In this paper, we study the fundamental problem of finding a stable matching in two-sided matching markets. In the classic variant, it is assumed that both sides of the market submit a ranked list of all agents on the other side. However, in large matching markets such as the National Resident Matching Program (NRMP), it is infeasible for hospitals to interview or mutually rank each resident. In this paper, we study the stable matching problem with truncated preference lists. In particular, we assume that, based on historical datasets, each hospital has a predicted rank of its likely match and only ranks residents within a bounded interval around that prediction. We use the algorithms-with-predictions framework and show that the classic deferred-acceptance (DA) algorithm used to compute stable matchings is robust to such truncation. We present two algorithms and theoretically and empirically evaluate their performance. Our results show that even with reasonably accurate predictions, it is possible to significantly cut down on both instance size (the length of preference lists) as well as the number of proposals made. These results explain the practical success of the DA algorithm and connect market design to the emerging theory of algorithms with predictions.

翻译：本文研究双边匹配市场中寻找稳定匹配这一基本问题。在经典模型中，假设市场双方均提交对另一侧所有智能体的排序列表。然而，在诸如国家住院医师匹配计划（NRMP）等大型匹配市场中，医院对所有住院医师进行面试或相互排序是不可行的。本文研究具有截断偏好列表的稳定匹配问题。具体而言，我们假设基于历史数据集，每家医院对其可能匹配对象具有预测排名，且仅对预测排名周围有限区间内的住院医师进行排序。我们采用带预测的算法框架，证明用于计算稳定匹配的经典延迟接受（DA）算法对此类截断具有鲁棒性。我们提出两种算法，并从理论与实证两方面评估其性能。结果表明，即使在预测精度有限的情况下，仍能显著缩减实例规模（偏好列表长度）及匹配提议次数。这些发现解释了DA算法的实际成功，并将市场设计与新兴的带预测算法理论建立联系。