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Stable Matching with Interviews

Authors Itai Ashlagi , Jiale Chen , Mohammad Roghani , Amin Saberi

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Author Details

Itai Ashlagi
  • Stanford University, CA, USA
Jiale Chen
  • Stanford University, CA, USA
Mohammad Roghani
  • Stanford University, CA, USA
Amin Saberi
  • Stanford University, CA, USA

Funding

The authors acknowledge the support of NSF awards 2209520, 2312156, and a gift from CISCO.

Cite As Get BibTex

Itai Ashlagi, Jiale Chen, Mohammad Roghani, and Amin Saberi. Stable Matching with Interviews. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 12:1-12:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.12

Abstract

In several two-sided markets, including labor and dating, agents typically have limited information about their preferences prior to mutual interactions. This issue can result in matching frictions, as arising in the labor market for medical residencies, where high application rates are followed by a large number of interviews. Yet, the extensive literature on two-sided matching primarily focuses on models where agents know their preferences, leaving the interactions necessary for preference discovery largely overlooked. This paper studies this problem using an algorithmic approach, extending Gale-Shapley’s deferred acceptance to this context.
Two algorithms are proposed. The first is an adaptive algorithm that expands upon Gale-Shapley’s deferred acceptance by incorporating interviews between applicants and positions. Similar to deferred acceptance, one side sequentially proposes to the other. However, the order of proposals is carefully chosen to ensure an interim stable matching is found. Furthermore, with high probability, the number of interviews conducted by each applicant or position is limited to O(log² n).
In many seasonal markets, interactions occur more simultaneously, consisting of an initial interview phase followed by a clearing stage. We present a non-adaptive algorithm for generating a single stage set of in tiered random markets. The algorithm finds an interim stable matching in such markets while assigning no more than O(log³ n) interviews to each applicant or position.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
Keywords
  • Stable Matching
  • Gale–Shapley Algorithm
  • Algorithmic Game Theory

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