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Binary operations and lattice structure for a model of matching with contracts

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  • Pepa Risma, Eliana

Abstract

We consider a restricted model of many-to-one matching with contracts and we order the set of stable allocations according both to the unanimous-for-doctors partial ordering and Blair’s partial ordering for hospitals. We define two binary operations to calculate the least upper bound and greatest lower bound for each pair of elements of this set in a simple way. By using these operations, we show that the set of stable allocations has dual lattice structures, thus reflecting an expected counterposition of interests between both sides of the market.

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  • Pepa Risma, Eliana, 2015. "Binary operations and lattice structure for a model of matching with contracts," Mathematical Social Sciences, Elsevier, vol. 73(C), pages 6-12.
    • Handle: RePEc:eee:matsoc:v:73:y:2015:i:c:p:6-12
    DOI: 10.1016/j.mathsocsci.2014.11.001
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    References listed on IDEAS

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    1. 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.
    2. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    3. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    4. 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.
    5. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2000. "Single Agents and the Set of Many-to-One Stable Matchings," Journal of Economic Theory, Elsevier, vol. 91(1), pages 91-105, March.
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    Cited by:

    1. Juárez, Noelia & Neme, Pablo & Oviedo, Jorge, 2022. "Lattice structure of the random stable set in many-to-many matching markets," Games and Economic Behavior, Elsevier, vol. 132(C), pages 255-273.
    2. Pablo R. Arribillaga & Eliana Pepa Risma, 2023. "Obvious Manipulations in Matching with and without Contracts," Working Papers 257, Red Nacional de Investigadores en Economía (RedNIE).
    3. He Yiming & Luo Biliang & Zou Baoling, 2018. "Do Heterogeneous Agricultural Factors Affect Farmland Contractual Choice?—Evidence from China," Man and the Economy, De Gruyter, vol. 5(1), pages 1-12, June.
    4. R. Pablo Arribillaga & E. Pepa Risma, 2023. "Obvious Manipulations in Matching without and with Contracts," Papers 2306.17773, arXiv.org, revised Oct 2024.

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