A parametric representation of totally mixed Nash equilibria

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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Detalles Bibliográficos
Autores principales:	Jeronimo, Gabriela Tali, Perrucci, Daniel, Sabia, Juan Vicente Rafael
Publicado:	2009
Materias:	Complexity Multihomogeneous resultants Nash equilibria Noncooperative game theory Polynomial equation solving Polynomials Game theory
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08981221_v58_n6_p1126_Jeronimo http://hdl.handle.net/20.500.12110/paper_08981221_v58_n6_p1126_Jeronimo
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_08981221_v58_n6_p1126_Jeronimo
record_format	dspace
spelling	paper:paper_08981221_v58_n6_p1126_Jeronimo2023-06-08T15:49:24Z A parametric representation of totally mixed Nash equilibria Jeronimo, Gabriela Tali Perrucci, Daniel Sabia, Juan Vicente Rafael 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 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. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08981221_v58_n6_p1126_Jeronimo http://hdl.handle.net/20.500.12110/paper_08981221_v58_n6_p1126_Jeronimo
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (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, Gabriela Tali Perrucci, Daniel Sabia, Juan Vicente Rafael 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.
author	Jeronimo, Gabriela Tali Perrucci, Daniel Sabia, Juan Vicente Rafael
author_facet	Jeronimo, Gabriela Tali Perrucci, Daniel Sabia, Juan Vicente Rafael
author_sort	Jeronimo, Gabriela Tali
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	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08981221_v58_n6_p1126_Jeronimo http://hdl.handle.net/20.500.12110/paper_08981221_v58_n6_p1126_Jeronimo
work_keys_str_mv	AT jeronimogabrielatali aparametricrepresentationoftotallymixednashequilibria AT perruccidaniel aparametricrepresentationoftotallymixednashequilibria AT sabiajuanvicenterafael aparametricrepresentationoftotallymixednashequilibria AT jeronimogabrielatali parametricrepresentationoftotallymixednashequilibria AT perruccidaniel parametricrepresentationoftotallymixednashequilibria AT sabiajuanvicenterafael parametricrepresentationoftotallymixednashequilibria
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A parametric representation of totally mixed Nash equilibria

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