互补性与偏好错位下的稳定匹配计算
Computing Stable Matchings under Complementarities and Preference Misalignment
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中文总结 AI 辅助
本文研究互补偏好与偏好错位下的多对一稳定匹配问题，提出两个充分条件及CDAR算法，证明其收敛性、稳定性和帕累托最优性，并应用于车辆路线分配与劳资谈判场景。
中文摘要 AI 辅助
我们研究了多对一、双边稳定匹配问题，其中偏好具有互补性，且企业与工人可能对同一分配给出不同排序。在此背景下，联盟是指一组可与企业联合匹配的工人。在互补偏好下，稳定匹配不一定存在。我们证明，当两个条件成立时，每个实例都存在稳定匹配。第一个条件要求每个企业都有一个锚定工人，该工人被包含在与该企业可匹配的每个可行联盟中。第二个条件是传递对齐，即必须存在一个与工人偏好一致的跨联盟总体排序。我们提出了CDAR（带重新提议的组合延迟接受算法），这是一种允许重新提议的延迟接受式算法，并通过构造一个$N$位势函数证明了其有限时间收敛性及其输出稳定匹配的性质。此外，我们证明，在严格偏好下，CDAR的输出在稳定匹配中是帕累托最优的。所提出的框架自然适用于交通安全中的车辆路线分配以及劳资谈判中劳动与管理层利益错位等应用场景。
英文摘要
We study many-to-one, two-sided stable matching problems in which preferences are complementary and firms and workers may rank the same allocation differently. Here a coalition is a group of workers that can be jointly matched with a firm. With complementary preferences, a stable matching need not exist. We show that a stable matching exists for every instance when two conditions hold. The first requires each firm to have an anchor worker who is included in every feasible coalition that can be matched with that firm. The second is Transitive Alignment, which means there must be an overall ranking across different coalitions that is consistent with the workers' preferences. We propose CDAR (Combinatorial Deferred Acceptance with Reproposals), a Deferred Acceptance-style algorithm that permits reproposals, and prove its finite-time convergence and its output of a stable matching by constructing an $N$-digit potential function. Moreover, we show that, under strict preferences, the output of CDAR is Pareto optimal among stable matchings. The proposed framework naturally captures applications such as vehicle-route assignment for traffic safety and the misaligned interests of labor and management in wage negotiation.
