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

Author

Listed:
  • Noelia Juárez

    (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 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 mar- ket. Moreover, these lattices are dual.

Suggested Citation

  • Noelia Juárez & Pablo Neme & Jorge Oviedo, 2020. "Lattice structure of the random stable set in many-to-many matching markets," Working Papers 18, Red Nacional de Investigadores en Economía (RedNIE).
    • Handle: RePEc:aoz:wpaper:18
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    Cited by:

    1. Chuanyang Ruan & Sinong Lin, 2025. "Fermatean Fuzzy Two-Sided Matching Model Considering Regret Aversion and Matching Willingness," Mathematics, MDPI, vol. 13(20), pages 1-29, October.
    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.
    3. Aziz, Haris & Brandl, Florian, 2022. "The vigilant eating rule: A general approach for probabilistic economic design with constraints," Games and Economic Behavior, Elsevier, vol. 135(C), pages 168-187.

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    Keywords

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    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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