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A characterization of strongly stable fractional matchings

Author

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  • Pablo A. Neme

    (Universidad Nacional de San Luis and CONICET)

  • Jorge Oviedo

    (Universidad Nacional de San Luis and CONICET)

Abstract

In this paper, we characterize the strongly stable fractional matchings for the marriage model as the union of the convex hull of connected sets of stable matchings. Moreover, we present an algorithm that computes the set of matchings necessary to generate the above-mentioned connected sets. Finally, we show that the set of strongly stable fractional matchings has a lattice structure.

Suggested Citation

  • Pablo A. Neme & Jorge Oviedo, 2020. "A characterization of strongly stable fractional matchings," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 97-122, April.
    • Handle: RePEc:spr:topjnl:v:28:y:2020:i:1:d:10.1007_s11750-019-00528-y
    DOI: 10.1007/s11750-019-00528-y
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    References listed on IDEAS

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    1. Alvin E. Roth & Uriel G. Rothblum & John H. Vande Vate, 1993. "Stable Matchings, Optimal Assignments, and Linear Programming," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 803-828, November.
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    Cited by:

    1. Neme, Pablo & Oviedo, Jorge, 2021. "On the set of many-to-one strongly stable fractional matchings," Mathematical Social Sciences, Elsevier, vol. 110(C), pages 1-13.
    2. 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.

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