On the Notions of Equilibria for Time-Inconsistent Stopping Problems in Continuous Time
11 Pages Posted: 14 Sep 2019
Date Written: September 3, 2019
A new notion of equilibrium, which we call strong equilibrium, is introduced for timeinconsistent stopping problems in continuous time. Compared to the existing notions introduced in Time-Consistent Stopping Under Decreasing Impatience and On Finding Equilibrium Stopping Times for Time-Inconsistent Markovian Problems, which in this paper are called mild equilibrium and weak equilibrium respectively, a strong equilibrium captures the idea of subgame perfect Nash equilibrium more accurately. When the state process is a continuous-time Markov chain and the discount function is log sub-additive, we show that an optimal mild equilibrium is always a strong equilibrium. Moreover, we provide a new iteration method that can directly construct an optimal mild equilibrium and thus also prove its existence.
Keywords: Time-inconsistency, optimal stopping, strong equilibria, weak equilibria, mild equilibria, non-exponential discounting, subgame perfect Nash equilibrium
JEL Classification: C73, G10
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