Agustin G. Bonifacio, Noelia Juarez, Paola B. Manasero
{"title":"Lattice operations for the stable set in substitutable matching markets via re-equilibration dynamics","authors":"Agustin G. Bonifacio, Noelia Juarez, Paola B. Manasero","doi":"arxiv-2407.21198","DOIUrl":null,"url":null,"abstract":"We compute the lattice operations for the (pairwise) stable set in two-sided\nmatching markets where only substitutability on agents' choice functions is\nimposed. To do this, we use Tarski operators defined on the lattices of\nworker-quasi-stable and firm-quasi-stable matchings. These operators resemble\nlay-off and vacancy chain dynamics, respectively. First, we compute the lattice\noperations in the many-to-one model. Then, we extend these operations to a\nmany-to-many model with substitutable choice functions on one side and\nresponsive preferences on the other, via a morphism that relates many-to-one\nwith many-to-many matchings in a natural way. Finally, we present the lattice\noperations in the many-to-many model with substitutable choice functions on\nboth sides.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"10 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - ECON - Theoretical Economics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.21198","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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 do this, we use Tarski operators defined on the lattices of
worker-quasi-stable and firm-quasi-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 choice functions 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 present the lattice
operations in the many-to-many model with substitutable choice functions on
both sides.
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