A new notion of equilibrium, which we call strong equilibrium, is introduced for time‐inconsistent stopping problems in continuous time. Compared to the existing notions introduced in Huang, Y.‐J., & Nguyen‐Huu, A. (2018, Jan 01). Time‐consistent stopping under decreasing impatience. Finance and Stochastics, 22(1), 69–95 and Christensen, S., & Lindensjö, K. (2018). On finding equilibrium stopping times for time‐inconsistent markovian problems. SIAM Journal on Control and Optimization, 56(6), 4228–4255, 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 subadditive, 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.

中文翻译：

---

连续时间中时间不一致的停车问题的平衡概念

针对连续时间中时间不一致的停车问题，引入了一种新的平衡概念，即强平衡。与Huang，Y.‐J.和Nguyen-Huu，A.（2018，Jan 01）中引入的现有概念进行比较。时间一致的停止，减少不耐烦。Finance and Stochastics，22（1），69-95 and Christensen，S.，＆Lindensjö，K.（2018）。在找到时间不一致的马尔可夫问题的平衡停止时间时。SIAM控制与优化杂志，56（6），4228-4255，在本文中被称为温和平衡和弱平衡分别说，一个强均衡更加准确地捕捉了子博弈完美纳什均衡的思想。当状态过程是连续时间的马尔可夫链且折扣函数是对数次加性时，我们表明最优的温和平衡始终是强平衡。此外，我们提供了一种新的迭代方法，可以直接构造最佳的温和平衡，从而证明其存在。