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The Lattice of Envy-Free Many-to-Many Matchings with Contracts

Author

Listed:
  • Agustín G. Bonifacio

    (Universidad Nacional de San Luis/CONICET)

  • Nadia Guiñazú

    (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)

Abstract

We study envy-free allocations in a many-to-many matching model with contracts in which agents on one side of the market (doctors) are endowed with substitutable choice functions and agents on the other side of the market (hospitals) are endowed with responsive preferences. Envy-freeness is a weakening of stability that allows blocking contracts involving a hospital with a vacant position and a doctor that does not envy any of the doctors that the hospital currently employs. We show that the set of envy-free allocations has a lattice structure. Furthermore, we define a Tarski operator on this lattice and use it to model a vacancy chain dynamic process by which, starting from any envy-free allocation, a stable one is reached.

Suggested Citation

  • Agustín G. Bonifacio & Nadia Guiñazú & Noelia Juarez & Pablo Neme & Jorge Oviedo, 2022. "The Lattice of Envy-Free Many-to-Many Matchings with Contracts," Working Papers 155, Red Nacional de Investigadores en Economía (RedNIE).
    • Handle: RePEc:aoz:wpaper:155
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    File URL: https://rednie.eco.unc.edu.ar/files/DT/155.pdf
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    References listed on IDEAS

    as
    1. Tamás Fleiner, 2003. "A Fixed-Point Approach to Stable Matchings and Some Applications," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 103-126, February.
    2. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2004. "An algorithm to compute the full set of many-to-many stable matchings," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 187-210, March.
    3. 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.
    4. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    5. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
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    More about this item

    Keywords

    Matching; envy-freeness; lattice; Tarski operator; re-equilibration process; vacancy chain.;
    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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