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Lattice structure of the random stable set in many-to-many matching markets

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  • Juárez, Noelia
  • Neme, Pablo
  • Oviedo, Jorge

Abstract

We study the lattice structure of the set of random stable matchings for a many-to-many matching market. We define a partial order on the random stable set and present two natural binary operations for computing the least upper bound and the greatest lower bound for each side of the matching market. Then we prove that with these binary operations the set of random stable matchings forms two distributive lattices for the appropriate partial order, one for each side of the market. Moreover, these lattices are dual.

Suggested Citation

  • Juárez, Noelia & Neme, Pablo & Oviedo, Jorge, 2022. "Lattice structure of the random stable set in many-to-many matching markets," Games and Economic Behavior, Elsevier, vol. 132(C), pages 255-273.
    • Handle: RePEc:eee:gamebe:v:132:y:2022:i:c:p:255-273
    DOI: 10.1016/j.geb.2021.12.005
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    2. Haris Aziz & Florian Brandl, 2020. "The Vigilant Eating Rule: A General Approach for Probabilistic Economic Design with Constraints," Papers 2008.08991, arXiv.org, revised Jul 2021.

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    More about this item

    Keywords

    Lattice structure; Random stable matching markets; Many-to-many matching markets;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D49 - Microeconomics - - Market Structure, Pricing, and Design - - - Other

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