The 2-Shapley value for bicooperative games

In this paper, we propose a new Shapley-type value (the 2-Shapley value) for bico- operative games. Unlike classical cooperative games, bicooperative games assign values to pairs of disjoint coalitions (bicoalitions) representing players who support change and those who defend the status quo, while...

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Detalhes bibliográficos
Autores: Jiménez Losada, Andrés, Basallote Galván, Manuela, Gallego Sánchez, Inés Magdalena
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2026
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:dnet:idus________::39ace3df7027b43155f1c10f6cf83d8e
Acesso em linha:https://hdl.handle.net/11441/186295
https://doi.org/10.1007/s10479-026-07245-3
Access Level:acceso abierto
Palavra-chave:Bicooperative game
Shapley value
Allocation rules
Antimatroid
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oai_identifier_str oai:dnet:idus________::39ace3df7027b43155f1c10f6cf83d8e
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spelling The 2-Shapley value for bicooperative gamesJiménez Losada, AndrésBasallote Galván, ManuelaGallego Sánchez, Inés MagdalenaJiménez Losada, AndrésBicooperative gameShapley valueAllocation rulesAntimatroidIn this paper, we propose a new Shapley-type value (the 2-Shapley value) for bico- operative games. Unlike classical cooperative games, bicooperative games assign values to pairs of disjoint coalitions (bicoalitions) representing players who support change and those who defend the status quo, while the remaining players abstain. To develop this new value, we employ antimatroid theory not as a structural constraint on the games, but as a methodological bridge. Specifically, we demonstrate that any bicooperative coalition structure is isomorphic to a specific antimatroid, which we term the ‘double antimatroid’. Leveraging this mathematical connection, we propose a new Shapley value, provide an axiomatization that preserves its fundamental axioms, and establish its consistency with existing solution concepts. Finally, we illustrate our theoretical proposal and the calculation of this value through an example modeling a decision-making process. This work provides a robust mathematical foundation connecting both structures, opening new perspectives for analysis within bicooperative game theory.Universidad de SevillaSpringerMatemática Aplicada IIDidáctica de las MatemáticasFQM237: Juegos con Estructuras Combinatorias y de OrdenFQM226: Grupo de Investigación en Educación MatemáticaMinisterio de Ciencia, Innovación y Universidades (MICIU). España2026info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/186295https://doi.org/10.1007/s10479-026-07245-3reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésAnnals of Operations Research, 13, 1664696. PID2022-138956NB-I00https://link.springer.com/article/10.1007/s10479-026-07245-3info:eu-repo/semantics/openAccessoai:dnet:idus________::39ace3df7027b43155f1c10f6cf83d8e2026-06-17T12:51:07Z
dc.title.none.fl_str_mv The 2-Shapley value for bicooperative games
title The 2-Shapley value for bicooperative games
spellingShingle The 2-Shapley value for bicooperative games
Jiménez Losada, Andrés
Bicooperative game
Shapley value
Allocation rules
Antimatroid
title_short The 2-Shapley value for bicooperative games
title_full The 2-Shapley value for bicooperative games
title_fullStr The 2-Shapley value for bicooperative games
title_full_unstemmed The 2-Shapley value for bicooperative games
title_sort The 2-Shapley value for bicooperative games
dc.creator.none.fl_str_mv Jiménez Losada, Andrés
Basallote Galván, Manuela
Gallego Sánchez, Inés Magdalena
Jiménez Losada, Andrés
author Jiménez Losada, Andrés
author_facet Jiménez Losada, Andrés
Basallote Galván, Manuela
Gallego Sánchez, Inés Magdalena
author_role author
author2 Basallote Galván, Manuela
Gallego Sánchez, Inés Magdalena
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada II
Didáctica de las Matemáticas
FQM237: Juegos con Estructuras Combinatorias y de Orden
FQM226: Grupo de Investigación en Educación Matemática
Ministerio de Ciencia, Innovación y Universidades (MICIU). España
dc.subject.none.fl_str_mv Bicooperative game
Shapley value
Allocation rules
Antimatroid
topic Bicooperative game
Shapley value
Allocation rules
Antimatroid
description In this paper, we propose a new Shapley-type value (the 2-Shapley value) for bico- operative games. Unlike classical cooperative games, bicooperative games assign values to pairs of disjoint coalitions (bicoalitions) representing players who support change and those who defend the status quo, while the remaining players abstain. To develop this new value, we employ antimatroid theory not as a structural constraint on the games, but as a methodological bridge. Specifically, we demonstrate that any bicooperative coalition structure is isomorphic to a specific antimatroid, which we term the ‘double antimatroid’. Leveraging this mathematical connection, we propose a new Shapley value, provide an axiomatization that preserves its fundamental axioms, and establish its consistency with existing solution concepts. Finally, we illustrate our theoretical proposal and the calculation of this value through an example modeling a decision-making process. This work provides a robust mathematical foundation connecting both structures, opening new perspectives for analysis within bicooperative game theory.
publishDate 2026
dc.date.none.fl_str_mv 2026
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/186295
https://doi.org/10.1007/s10479-026-07245-3
url https://hdl.handle.net/11441/186295
https://doi.org/10.1007/s10479-026-07245-3
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Annals of Operations Research, 13, 1664696.
PID2022-138956NB-I00
https://link.springer.com/article/10.1007/s10479-026-07245-3
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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