# American Institute of Mathematical Sciences

doi: 10.3934/jdg.2021001

## A note on the lattice structure for matching markets via linear programming

 Av. Italia 1556, San Luis, Argentina

Received  June 2020 Revised  November 2020 Published  December 2020

Fund Project: *Instituto de Matemática Aplicada San Luis, Universidad Nacional de San Luis and CONICET, San Luis, Argentina. RedNIE. We are grateful to the anonymous referees for their valuable comments. We acknowledge financial support from the UNSL through grant 032016, and from the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) through grant PIP 112-200801-00655, from Agencia Nacional de Promoción Científica y Tecnológica through grant PICT 2017-2355

Given two stable matchings in a many-to-one matching market with $q$-responsive preferences, by manipulating the objective function of the linear program that characterizes the stable matching set, we compute the least upper bound and greatest lower bound between them.

Citation: Pablo Neme, Jorge Oviedo. A note on the lattice structure for matching markets via linear programming. Journal of Dynamics & Games, doi: 10.3934/jdg.2021001
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