*Induction of time inconsistency in optimal stopping problem*

Time inconsistency is a common phenomenon of optimal control and optimal stopping problems, especially in finance and economics. It says a player will change his optimal strategy over time. To deal with such problem, we usually search for some consistent plan (equilibrium) instead of optimizing the original objective. This presentation first introduces this time inconsistency concept with some examples. Then focus on a special type of time-inconsistency problem in continuous Markov setting. I will first introduce a type of methodology to construct equilibrium and then talks about some results for existence of equilibria and existence of optimal equilibrium.