Time inconsistent problems of stochastic control and in particular optimal stopping, have been intensively studied in recent years. The main focus has been on the game theoretic formulation and the search for subgame perfect Nash equilibria. Different equilibrium concepts have been proposed and for some classes of problems, the existence of (pure) equilibria has been proved. In this talk, we introduce the concept of mixed equilibria in this framework and show how this leads to the solvability of larger classes of problems. In addition, we discuss the usefulness of the emergent class of special randomized stopping times in other contexts.

The talk is based on joint work with Kristoffer Lindensjö (Stockholm University).