Matching with Choice Correspondences: Persistence, Symmetry, and Stability

Varun Bansal, Mihir Bhattacharya and Ojasvi Khare ()

Papers from arXiv.org

Abstract: We study the existence of stable matchings in markets where agents are described by choice correspondences rather than preference relations. For many-to-many matching markets, we introduce a new condition called Individually Rational Persistence (IRP) and show that substitutability together with IRP guarantees the existence of a CY-stable matching. Our proof is constructive and yields a simple symmetric algorithm that processes contracts one at a time. Unlike Deferred Acceptance, it has no proposing side, treats firms and workers identically, and makes every accepted contract permanent. We further show that path independence and IRP are logically independent, so IRP provides an alternative sufficient condition for stable matching. For one-to-one matching markets, we introduce a replacement-based notion of stability together with a binary acyclicity condition on pairwise choices, and show that this condition guarantees the existence of stable matchings.

Date: 2026-03, Revised 2026-07
New Economics Papers: this item is included in nep-dcm, nep-des and nep-mic
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