On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game

Autores
Arribillaga, Roberto Pablo; Massó, Jordi; Neme, Alejandro José
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study cooperative and competitive solutions for a many-to-many generalization of Shapley and Shubik’s (1971) assignment game. We consider the Core, three other notions of group stability, and two alternative definitions of competitive equilibrium. We show that (i) each group stable set is closely related to the Core of certain games defined using a proper notion of blocking and (ii) each group stable set contains the set of payoff vectors associated with the two definitions of competitive equilibrium. We also show that all six solutions maintain a strictly nested structure. Moreover, each solution can be identified with a set of matrices of (discriminated) prices which indicate how gains from trade are distributed among buyers and sellers. In all cases such matrices arise as solutions of a system of linear inequalities. Hence, all six solutions have the same properties from a structural and computational point of view.
Fil: Arribillaga, Roberto Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Matemática Aplicada de San Luis; Argentina
Fil: Massó, Jordi. Universidad Autonoma de Barcelona. Departamento de Economia y Historia Economica; 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
Materia
ASSIGNMENT GAME
CORE
GROUP STABLE SET
COMPETITIVE EQUILIBRIUM
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/5803
Acceder
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network_name_str CONICET Digital (CONICET)
spelling On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment GameArribillaga, Roberto PabloMassó, JordiNeme, Alejandro JoséASSIGNMENT GAMECOREGROUP STABLE SETCOMPETITIVE EQUILIBRIUMhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study cooperative and competitive solutions for a many-to-many generalization of Shapley and Shubik’s (1971) assignment game. We consider the Core, three other notions of group stability, and two alternative definitions of competitive equilibrium. We show that (i) each group stable set is closely related to the Core of certain games defined using a proper notion of blocking and (ii) each group stable set contains the set of payoff vectors associated with the two definitions of competitive equilibrium. We also show that all six solutions maintain a strictly nested structure. Moreover, each solution can be identified with a set of matrices of (discriminated) prices which indicate how gains from trade are distributed among buyers and sellers. In all cases such matrices arise as solutions of a system of linear inequalities. Hence, all six solutions have the same properties from a structural and computational point of view.Fil: Arribillaga, Roberto Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Matemática Aplicada de San Luis; ArgentinaFil: Massó, Jordi. Universidad Autonoma de Barcelona. Departamento de Economia y Historia Economica; EspañaFil: Neme, Alejandro José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Matemática Aplicada de San Luis; ArgentinaHindawi Publishing Corporation2014-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/5803Arribillaga, Roberto Pablo; Massó, Jordi; Neme, Alejandro José; On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game; Hindawi Publishing Corporation; Journal of Applied Mathematics; 2014; 2-2014; 190614-1906141110-757Xenginfo:eu-repo/semantics/altIdentifier/url/http://www.hindawi.com/journals/jam/2014/190614info:eu-repo/semantics/altIdentifier/doi/10.1155/2014/190614info:eu-repo/semantics/altIdentifier/doi/info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:33:45Zoai:ri.conicet.gov.ar:11336/5803instacron: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:34982025-10-15 15:33:45.951CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game
title On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game
spellingShingle On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game
Arribillaga, Roberto Pablo
ASSIGNMENT GAME
CORE
GROUP STABLE SET
COMPETITIVE EQUILIBRIUM
title_short On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game
title_full On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game
title_fullStr On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game
title_full_unstemmed On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game
title_sort On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game
dc.creator.none.fl_str_mv Arribillaga, Roberto Pablo
Massó, Jordi
Neme, Alejandro José
author Arribillaga, Roberto Pablo
author_facet Arribillaga, Roberto Pablo
Massó, Jordi
Neme, Alejandro José
author_role author
author2 Massó, Jordi
Neme, Alejandro José
author2_role author
author
dc.subject.none.fl_str_mv ASSIGNMENT GAME
CORE
GROUP STABLE SET
COMPETITIVE EQUILIBRIUM
topic ASSIGNMENT GAME
CORE
GROUP STABLE SET
COMPETITIVE EQUILIBRIUM
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study cooperative and competitive solutions for a many-to-many generalization of Shapley and Shubik’s (1971) assignment game. We consider the Core, three other notions of group stability, and two alternative definitions of competitive equilibrium. We show that (i) each group stable set is closely related to the Core of certain games defined using a proper notion of blocking and (ii) each group stable set contains the set of payoff vectors associated with the two definitions of competitive equilibrium. We also show that all six solutions maintain a strictly nested structure. Moreover, each solution can be identified with a set of matrices of (discriminated) prices which indicate how gains from trade are distributed among buyers and sellers. In all cases such matrices arise as solutions of a system of linear inequalities. Hence, all six solutions have the same properties from a structural and computational point of view.
Fil: Arribillaga, Roberto Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Matemática Aplicada de San Luis; Argentina
Fil: Massó, Jordi. Universidad Autonoma de Barcelona. Departamento de Economia y Historia Economica; 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
description We study cooperative and competitive solutions for a many-to-many generalization of Shapley and Shubik’s (1971) assignment game. We consider the Core, three other notions of group stability, and two alternative definitions of competitive equilibrium. We show that (i) each group stable set is closely related to the Core of certain games defined using a proper notion of blocking and (ii) each group stable set contains the set of payoff vectors associated with the two definitions of competitive equilibrium. We also show that all six solutions maintain a strictly nested structure. Moreover, each solution can be identified with a set of matrices of (discriminated) prices which indicate how gains from trade are distributed among buyers and sellers. In all cases such matrices arise as solutions of a system of linear inequalities. Hence, all six solutions have the same properties from a structural and computational point of view.
publishDate 2014
dc.date.none.fl_str_mv 2014-02
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/11336/5803
Arribillaga, Roberto Pablo; Massó, Jordi; Neme, Alejandro José; On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game; Hindawi Publishing Corporation; Journal of Applied Mathematics; 2014; 2-2014; 190614-190614
1110-757X
url http://hdl.handle.net/11336/5803
identifier_str_mv Arribillaga, Roberto Pablo; Massó, Jordi; Neme, Alejandro José; On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game; Hindawi Publishing Corporation; Journal of Applied Mathematics; 2014; 2-2014; 190614-190614
1110-757X
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.hindawi.com/journals/jam/2014/190614
info:eu-repo/semantics/altIdentifier/doi/10.1155/2014/190614
info:eu-repo/semantics/altIdentifier/doi/
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Hindawi Publishing Corporation
publisher.none.fl_str_mv Hindawi Publishing Corporation
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 13.22299

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