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Stable Matchings with Choice Correspondences Under Acyclicity

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  • Varun Bansal
  • Mihir Bhattacharya
  • Ojasvi Khare

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.

Suggested Citation

  • Varun Bansal & Mihir Bhattacharya & Ojasvi Khare, 2026. "Stable Matchings with Choice Correspondences Under Acyclicity," Papers 2603.23038, arXiv.org, revised May 2026.
    • Handle: RePEc:arx:papers:2603.23038
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    References listed on IDEAS

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    1. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    2. A. Alkan & D. Gale, 2003. "Stable Schedule Matching under Revealed Preference," Springer Books, in: Leon A. Petrosyan & David W. K. Yeung (ed.), ICM Millennium Lectures on Games, pages 3-19, Springer.
    3. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, vol. 112(2), pages 289-306, October.
    4. Orhan Ayg?n & Tayfun S?nmez, 2013. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 103(5), pages 2050-2051, August.
    5. Ahmet Alkan, 2001. "original papers : On preferences over subsets and the lattice structure of stable matchings," Review of Economic Design, Springer;Society for Economic Design, vol. 6(1), pages 99-111.
    6. Charles Blair, 1988. "The Lattice Structure of the Set of Stable Matchings with Multiple Partners," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 619-628, November.
    7. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    8. John William Hatfield & Fuhito Kojima, 2008. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 98(3), pages 1189-1194, June.
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    Keywords

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    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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