A parametric representation of totally mixed Nash equilibria

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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 numbe...

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Autores principales: Jeronimo, G., Perrucci, D., Sabia, J.
Formato: Artículo publishedVersion
Publicado: 2009
Materias:
Complexity
Multihomogeneous resultants
Nash equilibria
Noncooperative game theory
Polynomial equation solving
Polynomials
Game theory
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_08981221_v58_n6_p1126_Jeronimo
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_08981221_v58_n6_p1126_Jeronimo_oai
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id I28-R145-paper_08981221_v58_n6_p1126_Jeronimo_oai
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spelling I28-R145-paper_08981221_v58_n6_p1126_Jeronimo_oai2024-08-16 Jeronimo, G. Perrucci, D. Sabia, J. 2009 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. application/pdf http://hdl.handle.net/20.500.12110/paper_08981221_v58_n6_p1126_Jeronimo info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar Comput Math Appl 2009;58(6):1126-1141 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 A parametric representation of totally mixed Nash equilibria info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_08981221_v58_n6_p1126_Jeronimo_oai
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-145
collection Repositorio Digital de la Universidad de Buenos Aires (UBA)
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
spellingShingle 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
Jeronimo, G.
Perrucci, D.
Sabia, J.
A parametric representation of totally mixed Nash equilibria
topic_facet 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
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.
format Artículo
Artículo
publishedVersion
author Jeronimo, G.
Perrucci, D.
Sabia, J.
author_facet Jeronimo, G.
Perrucci, D.
Sabia, J.
author_sort Jeronimo, G.
title A parametric representation of totally mixed Nash equilibria
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 parametric representation of totally mixed nash equilibria
publishDate 2009
url http://hdl.handle.net/20.500.12110/paper_08981221_v58_n6_p1126_Jeronimo
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_08981221_v58_n6_p1126_Jeronimo_oai
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