From signaling to interviews in random matching markets

Maxwell Allman, Itai Ashlagi, Amin Saberi and Sophie H. Yu

Papers from arXiv.org

Abstract: 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 $d=\omega(1)$, 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 $d \ge \Omega(\log^2 n)$, 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.

Date: 2025-01, Revised 2026-10
New Economics Papers: this item is included in nep-des and nep-mic
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