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Lattice Operations for the Stable Set in Substitutable Matching Markets via re-equilibration Dynamics

Author

Listed:
  • Agustín Bonifacio

    (UNSL-CONICET)

  • Noelia Juarez

    (UNSL-CONICET)

  • Paola Manasero

    (UNSL-CONICET)

Abstract

We compute the lattice operations for the (pairwise) stable set in two-sided matching markets where only substitutability on agents’ choice functions is imposed. To dothis, we use Tarski operators defined on the lattices of worker-quasi-stable and firmquasi-stable matchings. These operators resemble lay-off and vacancy chain dynamics, respectively. First, we compute the lattice operations in the many-to-one model. Then, we extend these operations to a many-to-many model with substitutable choicefunctions on one side and responsive preferences on the other, via a morphism that relates many-to-one with many-to-many matchings in a natural way. Finally, we presentthe lattice operations in the many-to-many model with substitutable choice functionson both sides.

Suggested Citation

  • Agustín Bonifacio & Noelia Juarez & Paola Manasero, 2024. "Lattice Operations for the Stable Set in Substitutable Matching Markets via re-equilibration Dynamics," Working Papers 333, Red Nacional de Investigadores en Economía (RedNIE).
    • Handle: RePEc:aoz:wpaper:333
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    File URL: https://rednie.eco.unc.edu.ar/files/DT/333.pdf
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    Keywords

    two-sided matching; worker-quasi-stability; firm-quasi-stability; Tarski operator; lattice operations; re-equilibration;
    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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