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.
Token systems support repeated service exchange without monetary transfers, but their viability depends on the stability of token balances. We study token systems with compatibility constraints among agents. A requester is randomly sampled in each period, and only a few randomly sampled agents are available to provide service. We establish a necessary and sufficient condition for stability and show that the minimum-token rule, which selects the available provider with the lowest token balance, achieves the optimal stability region. We then apply this stability criterion to a random token system generated from stochastic block models with uniformly sampled requesters. We tightly characterize the stability regime by identifying two obstructions to stability: insufficient service opportunities for a group of communities or for an individual agent.
Süleyman Kerimov, Pengyu Qian, Mingwei Yang, Sophie H. Yu
We study centralized two-way dynamic matching markets in which agents arrive stochastically over time and wait in queues associated with their types. We focus on static priority policies that assign each agent type a fixed ranking over its neighbors and make online matching decisions using only queue availability. We propose the General Priority ($\mathbf{GP}$) policy, which builds on the Tree Priority ($\mathbf{TP}$) policy introduced in [KAG25]. Under the general position gap condition, $\mathbf{GP}$ selects matches using a nondegenerate optimal basic solution of the fluid relaxation. It prioritizes children over parents within trees and consistently gives clockwise neighbors priority over counterclockwise neighbors on each cycle. We establish the optimal all-time regret scaling $O(ε^{-1})$ for $\mathbf{GP}$ on general two-way matching networks, where the general position gap $ε$ measures the fluid relaxation's distance from degeneracy. In particular, this resolves the conjecture by [KAG25] on the optimal $ε$-dependence for $\mathbf{TP}$.