论文标题
平衡在时间不一致的停止问题上的稳定性
Stability of Equilibria in Time-inconsistent Stopping Problems
论文作者
论文摘要
我们研究了平衡诱导的最佳值相对于（W.R.T.）奖励功能$ f $和过渡内核$ Q $，用于在离散时间内无X级折扣下停止问题的时间。首先，具有$ f $ $ f $的本地均匀收敛性和配备了总变化距离的$ Q $，我们表明最佳值是半连续的W.R.T. $（f，q）$。我们提供的示例表明，连续性一般可能会失败，并且总变化的$ Q $的收敛性不能被弱收敛所取代。接下来，我们表明，随着$ F $和$ Q $的均匀收敛，最佳值是连续的W.R.T. $（f，q）$当我们考虑超过$ \ varepsilon $ equilibria的轻松极限时。我们还提供了一个示例，表明对于这种连续性，$（f，q）$的均匀收敛不能被局部均匀的收敛代替。
We investigate the stability of equilibrium-induced optimal values with respect to (w.r.t.) reward functions $f$ and transition kernels $Q$ for time-inconsistent stopping problems under nonexponential discounting in discrete time. First, with locally uniform convergence of $f$ and $Q$ equipped with total variation distance, we show that the optimal value is semi-continuous w.r.t. $(f,Q)$. We provide examples showing that continuity may fail in general, and the convergence for $Q$ in total variation cannot be replaced by weak convergence. Next we show that with the uniform convergence of $f$ and $Q$, the optimal value is continuous w.r.t. $(f,Q)$ when we consider a relaxed limit over $\varepsilon$-equilibria. We also provide an example showing that for such continuity the uniform convergence of $(f,Q)$ cannot be replaced by locally uniform convergence.
