The Blocking Lemma for a many-to-one matching model

Autores
Martínez, Ruth; Massó, Jordi; Neme, Alejandro José; Oviedo, Jorge Armando
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The Blocking Lemma identifies a particular blocking pair for each non-stable and individually rational matching that is preferred by some agents of one side of the market to their optimal stable matching. Its interest lies in the fact that it has been an instrumental result to prove key results on matching. For instance, the fact that in the college admissions problem the workers-optimal stable mechanism is group strategy-proof for the workers and the strong stability theorem in the marriage model follow directly from the Blocking Lemma. However, it is known that the Blocking Lemma and its consequences do not hold in the general many-to-one matching model in which firms have substitutable preference relations. We show that the Blocking Lemma holds for the many-to-one matching model in which firms’ preference relations are, in addition to substitutable, quota q-separable. We also show that the Blocking Lemma holds on a subset of substitutable preference profiles if and only if the workers-optimal stable mechanism is group strategy-proof for the workers on this subset of profiles.
Fil: Martínez, Ruth. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Matemática Aplicada de San Luis; Argentina. Universidad Nacional de San Luis; Argentina
Fil: Massó, Jordi. Universitat Autonoma de Barcelona; España
Fil: Neme, Alejandro José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Matemática Aplicada de San Luis; Argentina. Universidad Nacional de San Luis; Argentina
Fil: Oviedo, Jorge Armando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Matemática Aplicada de San Luis; Argentina. Universidad Nacional de San Luis; Argentina
Materia
Matching
Stability
Blocking Lemma
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/15396
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The Blocking Lemma for a many-to-one matching modelMartínez, RuthMassó, JordiNeme, Alejandro JoséOviedo, Jorge ArmandoMatchingStabilityBlocking Lemmahttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The Blocking Lemma identifies a particular blocking pair for each non-stable and individually rational matching that is preferred by some agents of one side of the market to their optimal stable matching. Its interest lies in the fact that it has been an instrumental result to prove key results on matching. For instance, the fact that in the college admissions problem the workers-optimal stable mechanism is group strategy-proof for the workers and the strong stability theorem in the marriage model follow directly from the Blocking Lemma. However, it is known that the Blocking Lemma and its consequences do not hold in the general many-to-one matching model in which firms have substitutable preference relations. We show that the Blocking Lemma holds for the many-to-one matching model in which firms’ preference relations are, in addition to substitutable, quota q-separable. We also show that the Blocking Lemma holds on a subset of substitutable preference profiles if and only if the workers-optimal stable mechanism is group strategy-proof for the workers on this subset of profiles.Fil: Martínez, Ruth. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Matemática Aplicada de San Luis; Argentina. Universidad Nacional de San Luis; ArgentinaFil: Massó, Jordi. Universitat Autonoma de Barcelona; EspañaFil: Neme, Alejandro José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Matemática Aplicada de San Luis; Argentina. Universidad Nacional de San Luis; ArgentinaFil: Oviedo, Jorge Armando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Matemática Aplicada de San Luis; Argentina. Universidad Nacional de San Luis; ArgentinaElsevier Science2010-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/15396Martínez, Ruth; Massó, Jordi; Neme, Alejandro José; Oviedo, Jorge Armando; The Blocking Lemma for a many-to-one matching model; Elsevier Science; Journal Of Mathematical Economics; 46; 5; 9-2010; 937-9490304-4068enginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0304406810000856info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmateco.2010.08.010info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:49:23Zoai:ri.conicet.gov.ar:11336/15396instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:49:24.185CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The Blocking Lemma for a many-to-one matching model
title The Blocking Lemma for a many-to-one matching model
spellingShingle The Blocking Lemma for a many-to-one matching model
Martínez, Ruth
Matching
Stability
Blocking Lemma
title_short The Blocking Lemma for a many-to-one matching model
title_full The Blocking Lemma for a many-to-one matching model
title_fullStr The Blocking Lemma for a many-to-one matching model
title_full_unstemmed The Blocking Lemma for a many-to-one matching model
title_sort The Blocking Lemma for a many-to-one matching model
dc.creator.none.fl_str_mv Martínez, Ruth
Massó, Jordi
Neme, Alejandro José
Oviedo, Jorge Armando
author Martínez, Ruth
author_facet Martínez, Ruth
Massó, Jordi
Neme, Alejandro José
Oviedo, Jorge Armando
author_role author
author2 Massó, Jordi
Neme, Alejandro José
Oviedo, Jorge Armando
author2_role author
author
author
dc.subject.none.fl_str_mv Matching
Stability
Blocking Lemma
topic Matching
Stability
Blocking Lemma
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The Blocking Lemma identifies a particular blocking pair for each non-stable and individually rational matching that is preferred by some agents of one side of the market to their optimal stable matching. Its interest lies in the fact that it has been an instrumental result to prove key results on matching. For instance, the fact that in the college admissions problem the workers-optimal stable mechanism is group strategy-proof for the workers and the strong stability theorem in the marriage model follow directly from the Blocking Lemma. However, it is known that the Blocking Lemma and its consequences do not hold in the general many-to-one matching model in which firms have substitutable preference relations. We show that the Blocking Lemma holds for the many-to-one matching model in which firms’ preference relations are, in addition to substitutable, quota q-separable. We also show that the Blocking Lemma holds on a subset of substitutable preference profiles if and only if the workers-optimal stable mechanism is group strategy-proof for the workers on this subset of profiles.
Fil: Martínez, Ruth. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Matemática Aplicada de San Luis; Argentina. Universidad Nacional de San Luis; Argentina
Fil: Massó, Jordi. Universitat Autonoma de Barcelona; España
Fil: Neme, Alejandro José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Matemática Aplicada de San Luis; Argentina. Universidad Nacional de San Luis; Argentina
Fil: Oviedo, Jorge Armando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Matemática Aplicada de San Luis; Argentina. Universidad Nacional de San Luis; Argentina
description The Blocking Lemma identifies a particular blocking pair for each non-stable and individually rational matching that is preferred by some agents of one side of the market to their optimal stable matching. Its interest lies in the fact that it has been an instrumental result to prove key results on matching. For instance, the fact that in the college admissions problem the workers-optimal stable mechanism is group strategy-proof for the workers and the strong stability theorem in the marriage model follow directly from the Blocking Lemma. However, it is known that the Blocking Lemma and its consequences do not hold in the general many-to-one matching model in which firms have substitutable preference relations. We show that the Blocking Lemma holds for the many-to-one matching model in which firms’ preference relations are, in addition to substitutable, quota q-separable. We also show that the Blocking Lemma holds on a subset of substitutable preference profiles if and only if the workers-optimal stable mechanism is group strategy-proof for the workers on this subset of profiles.
publishDate 2010
dc.date.none.fl_str_mv 2010-09
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/15396
Martínez, Ruth; Massó, Jordi; Neme, Alejandro José; Oviedo, Jorge Armando; The Blocking Lemma for a many-to-one matching model; Elsevier Science; Journal Of Mathematical Economics; 46; 5; 9-2010; 937-949
0304-4068
url http://hdl.handle.net/11336/15396
identifier_str_mv Martínez, Ruth; Massó, Jordi; Neme, Alejandro José; Oviedo, Jorge Armando; The Blocking Lemma for a many-to-one matching model; Elsevier Science; Journal Of Mathematical Economics; 46; 5; 9-2010; 937-949
0304-4068
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0304406810000856
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmateco.2010.08.010
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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