Equilibrium concepts for time-inconsistent stopping problems in continuous time
Abstract
A \emph{new} notion of equilibrium, which we call \emph{strong equilibrium}, is introduced for time-inconsistent stopping problems in continuous time. Compared to the existing notions introduced in ArXiv: 1502.03998 and ArXiv: 1709.05181, which in this paper are called \emph{mild equilibrium} and \emph{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.
Cite
@article{arxiv.1909.01112,
title = {Equilibrium concepts for time-inconsistent stopping problems in continuous time},
author = {Erhan Bayraktar and Jingjie Zhang and Zhou Zhou},
journal= {arXiv preprint arXiv:1909.01112},
year = {2020}
}
Comments
Final version. To appear in Mathematical Finance. Keywords:Time-inconsistency, optimal stopping, strong equilibria, weak equilibria, mild equilibria, non-exponential discounting, subgame perfect Nash equilibrium