The Optimal Equilibrium for Time-Inconsistent Stopping Problems -- the Discrete-Time Case

Abstract

We study an infinite-horizon discrete-time optimal stopping problem under non-exponential discounting. A new method, which we call the iterative approach, is developed to find subgame perfect Nash equilibria. When the discount function induces decreasing impatience, we establish the existence of an equilibrium through fixed-point iterations. Moreover, we show that there exists a unique optimal equilibrium, which generates larger value than any other equilibrium does at all times. To the best of our knowledge, this is the first time a dominating subgame perfect Nash equilibrium is shown to exist in the literature of time-inconsistency.

Cited by in corpus (6)

• On time-inconsistent stopping problems and mixed strategy stopping times
• Optimal Equilibria for Time-Inconsistent Stopping Problems in Continuous Time
• Optimal Stopping under Model Ambiguity: a Time-Consistent Equilibrium Approach
• Optimal Equilibria for Multi-dimensional Time-inconsistent Stopping Problems
• A Time-Inconsistent Dynkin Game: from Intra-personal to Inter-personal Equilibria
• Partial Information in a Mean-Variance Portfolio Selection Game