On the Notions of Equilibria for Time-Inconsistent Stopping Problems in Continuous Time

11 Pages Posted: 14 Sep 2019

See all articles by Erhan Bayraktar

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Jingjie Zhang

University of Michigan at Ann Arbor - Department of Mathematics

Zhou Zhou

The University of Sydney

Date Written: September 3, 2019

Abstract

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

Suggested Citation

Bayraktar, Erhan and Zhang, Jingjie and Zhou, Zhou, On the Notions of Equilibria for Time-Inconsistent Stopping Problems in Continuous Time (September 3, 2019). Available at SSRN: https://ssrn.com/abstract=3448620 or http://dx.doi.org/10.2139/ssrn.3448620

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Jingjie Zhang (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2860 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Zhou Zhou

The University of Sydney ( email )

University of Sydney
Sydney, NSW 2006
Australia

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