Almost strong equilibria for time‐inconsistent stopping problems under finite horizon in continuous time
研究了连续时间马尔可夫链在有限时间范围内非指数贴现下的时间不一致停止问题，提出几乎强均衡概念，并给出迭代构造方法，证明其唯一性。
Abstract We consider time‐inconsistent stopping problems for a continuous‐time Markov chain under finite time horizon with non‐exponential discounting. We provide an example indicating that strong equilibria may not exist in general. As a result, we propose a notion of equilibrium called almost strong equilibrium (ASE), which is a weak equilibrium and satisfies the condition of strong equilibria except at the boundary points of the associated stopping region. We provide an iteration procedure and show that this procedure leads to an ASE. Moreover, we prove that this ASE is the unique ASE among all regular stopping policies under finite horizon . In contrast, we show that strong equilibria (and thus ASE) exist and may not be unique for the infinite horizon case . Furthermore, we show that the limit of the finite‐horizon ASE as is a weak equilibrium for the infinite‐horizon problem, and may not be a strong equilibrium or ASE.