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On the set of many-to-one strongly stable fractional matchings

Author

Listed:
  • Pablo Neme

    (Universidad Nacional de San Luis/CONICET)

  • Jorge Oviedo

    (Universidad Nacional de San Luis/CONICET)

Abstract

For a many-to-one matching market where firms have strict and q-responsive preferences, we give a characterization of the set of strongly stable fractional match- ings as the union of the convex hull of all connected sets of stable matchings. We also prove that a strongly stable fractional matching is represented as a convex combination of stable matchings that are ordered in the common preferences of all firms.

Suggested Citation

  • Pablo Neme & Jorge Oviedo, 2020. "On the set of many-to-one strongly stable fractional matchings," Working Papers 19, Red Nacional de Investigadores en Economía (RedNIE).
    • Handle: RePEc:aoz:wpaper:19
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    References listed on IDEAS

    as
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    6. Abeledo, Hernan G & Blum, Yosef & Rothblum, Uriel G, 1996. "Canonical Monotone Decompositions of Fractional Stable Matchings," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(2), pages 161-176.
    7. Federico Echenique & Sangmok Lee & Matthew Shum & M. Bumin Yenmez, 2013. "The Revealed Preference Theory of Stable and Extremal Stable Matchings," Econometrica, Econometric Society, vol. 81(1), pages 153-171, January.
    8. Roth, Alvin E, 1986. "On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets," Econometrica, Econometric Society, vol. 54(2), pages 425-427, March.
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    10. Jay Sethuraman & Chung-Piaw Teo & Liwen Qian, 2006. "Many-to-One Stable Matching: Geometry and Fairness," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 581-596, August.
    11. 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.
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    Keywords

    Matching Markets Many-to-one Matching Market Strongly Stable Fractional Matchings Linear Programming;

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