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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/182769
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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 Técnicas2025-09-29T10:26:28Zoai: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:34982025-09-29 10:26:29.108CONICET 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 |
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info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
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openAccess |
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https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
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Springer |
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Springer |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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