Original title: Mean-field optimal stopping with endogenous quantile cutoffs
Erhan Bayraktar, Ibrahim Ekren, Xihao He · September 2026
Imagine a huge group of participants who each want to choose the best time to quit a process. But there is a catch: if the total fraction of remaining participants drops below a set cutoff point, everyone gets shut down at once. The researchers studied this mass decision problem. To handle the abrupt shutdown rule, they framed it mathematically as forcing the surviving group size to sit either at zero or above a specific limit. They proved that an optimal stopping strategy exists and that step-by-step decision rules still function properly. Finally, they found that when groups start safely above the limit, large finite crowds match the idealized infinite-group outcome. However, if they start right at the cutoff boundary, this match can fail completely.
Imagine you're in a long queue for a concert, and you plan to leave if it seems too short. But if you and others leave when the line dips below a point, it might suddenly collapse entirely. Here, the paper models how individuals in a large group decide when to stop, with a rule that triggers everyone to stop if too few are left. It finds that while decisions usually stabilize in very large groups, right at the cutoff point, they can become unpredictable.
This work helps predict when large-group decisions remain stable as the group size grows. It matters for fields like economics or network theory where individual choices aggregate, and thresholds can cause abrupt changes. The finding that convergence may fail at the threshold means small errors near cutoffs could lead to large discrepancies.
The paper does not provide methods to handle the failure of convergence at the threshold. It assumes strict initial feasibility for its convergence results. The analysis is limited to mean-field models and may not directly apply to all real-world settings.
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Mean-field optimal stopping with endogenous quantile cutoffs — Erhan Bayraktar, Ibrahim Ekren, Xihao He
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.