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
- Institución
- Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
- OAI Identificador
- paperaa:paper_08981221_v58_n6_p1126_Jeronimo
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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/ar2025-09-29T13:42:55Zpaperaa: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:18962025-09-29 13:42:56.487Biblioteca 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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1844618735510355968 |
score |
13.070432 |