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Doctor-Optimal Stability in Unitary Many-to-Many Markets

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  • Yi-You Yang

Abstract

We study bilaterally unitary many-to-many doctor--hospital matching with contracts, taking choice functions as primitives. Doctor choices are substitutable and satisfy irrelevance of rejected contracts, while hospital choices are unilaterally substitutable and satisfy the same condition. Every trajectory of the doctor-proposing cumulative offer process terminates at the greatest stable allocation under the doctor Blair order. We also introduce weakly hospital-quasi-stable allocations and show that they form a finite lattice whose greatest element is stable. Hence, the cumulative-offer outcome, the greatest weakly hospital-quasi-stable allocation, and the doctor-optimal stable allocation coincide. The common allocation is hospital-pessimal in the revealed-choice sense. Under the law of aggregate demand, every agent signs the same number of contracts at all stable allocations.

Suggested Citation

  • Yi-You Yang, 2026. "Doctor-Optimal Stability in Unitary Many-to-Many Markets," Papers 2607.10756, arXiv.org.
    • Handle: RePEc:arx:papers:2607.10756
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    References listed on IDEAS

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    1. Hatfield, John William & Kojima, Fuhito, 2010. "Substitutes and stability for matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1704-1723, September.
    2. Yi-You Yang, 2025. "On the existence of stable matchings with contracts," Theory and Decision, Springer, vol. 98(3), pages 367-372, May.
    3. Bando, Keisuke & Hirai, Toshiyuki, 2026. "Substitutes for nonunitary many-to-many matching with contracts," Games and Economic Behavior, Elsevier, vol. 158(C), pages 527-546.
    4. 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.
    5. Sotomayor, Marilda, 1996. "A Non-constructive Elementary Proof of the Existence of Stable Marriages," Games and Economic Behavior, Elsevier, vol. 13(1), pages 135-137, March.
    6. Kasuya, Yusuke, 2021. "Unilateral substitutability is necessary for doctor-optimal stability," Economics Letters, Elsevier, vol. 207(C).
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