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Core and stability notions in many-to-one matching markets with indifferences

Author

Listed:
  • Agustín G. Bonifacio

    (UNSL-CONICET
    Universidad Nacional de San Luis)

  • Noelia Juarez

    (UNSL-CONICET
    Universidad Nacional de San Luis)

  • Pablo Neme

    (UNSL-CONICET
    Universidad Nacional de San Luis)

  • Jorge Oviedo

    (UNSL-CONICET
    Universidad Nacional de San Luis)

Abstract

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, 2024. "Core and stability notions in many-to-one matching markets with indifferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(1), pages 143-157, March.
    • Handle: RePEc:spr:jogath:v:53:y:2024:i:1:d:10.1007_s00182-023-00865-0
    DOI: 10.1007/s00182-023-00865-0
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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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    5. 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.
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    More about this item

    Keywords

    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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