The Banzhaf value in the presence of externalities

We propose two generalizations of the Banzhaf value for partition function form games. In both cases our approach is based on probability distributions over the set of coalition structures that may arise for any given set of players. First, we introduce a family of values, one for each collection of...

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Detalhes bibliográficos
Autores: Álvarez-Mozos, Mikel, Tejada, Oriol
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2014
País:España
Recursos:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/63637
Acesso em linha:https://hdl.handle.net/2445/63637
Access Level:acceso abierto
Palavra-chave:Teoria de jocs
Teoria de l'estimació
Jocs cooperatius (Matemàtica)
Presa de decisions (Estadística)
Ciències socials
Game theory
Estimation theory
Cooperative games (Mathematics)
Statistical decision
Social sciences
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spelling The Banzhaf value in the presence of externalitiesÁlvarez-Mozos, MikelTejada, OriolTeoria de jocsTeoria de l'estimacióJocs cooperatius (Matemàtica)Presa de decisions (Estadística)Ciències socialsGame theoryEstimation theoryCooperative games (Mathematics)Statistical decisionSocial sciencesWe propose two generalizations of the Banzhaf value for partition function form games. In both cases our approach is based on probability distributions over the set of coalition structures that may arise for any given set of players. First, we introduce a family of values, one for each collection of these latter probability distributions, defined as the Banzhaf value of a coalitional game obtained as the expectation taken according to the given probability distributions of the original partition function form game. For each value of the family we provide two characterization results within the set of all partition function form games. Both results rely on a property of neutrality with respect to the amalgamation of players. Second, we propose another family of values that differ from the previous ones in that the latter values take into account only the information about the most likely coalition structure that may arise according to the given probability distributions. Each value of the second family is also characterized in two results by means of a collusion neutrality property. Unlike the characterizations of the first approach, these characterizations can be restricted to the set of simple games in partition function form.Springer Verlag2014info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/63637Articles publicats en revistes (Matemàtica Econòmica, Financera i Actuarial)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió postprint del document publicat a: http://dx.doi.org/10.1007/s00355-014-0861-4Social Choice and Welfare, 2015, vol. 44, num.4, p. 781-805http://dx.doi.org/10.1007/s00355-014-0861-4(c) Springer Verlag, 2014info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/636372026-05-27T06:46:51Z
dc.title.none.fl_str_mv The Banzhaf value in the presence of externalities
title The Banzhaf value in the presence of externalities
spellingShingle The Banzhaf value in the presence of externalities
Álvarez-Mozos, Mikel
Teoria de jocs
Teoria de l'estimació
Jocs cooperatius (Matemàtica)
Presa de decisions (Estadística)
Ciències socials
Game theory
Estimation theory
Cooperative games (Mathematics)
Statistical decision
Social sciences
title_short The Banzhaf value in the presence of externalities
title_full The Banzhaf value in the presence of externalities
title_fullStr The Banzhaf value in the presence of externalities
title_full_unstemmed The Banzhaf value in the presence of externalities
title_sort The Banzhaf value in the presence of externalities
dc.creator.none.fl_str_mv Álvarez-Mozos, Mikel
Tejada, Oriol
author Álvarez-Mozos, Mikel
author_facet Álvarez-Mozos, Mikel
Tejada, Oriol
author_role author
author2 Tejada, Oriol
author2_role author
dc.subject.none.fl_str_mv Teoria de jocs
Teoria de l'estimació
Jocs cooperatius (Matemàtica)
Presa de decisions (Estadística)
Ciències socials
Game theory
Estimation theory
Cooperative games (Mathematics)
Statistical decision
Social sciences
topic Teoria de jocs
Teoria de l'estimació
Jocs cooperatius (Matemàtica)
Presa de decisions (Estadística)
Ciències socials
Game theory
Estimation theory
Cooperative games (Mathematics)
Statistical decision
Social sciences
description We propose two generalizations of the Banzhaf value for partition function form games. In both cases our approach is based on probability distributions over the set of coalition structures that may arise for any given set of players. First, we introduce a family of values, one for each collection of these latter probability distributions, defined as the Banzhaf value of a coalitional game obtained as the expectation taken according to the given probability distributions of the original partition function form game. For each value of the family we provide two characterization results within the set of all partition function form games. Both results rely on a property of neutrality with respect to the amalgamation of players. Second, we propose another family of values that differ from the previous ones in that the latter values take into account only the information about the most likely coalition structure that may arise according to the given probability distributions. Each value of the second family is also characterized in two results by means of a collusion neutrality property. Unlike the characterizations of the first approach, these characterizations can be restricted to the set of simple games in partition function form.
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/2445/63637
url https://hdl.handle.net/2445/63637
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: http://dx.doi.org/10.1007/s00355-014-0861-4
Social Choice and Welfare, 2015, vol. 44, num.4, p. 781-805
http://dx.doi.org/10.1007/s00355-014-0861-4
dc.rights.none.fl_str_mv (c) Springer Verlag, 2014
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Springer Verlag, 2014
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Verlag
publisher.none.fl_str_mv Springer Verlag
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtica Econòmica, Financera i Actuarial)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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