匹配市场是否应放宽稳定性假设？
最优化与控制
2025-09-19 v1
摘要
中心化的分配市场一直依赖延迟接受（DA）算法，而该算法未将多个目标纳入分配决策。本文提出一种基于优化的多对一分配算法，探讨在减少阻塞配对数量与其他重要目标之间进行权衡。为了扩展到高维问题，我们 developed an algorithm using inverse optimization to obtain the optimal cost vector that implicitly optimizes for stability. This is empirically tested on two application areas for which the DA algorithm is widely used: school assignment and medical residency match. Computational tests on a simulated Boston Public Schools (BPS) match show that this method effectively reduces transportation cost and increases number of students receiving an offer in the first round of match at the expense of a small percentage of blocking pairs. Similar improvement in the number of couples matched to the same location is observed in a synthetic residency match.
引用
@article{arxiv.2509.14475,
title = {Should We Relax Stability in Matching Markets?},
author = {Dimitris Bertsimas and Carol Gao},
journal= {arXiv preprint arXiv:2509.14475},
year = {2025}
}