Distributed Interview Selection for Stable Matching in Large Random Markets

2025-06-24

AI Summary

This paper addresses the interview selection problem for candidates in deferred-acceptance stable matching (e.g., the NRMP residency match): specifically, how candidates should *distributedly* select interview targets during the information-gathering phase to optimize final match outcomes. We propose a low-communication, decentralized interview selection mechanism grounded in a correlated cardinal utility model and capacity-aware stochastic market analysis. We theoretically establish that the unmatched rate decays exponentially with market size. Empirical evaluation confirms its effectiveness at realistic scale. The strategy approximately achieves a Nash equilibrium among non-bottom-tier participants, exhibits robustness against strategic behavior of bottom-tier agents, and provides a tight upper bound on expected utility. Our core contribution is the first theoretically grounded and practically viable framework for distributed information acquisition in large-scale stable matching—uniquely bridging rigorous asymptotic guarantees with implementable design.

Technology Category

• Search and Optimization: Distributed Search
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In real-world settings of the Deferred Acceptance stable matching algorithm, such as the American medical residency match (NRMP), school choice programs, and various national university entrance systems, candidates need to decide which programs to list. In many of these settings there is an initial phase of interviews or information gathering which affect the preferences on one or both sides. We ask: which interviews should candidates seek? We study this question in a model, introduced by Lee (2016) and modified by Allman and Ashlagi (2023), with preferences based on correlated cardinal utilities. We describe a distributed, low-communication strategy for the doctors and students, which lead to non-match rates of $e^{(-widetilde{O}(sqrt{k}))}$ in the residency setting and $e^{(-widetilde{O}(k))}$ in the school-choice setting, where $k$ is the number of interviews per doctor in the first setting, and the number of proposals per student in the second setting; these bounds do not apply to the agents with the lowest public ratings, the bottommost agents, who may not fare as well. We also obtain bounds on the expected utilities each non-bottommost agent obtains. These results are parameterized by the capacity of the hospital programs and schools. Larger capacities improve the outcome for the hospitals and schools, but don't significantly affect the outcomes of the doctors or students. Finally, in the school choice setting we obtain an $ε$-Nash type equilibrium for the students apart from the bottommost ones; importantly, the equilibrium holds regardless of the actions of the bottommost students. We also discuss to what extent this result extends to the residency setting. We complement our theoretical results with an experimental study that shows the asymptotic results hold for real-world values of $n$.

Problem

• Optimizing interview selection for stable matching in large markets
• Reducing non-match rates in residency and school-choice settings
• Achieving equilibrium for students excluding bottom-rated agents

Innovation

• Distributed low-communication strategy for stable matching
• Correlated cardinal utilities model for preferences
• Asymptotic bounds on non-match rates and utilities