild.