We study the problem of capacity modification in the many-to-one stable matching of workers and firms. Our goal is to systematically study how the set of stable matchings changes when some seats are added to or removed from the firms. We make three main contributions: First, we examine whether firms and workers can improve or worsen upon changing the capacities under worker-proposing and firm-proposing deferred acceptance algorithms. Second, we study the computational problem of adding or removing seats to either match a fixed worker-firm pair in some stable matching or make a fixed matching stable with respect to the modified problem. We develop polynomial-time algorithms for these problems when only the overall change in the firms' capacities is restricted, and show NP-hardness when there are additional constraints for individual firms. Lastly, we compare capacity modification with the classical model of preference manipulation by firms and identify scenarios under which one mode of manipulation outperforms the other. We find that a threshold on a given firm's capacity, which we call its peak, crucially determines the effectiveness of different manipulation actions.

翻译：本研究探讨了工人与企业在多对一稳定匹配中的容量调整问题。我们的目标是系统性地分析当企业增加或减少部分席位时，稳定匹配集合如何变化。我们取得以下三项主要成果：首先，我们考察了在工人主导与企业主导的延迟接受算法框架下，容量变化如何影响工人和企业的匹配结果改善或恶化。其次，我们研究了通过增减席位实现以下两种目标的计算问题：(1) 使特定工人-企业组合出现在某个稳定匹配中；(2) 使特定匹配在调整后的问题中保持稳定性。针对仅限制企业总容量变化的情况，我们提出了多项式时间算法；而对于存在单个企业额外约束的情形，我们证明了该问题的NP难性。最后，我们将容量调整机制与企业偏好操纵的经典模型进行对比，识别了不同操纵策略占优的场景。研究发现，特定企业的容量阈值（我们称之为峰值）是决定不同操纵行为有效性的关键因素。