{"paper":{"title":"Stable Matchings with Choice Correspondences Under Acyclicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Stable matchings exist in many-to-many markets when choice correspondences are substitutable and generally acyclic.","cross_cats":[],"primary_cat":"econ.TH","authors_text":"Mihir Bhattacharya, Ojasvi Khare, Varun Bansal","submitted_at":"2026-03-24T10:18:07Z","abstract_excerpt":"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 "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Choice correspondences satisfy substitutability together with the newly introduced general acyclicity condition (weaker than path independence) for the many-to-many case.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Stable matchings exist under substitutability and general acyclicity for choice correspondences in many-to-many markets, constructed via a Grow or Discard algorithm that avoids permanent rejection of contracts.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Stable matchings exist in many-to-many markets when choice correspondences are substitutable and generally acyclic.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9a60602f5c6989ddca36930b931928de919f39b76c02acdc3baaa36e76cc32b6"},"source":{"id":"2603.23038","kind":"arxiv","version":5},"verdict":{"id":"b16ff5fa-2fe5-4cd2-9bcf-2f1e2885898e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:19:15.770611Z","strongest_claim":"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.","one_line_summary":"Stable matchings exist under substitutability and general acyclicity for choice correspondences in many-to-many markets, constructed via a Grow or Discard algorithm that avoids permanent rejection of contracts.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Choice correspondences satisfy substitutability together with the newly introduced general acyclicity condition (weaker than path independence) for the many-to-many case.","pith_extraction_headline":"Stable matchings exist in many-to-many markets when choice correspondences are substitutable and generally acyclic."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.23038/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}