Stable Matchings with Choice Correspondences Under Acyclicity

Varun Bansal, Mihir Bhattacharya and Ojasvi Khare ()

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Abstract: We study the existence of stable matchings when agents have choice correspondences instead of preference relations. We extend the framework of \cite{chambers2017choice} by weakening the path independence assumption. For many-to-many markets, we show that stable matchings exist when choice correspondences satisfy substitutability and a new general acyclicity condition. We provide a constructive proof using a Grow or Discard Algorithm that iteratively expands or eliminates contracts until a strongly maximal individually rational set is reached. We provide an algorithm to obtain stable matchings in which rejected contracts are not permanently discarded, distinguishing our approach significantly from standard DAA-type algorithms. For one-to-one markets, we introduce a replacement-based notion of stability and provide an algorithm that constructs stable matchings when choice correspondences satisfy binary acyclicity, a property weaker than path independence. JEL classification: C62, C78, D01, D47 Keywords: choice correspondences, substitutability, general acyclicity, many-to-many matching, matching with contracts, Grow or Discard algorithm, replacement stability, binary acyclicity.

Date: 2026-03, Revised 2026-04
New Economics Papers: this item is included in nep-dcm, nep-des and nep-mic
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