发表机构
University of Michigan; University of Southern California（密歇根大学; 南加州大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对带内生分位数截止的平均场最优停止问题，通过重构约束、证明等价性与收敛性，分析其值的连续性及有限种群与平均场值的收敛关系。
AI 中文摘要
我们研究一类带有内生种群层面关停机制的平均场最优停止问题：当存活质量降至规定阈值以下时，所有剩余智能体将停止行动。我们将不连续目标重构为奇异非凸约束，要求存活质量处于{0}∪[α,1]区间内。我们通过逼近法证明强值与弱值等价，利用紧性与惩罚项方法证明最优规则的存在性，还证明了动态规划原理：该值在临界边界外连续，但在边界处可能不连续。在严格初始可行性条件下，有限种群的值收敛到平均场值；在同一 regime 下，近最优经验测度的律是紧的，且每个平均场优化器都存在恢复序列，但在阈值处，有限种群的收敛可能失效。
英文摘要
We study a mean-field optimal stopping problem with an endogenous population-level shutdown. All remaining agents stop when the survival mass falls below a prescribed threshold. We recast the discontinuous objective as the singular, nonconvex constraint that the survival mass lie in $\{0\}\cup[α,1]$. We prove the equivalence of strong and weak values via an approximation and the existence of an optimal rule via compactness and penalization. We also prove a dynamic programming principle. The value is continuous away from the critical boundary but may be discontinuous at the boundary itself. Under strict initial feasibility, finite-population values converge to the mean-field value. In the same regime, the laws of near-optimal empirical measures are tight and every mean-field optimizer admits a recovery sequence. At the threshold, however, finite-population convergence may fail.
