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The lattice of envy-free many-to-many matchings with contracts

Author

Listed:
  • Agustin G. Bonifacio
  • Nadia Guinazu
  • Noelia Juarez
  • Pablo Neme
  • Jorge Oviedo

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

  • Agustin G. Bonifacio & Nadia Guinazu & Noelia Juarez & Pablo Neme & Jorge Oviedo, 2022. "The lattice of envy-free many-to-many matchings with contracts," Papers 2206.10758, arXiv.org.
    • Handle: RePEc:arx:papers:2206.10758
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    References listed on IDEAS

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    1. 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.
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    More about this item

    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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