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Core and Stability Notions in Many-to-one Matching Markets with Indifferences


  • Agustín G. Bonifacio

    (Universidad Nacional de San Luis/CONICET)

  • Noelia Juarez

    (Universidad Nacional de San Luis/CONICET)

  • Pablo Neme

    (Universidad Nacional de San Luis/CONICET)

  • Jorge Oviedo

    (Universidad Nacional de San Luis/CONICET)


In a many-to-one matching model with responsive preferences in which indifferences are allowed, we study three notions of core, three notions of stability, and their relationships. We show that (i) the core contains the stable set, (ii) the strong core coincides with the strongly stable set, and (iii) the super core coincides with the super stable set. We also show how the core and the strong core in markets with indifferences relate to the stable matchings of their associated tie-breaking strict markets.

Suggested Citation

  • Agustín G. Bonifacio & Noelia Juarez & Pablo Neme & Jorge Oviedo, 2022. "Core and Stability Notions in Many-to-one Matching Markets with Indifferences," Working Papers 138, Red Nacional de Investigadores en Economía (RedNIE).
  • Handle: RePEc:aoz:wpaper:138

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    References listed on IDEAS

    1. Roth, Alvin E., 1985. "Common and conflicting interests in two-sided matching markets," European Economic Review, Elsevier, vol. 27(1), pages 75-96, February.
    2. Augustine Kwanashie & David F. Manlove, 2014. "An Integer Programming Approach to the Hospitals/Residents Problem with Ties," Operations Research Proceedings, in: Dennis Huisman & Ilse Louwerse & Albert P.M. Wagelmans (ed.), Operations Research Proceedings 2013, edition 127, pages 263-269, Springer.
    3. Erdil, Aytek & Ergin, Haluk, 2017. "Two-sided matching with indifferences," Journal of Economic Theory, Elsevier, vol. 171(C), pages 268-292.
    4. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match," American Economic Review, American Economic Association, vol. 99(5), pages 1954-1978, December.
    5. Marilda Sotomayor, 2011. "The pareto-stability concept is a natural solution concept for discrete matching markets with indifferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 631-644, August.
    6. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the New York City High School Match," NBER Working Papers 14864, National Bureau of Economic Research, Inc.
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    More about this item


    Matching with indifferences; Stability; Strong Stability; Super Stability; Core; Strong Core; Super Core;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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