Optimal Equilibria for Multidimensional Time-Inconsistent Stopping Problems

We study an optimal stopping problem under non-exponential discounting, where the state process is a multi-dimensional continuous strong Markov process. The discount function taken to be log sub-additive, capturing decreasing impatience in behavioral economics. On strength of probabilistic potential theory, we establish existence equilibrium among sufficiently large collection equilibria, consisting finely closed equilibria satisfying boundary condition. This generalizes for one-dimensional problems prior literature.