Cooperative and axiomatic approaches to the knapsack allocation problem

Autores
Arribillaga, Roberto Pablo; Bergantiños, Gustavo
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In the knapsack problem a group of agents want to fill a knapsack with several goods. Two issues must be considered. The first is to decide optimally what goods to select for the knapsack. This issue has been studied in many papers in the literature on Operations Research and Management Science. The second issue is to divide the total revenue among the agents. This issue has been studied in only a few papers, and this is one of them. For each knapsack problem we consider three associated cooperative games. One of them (the pessimistic game) has already been considered in the literature. The other two (realistic and optimistic games) are defined in this paper. The pessimistic and realistic games have non-empty cores but the core of the optimistic game could be empty. We then follow the axiomatic approach. We propose two rules: The first is based on the optimal solution of the knapsack problem. The second is the Shapley value of the so called optimistic game. We offer axiomatic characterizations of both rules.
Fil: Arribillaga, Roberto Pablo. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina
Fil: Bergantiños, Gustavo. Universidad de Vigo; España
Materia
AXIOMATIC APPROACH
COOPERATIVE GAMES
KNAPSACK PROBLEM
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:11336/182769
Acceder
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spelling Cooperative and axiomatic approaches to the knapsack allocation problemArribillaga, Roberto PabloBergantiños, GustavoAXIOMATIC APPROACHCOOPERATIVE GAMESKNAPSACK PROBLEMhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In the knapsack problem a group of agents want to fill a knapsack with several goods. Two issues must be considered. The first is to decide optimally what goods to select for the knapsack. This issue has been studied in many papers in the literature on Operations Research and Management Science. The second issue is to divide the total revenue among the agents. This issue has been studied in only a few papers, and this is one of them. For each knapsack problem we consider three associated cooperative games. One of them (the pessimistic game) has already been considered in the literature. The other two (realistic and optimistic games) are defined in this paper. The pessimistic and realistic games have non-empty cores but the core of the optimistic game could be empty. We then follow the axiomatic approach. We propose two rules: The first is based on the optimal solution of the knapsack problem. The second is the Shapley value of the so called optimistic game. We offer axiomatic characterizations of both rules.Fil: Arribillaga, Roberto Pablo. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; ArgentinaFil: Bergantiños, Gustavo. Universidad de Vigo; EspañaSpringer2021-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/182769Arribillaga, Roberto Pablo; Bergantiños, Gustavo; Cooperative and axiomatic approaches to the knapsack allocation problem; Springer; Annals Of Operations Research; 318; 2; 10-2021; 805-8300254-5330CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/10.1007/s10479-021-04315-6info:eu-repo/semantics/altIdentifier/doi/10.1007/s10479-021-04315-6info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:59:09Zoai:ri.conicet.gov.ar:11336/182769instacron: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:34982025-10-22 11:59:09.58CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Cooperative and axiomatic approaches to the knapsack allocation problem
title Cooperative and axiomatic approaches to the knapsack allocation problem
spellingShingle Cooperative and axiomatic approaches to the knapsack allocation problem
Arribillaga, Roberto Pablo
AXIOMATIC APPROACH
COOPERATIVE GAMES
KNAPSACK PROBLEM
title_short Cooperative and axiomatic approaches to the knapsack allocation problem
title_full Cooperative and axiomatic approaches to the knapsack allocation problem
title_fullStr Cooperative and axiomatic approaches to the knapsack allocation problem
title_full_unstemmed Cooperative and axiomatic approaches to the knapsack allocation problem
title_sort Cooperative and axiomatic approaches to the knapsack allocation problem
dc.creator.none.fl_str_mv Arribillaga, Roberto Pablo
Bergantiños, Gustavo
author Arribillaga, Roberto Pablo
author_facet Arribillaga, Roberto Pablo
Bergantiños, Gustavo
author_role author
author2 Bergantiños, Gustavo
author2_role author
dc.subject.none.fl_str_mv AXIOMATIC APPROACH
COOPERATIVE GAMES
KNAPSACK PROBLEM
topic AXIOMATIC APPROACH
COOPERATIVE GAMES
KNAPSACK PROBLEM
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 the knapsack problem a group of agents want to fill a knapsack with several goods. Two issues must be considered. The first is to decide optimally what goods to select for the knapsack. This issue has been studied in many papers in the literature on Operations Research and Management Science. The second issue is to divide the total revenue among the agents. This issue has been studied in only a few papers, and this is one of them. For each knapsack problem we consider three associated cooperative games. One of them (the pessimistic game) has already been considered in the literature. The other two (realistic and optimistic games) are defined in this paper. The pessimistic and realistic games have non-empty cores but the core of the optimistic game could be empty. We then follow the axiomatic approach. We propose two rules: The first is based on the optimal solution of the knapsack problem. The second is the Shapley value of the so called optimistic game. We offer axiomatic characterizations of both rules.
Fil: Arribillaga, Roberto Pablo. Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina
Fil: Bergantiños, Gustavo. Universidad de Vigo; España
description In the knapsack problem a group of agents want to fill a knapsack with several goods. Two issues must be considered. The first is to decide optimally what goods to select for the knapsack. This issue has been studied in many papers in the literature on Operations Research and Management Science. The second issue is to divide the total revenue among the agents. This issue has been studied in only a few papers, and this is one of them. For each knapsack problem we consider three associated cooperative games. One of them (the pessimistic game) has already been considered in the literature. The other two (realistic and optimistic games) are defined in this paper. The pessimistic and realistic games have non-empty cores but the core of the optimistic game could be empty. We then follow the axiomatic approach. We propose two rules: The first is based on the optimal solution of the knapsack problem. The second is the Shapley value of the so called optimistic game. We offer axiomatic characterizations of both rules.
publishDate 2021
dc.date.none.fl_str_mv 2021-10
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/11336/182769
Arribillaga, Roberto Pablo; Bergantiños, Gustavo; Cooperative and axiomatic approaches to the knapsack allocation problem; Springer; Annals Of Operations Research; 318; 2; 10-2021; 805-830
0254-5330
CONICET Digital
CONICET
url http://hdl.handle.net/11336/182769
identifier_str_mv Arribillaga, Roberto Pablo; Bergantiños, Gustavo; Cooperative and axiomatic approaches to the knapsack allocation problem; Springer; Annals Of Operations Research; 318; 2; 10-2021; 805-830
0254-5330
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/10.1007/s10479-021-04315-6
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10479-021-04315-6
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 Springer
publisher.none.fl_str_mv Springer
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 12.982451

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