On the geometric dimension of the core of a TU-game

Autores
Cesco, Juan Carlos; Marchi, Ezio
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we state a condition which characterizes the sub-class of TU-games (games with transferable utility) having non-empty core of dimension k; for any 0 <= k <= n. It improves and generalizes the adding up (AU) property used by Brandenburger and Stuart for the case k = 0 (games with one-point core) to study biform games. It also embraces one of the two conditions stated by Zhao for the case k = n - 1 (games having core with non-empty interior, relative to the set of pre-imputations) while studying some geometric properties of the core. The condition allows us to show that all the information about the geometric dimension of the core is contained in the vector of excesses associated to the nucleolus of the game. It also allows us to get some insight about the geometric properties of the cone of balanced games as well. In particular, we prove that all the games in the relative interior of each face of the cone have a core with the same geometric dimension. This fact is illustrated for the case of three-person games. We also present a couple of examples to show how the results of the paper can be used to deal with biform games from a new perspective
Fil: Cesco, Juan Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Matemática Aplicada de San Luis; Argentina
Fil: Marchi, Ezio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Matemática Aplicada de San Luis; Argentina
Materia
Tu-Games
Core
Geometric Dimension
Biform Games
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/14644
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/14644
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On the geometric dimension of the core of a TU-gameCesco, Juan CarlosMarchi, EzioTu-GamesCoreGeometric DimensionBiform Gameshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we state a condition which characterizes the sub-class of TU-games (games with transferable utility) having non-empty core of dimension k; for any 0 <= k <= n. It improves and generalizes the adding up (AU) property used by Brandenburger and Stuart for the case k = 0 (games with one-point core) to study biform games. It also embraces one of the two conditions stated by Zhao for the case k = n - 1 (games having core with non-empty interior, relative to the set of pre-imputations) while studying some geometric properties of the core. The condition allows us to show that all the information about the geometric dimension of the core is contained in the vector of excesses associated to the nucleolus of the game. It also allows us to get some insight about the geometric properties of the cone of balanced games as well. In particular, we prove that all the games in the relative interior of each face of the cone have a core with the same geometric dimension. This fact is illustrated for the case of three-person games. We also present a couple of examples to show how the results of the paper can be used to deal with biform games from a new perspectiveFil: Cesco, Juan Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Matemática Aplicada de San Luis; ArgentinaFil: Marchi, Ezio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Matemática Aplicada de San Luis; ArgentinaAmerican Scientific Publishers2014-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/14644Cesco, Juan Carlos; Marchi, Ezio; On the geometric dimension of the core of a TU-game; American Scientific Publishers; Journal of Advanced Mathematics and Applications; 3; 1; 6-2014; 55-592156-75652156-7557enginfo:eu-repo/semantics/altIdentifier/url/http://www.ingentaconnect.com/content/asp/jama/2014/00000003/00000001/art00008info:eu-repo/semantics/altIdentifier/doi/10.1166/jama.2014.1051info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:47:18Zoai:ri.conicet.gov.ar:11336/14644instacron: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:34982025-09-03 09:47:18.634CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the geometric dimension of the core of a TU-game
title On the geometric dimension of the core of a TU-game
spellingShingle On the geometric dimension of the core of a TU-game
Cesco, Juan Carlos
Tu-Games
Core
Geometric Dimension
Biform Games
title_short On the geometric dimension of the core of a TU-game
title_full On the geometric dimension of the core of a TU-game
title_fullStr On the geometric dimension of the core of a TU-game
title_full_unstemmed On the geometric dimension of the core of a TU-game
title_sort On the geometric dimension of the core of a TU-game
dc.creator.none.fl_str_mv Cesco, Juan Carlos
Marchi, Ezio
author Cesco, Juan Carlos
author_facet Cesco, Juan Carlos
Marchi, Ezio
author_role author
author2 Marchi, Ezio
author2_role author
dc.subject.none.fl_str_mv Tu-Games
Core
Geometric Dimension
Biform Games
topic Tu-Games
Core
Geometric Dimension
Biform Games
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we state a condition which characterizes the sub-class of TU-games (games with transferable utility) having non-empty core of dimension k; for any 0 <= k <= n. It improves and generalizes the adding up (AU) property used by Brandenburger and Stuart for the case k = 0 (games with one-point core) to study biform games. It also embraces one of the two conditions stated by Zhao for the case k = n - 1 (games having core with non-empty interior, relative to the set of pre-imputations) while studying some geometric properties of the core. The condition allows us to show that all the information about the geometric dimension of the core is contained in the vector of excesses associated to the nucleolus of the game. It also allows us to get some insight about the geometric properties of the cone of balanced games as well. In particular, we prove that all the games in the relative interior of each face of the cone have a core with the same geometric dimension. This fact is illustrated for the case of three-person games. We also present a couple of examples to show how the results of the paper can be used to deal with biform games from a new perspective
Fil: Cesco, Juan Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Matemática Aplicada de San Luis; Argentina
Fil: Marchi, Ezio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Matemática Aplicada de San Luis; Argentina
description In this paper we state a condition which characterizes the sub-class of TU-games (games with transferable utility) having non-empty core of dimension k; for any 0 <= k <= n. It improves and generalizes the adding up (AU) property used by Brandenburger and Stuart for the case k = 0 (games with one-point core) to study biform games. It also embraces one of the two conditions stated by Zhao for the case k = n - 1 (games having core with non-empty interior, relative to the set of pre-imputations) while studying some geometric properties of the core. The condition allows us to show that all the information about the geometric dimension of the core is contained in the vector of excesses associated to the nucleolus of the game. It also allows us to get some insight about the geometric properties of the cone of balanced games as well. In particular, we prove that all the games in the relative interior of each face of the cone have a core with the same geometric dimension. This fact is illustrated for the case of three-person games. We also present a couple of examples to show how the results of the paper can be used to deal with biform games from a new perspective
publishDate 2014
dc.date.none.fl_str_mv 2014-06
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/11336/14644
Cesco, Juan Carlos; Marchi, Ezio; On the geometric dimension of the core of a TU-game; American Scientific Publishers; Journal of Advanced Mathematics and Applications; 3; 1; 6-2014; 55-59
2156-7565
2156-7557
url http://hdl.handle.net/11336/14644
identifier_str_mv Cesco, Juan Carlos; Marchi, Ezio; On the geometric dimension of the core of a TU-game; American Scientific Publishers; Journal of Advanced Mathematics and Applications; 3; 1; 6-2014; 55-59
2156-7565
2156-7557
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.ingentaconnect.com/content/asp/jama/2014/00000003/00000001/art00008
info:eu-repo/semantics/altIdentifier/doi/10.1166/jama.2014.1051
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Scientific Publishers
publisher.none.fl_str_mv American Scientific Publishers
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 13.13397

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