A parametric representation of totally mixed Nash equilibria

Autores
Jeronimo, G.; Perrucci, D.; Sabia, J.
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present an algorithm to compute a parametric description of the totally mixed Nash equilibria of a generic game in normal form with a fixed structure. Using this representation, we also show an algorithm to compute polynomial inequality conditions under which a game has the maximum possible number of this kind of equilibria. Then, we present symbolic procedures to describe the set of isolated totally mixed Nash equilibria of an arbitrary game and to compute, under certain general assumptions, the exact number of these equilibria. The complexity of all these algorithms is polynomial in the number of players, the number of each player's strategies and the generic number of totally mixed Nash equilibria of a game with the considered structure. © 2009 Elsevier Ltd. All rights reserved.
Fil:Jeronimo, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Perrucci, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Sabia, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fuente
Comput Math Appl 2009;58(6):1126-1141
Materia
Complexity
Multihomogeneous resultants
Nash equilibria
Noncooperative game theory
Polynomial equation solving
Complexity
Multihomogeneous resultants
Nash equilibria
Noncooperative game theory
Polynomial equation solving
Polynomials
Game theory
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_08981221_v58_n6_p1126_Jeronimo
Acceder
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oai_identifier_str paperaa:paper_08981221_v58_n6_p1126_Jeronimo
network_acronym_str BDUBAFCEN
repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling A parametric representation of totally mixed Nash equilibriaJeronimo, G.Perrucci, D.Sabia, J.ComplexityMultihomogeneous resultantsNash equilibriaNoncooperative game theoryPolynomial equation solvingComplexityMultihomogeneous resultantsNash equilibriaNoncooperative game theoryPolynomial equation solvingPolynomialsGame theoryWe present an algorithm to compute a parametric description of the totally mixed Nash equilibria of a generic game in normal form with a fixed structure. Using this representation, we also show an algorithm to compute polynomial inequality conditions under which a game has the maximum possible number of this kind of equilibria. Then, we present symbolic procedures to describe the set of isolated totally mixed Nash equilibria of an arbitrary game and to compute, under certain general assumptions, the exact number of these equilibria. The complexity of all these algorithms is polynomial in the number of players, the number of each player's strategies and the generic number of totally mixed Nash equilibria of a game with the considered structure. © 2009 Elsevier Ltd. All rights reserved.Fil:Jeronimo, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Perrucci, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Sabia, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2009info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_08981221_v58_n6_p1126_JeronimoComput Math Appl 2009;58(6):1126-1141reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-10-16T09:30:04Zpaperaa:paper_08981221_v58_n6_p1126_JeronimoInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-10-16 09:30:05.872Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv A parametric representation of totally mixed Nash equilibria
title A parametric representation of totally mixed Nash equilibria
spellingShingle A parametric representation of totally mixed Nash equilibria
Jeronimo, G.
Complexity
Multihomogeneous resultants
Nash equilibria
Noncooperative game theory
Polynomial equation solving
Complexity
Multihomogeneous resultants
Nash equilibria
Noncooperative game theory
Polynomial equation solving
Polynomials
Game theory
title_short A parametric representation of totally mixed Nash equilibria
title_full A parametric representation of totally mixed Nash equilibria
title_fullStr A parametric representation of totally mixed Nash equilibria
title_full_unstemmed A parametric representation of totally mixed Nash equilibria
title_sort A parametric representation of totally mixed Nash equilibria
dc.creator.none.fl_str_mv Jeronimo, G.
Perrucci, D.
Sabia, J.
author Jeronimo, G.
author_facet Jeronimo, G.
Perrucci, D.
Sabia, J.
author_role author
author2 Perrucci, D.
Sabia, J.
author2_role author
author
dc.subject.none.fl_str_mv Complexity
Multihomogeneous resultants
Nash equilibria
Noncooperative game theory
Polynomial equation solving
Complexity
Multihomogeneous resultants
Nash equilibria
Noncooperative game theory
Polynomial equation solving
Polynomials
Game theory
topic Complexity
Multihomogeneous resultants
Nash equilibria
Noncooperative game theory
Polynomial equation solving
Complexity
Multihomogeneous resultants
Nash equilibria
Noncooperative game theory
Polynomial equation solving
Polynomials
Game theory
dc.description.none.fl_txt_mv We present an algorithm to compute a parametric description of the totally mixed Nash equilibria of a generic game in normal form with a fixed structure. Using this representation, we also show an algorithm to compute polynomial inequality conditions under which a game has the maximum possible number of this kind of equilibria. Then, we present symbolic procedures to describe the set of isolated totally mixed Nash equilibria of an arbitrary game and to compute, under certain general assumptions, the exact number of these equilibria. The complexity of all these algorithms is polynomial in the number of players, the number of each player's strategies and the generic number of totally mixed Nash equilibria of a game with the considered structure. © 2009 Elsevier Ltd. All rights reserved.
Fil:Jeronimo, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Perrucci, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Sabia, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
description We present an algorithm to compute a parametric description of the totally mixed Nash equilibria of a generic game in normal form with a fixed structure. Using this representation, we also show an algorithm to compute polynomial inequality conditions under which a game has the maximum possible number of this kind of equilibria. Then, we present symbolic procedures to describe the set of isolated totally mixed Nash equilibria of an arbitrary game and to compute, under certain general assumptions, the exact number of these equilibria. The complexity of all these algorithms is polynomial in the number of players, the number of each player's strategies and the generic number of totally mixed Nash equilibria of a game with the considered structure. © 2009 Elsevier Ltd. All rights reserved.
publishDate 2009
dc.date.none.fl_str_mv 2009
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/20.500.12110/paper_08981221_v58_n6_p1126_Jeronimo
url http://hdl.handle.net/20.500.12110/paper_08981221_v58_n6_p1126_Jeronimo
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Comput Math Appl 2009;58(6):1126-1141
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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score 12.712165

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