随机匹配市场中的信号机制与面试
From signaling to interviews in random matching markets
Maxwell Allman, Itai Ashlagi, Amin Saberi, Sophie H. Yu
AI 速览：研究在带面试后冲击的集中式随机匹配市场中，申请人向有限数量偏好对象发送信号如何减少面试并影响临时稳定性。
In two-sided labor markets, interviews precede matches. Rising interview volumes in medical residency markets have motivated signaling mechanisms that let applicants express interest in a limited number of partners. We study how signaling reduces interviews in centralized random matching markets with post-interview shocks. We focus on interim stability, which ensures that agents do not regret not interviewing with each other. A matching is almost interim stable if it becomes interim stable after removing a vanishing fraction of agents. We consider markets with $n$ agents in which agents on the short side, long side, or both sides signal their top $d$ preferred partners. An interview occurs whenever at least one party signals the other. When the probability of a nonnegative interview shock is bounded away from zero and $d=ω(1)$, short-side signaling leads to almost interim stable matchings. Long-side signaling can fail in strongly imbalanced markets when pre-interview scores outweigh interview shocks. In balanced markets without interview shocks, both-side signaling fails to achieve almost interim stability when $d=o(\log n)$. For larger $d \ge Ω(\log^2 n)$, under the same probability condition, short-side signaling achieves perfect interim stability, while long-side signaling can fail in imbalanced markets. We extend these findings to propose a signaling mechanism for multi-tiered random markets and identify conditions for incentive compatibility. A technical contribution is the analysis of a message-passing algorithm for stable matchings on trees, together with local availability certificates used to study interim stability on general graphs.