Pyramidal values

We propose and analyze a new type of values for cooperative TU-games, which we call pyramidal values. Assuming that the grand coalition is sequentially formed, and all orderings are equally likely, we define a pyramidal value to be any expected payoff in which the entrant player receives a salary, a...

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Autores: Flores Díaz, Ramón Jesús, Molina Ferragut, Elisenda, Tejada Cazorla, Juan Antonio
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2014
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/72240
Acceso en línea:https://hdl.handle.net/11441/72240
https://doi.org/10.1007/s10479-013-1509-y
Access Level:acceso abierto
Palabra clave:Game theory
TU games
Pyramidal values
Procedural values
Shapley value
Co-values
Consensus values
Egalitarian Shapley values
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spelling Pyramidal valuesFlores Díaz, Ramón JesúsMolina Ferragut, ElisendaTejada Cazorla, Juan AntonioGame theoryTU gamesPyramidal valuesProcedural valuesShapley valueCo-valuesConsensus valuesEgalitarian Shapley valuesWe propose and analyze a new type of values for cooperative TU-games, which we call pyramidal values. Assuming that the grand coalition is sequentially formed, and all orderings are equally likely, we define a pyramidal value to be any expected payoff in which the entrant player receives a salary, and the rest of his marginal contribution to the just formed coalition is distributed among the incumbent players. We relate the pyramidal-type sharing scheme we propose with other sharing schemes, and we also obtain some known values by means of this kind of pyramidal procedures. In particular, we show that the Shapley value can be obtained by means of an interesting pyramidal procedure that distributes nonzero dividends among the incumbents. As a result, we obtain an alternative formulation of the Shapley value based on a measure of complementarity between two players. Finally, we introduce the family of proportional pyramidal values, in which an incumbent receives a dividend in proportion to his initial investment, measured by means of his marginal contribution.Ministerio de Ciencia e InnovaciónSpringerGeometría y TopologíaFQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y HomotopíaMinisterio de Ciencia e Innovación (MICIN). España2014info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/72240https://doi.org/10.1007/s10479-013-1509-yreponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésAnnals of Operations Research, 217 (1), 233-252.MTM2011-27892https://link.springer.com/content/pdf/10.1007%2Fs10479-013-1509-y.pdfinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/722402026-06-17T12:51:07Z
dc.title.none.fl_str_mv Pyramidal values
title Pyramidal values
spellingShingle Pyramidal values
Flores Díaz, Ramón Jesús
Game theory
TU games
Pyramidal values
Procedural values
Shapley value
Co-values
Consensus values
Egalitarian Shapley values
title_short Pyramidal values
title_full Pyramidal values
title_fullStr Pyramidal values
title_full_unstemmed Pyramidal values
title_sort Pyramidal values
dc.creator.none.fl_str_mv Flores Díaz, Ramón Jesús
Molina Ferragut, Elisenda
Tejada Cazorla, Juan Antonio
author Flores Díaz, Ramón Jesús
author_facet Flores Díaz, Ramón Jesús
Molina Ferragut, Elisenda
Tejada Cazorla, Juan Antonio
author_role author
author2 Molina Ferragut, Elisenda
Tejada Cazorla, Juan Antonio
author2_role author
author
dc.contributor.none.fl_str_mv Geometría y Topología
FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
Ministerio de Ciencia e Innovación (MICIN). España
dc.subject.none.fl_str_mv Game theory
TU games
Pyramidal values
Procedural values
Shapley value
Co-values
Consensus values
Egalitarian Shapley values
topic Game theory
TU games
Pyramidal values
Procedural values
Shapley value
Co-values
Consensus values
Egalitarian Shapley values
description We propose and analyze a new type of values for cooperative TU-games, which we call pyramidal values. Assuming that the grand coalition is sequentially formed, and all orderings are equally likely, we define a pyramidal value to be any expected payoff in which the entrant player receives a salary, and the rest of his marginal contribution to the just formed coalition is distributed among the incumbent players. We relate the pyramidal-type sharing scheme we propose with other sharing schemes, and we also obtain some known values by means of this kind of pyramidal procedures. In particular, we show that the Shapley value can be obtained by means of an interesting pyramidal procedure that distributes nonzero dividends among the incumbents. As a result, we obtain an alternative formulation of the Shapley value based on a measure of complementarity between two players. Finally, we introduce the family of proportional pyramidal values, in which an incumbent receives a dividend in proportion to his initial investment, measured by means of his marginal contribution.
publishDate 2014
dc.date.none.fl_str_mv 2014
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/11441/72240
https://doi.org/10.1007/s10479-013-1509-y
url https://hdl.handle.net/11441/72240
https://doi.org/10.1007/s10479-013-1509-y
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Annals of Operations Research, 217 (1), 233-252.
MTM2011-27892
https://link.springer.com/content/pdf/10.1007%2Fs10479-013-1509-y.pdf
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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score 15,301603

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