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: Jeronimo, G., Perrucci, D., Sabia, J.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2009
País:Argentina
Institución:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
Repositorio:Biblioteca Digital (UBA-FCEN)
Idioma:inglés
OAI Identifier:paperaa:paper_08981221_v58_n6_p1126_Jeronimo
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_08981221_v58_n6_p1126_Jeronimo
Access Level:acceso abierto
Palabra clave:Complexity
Multihomogeneous resultants
Nash equilibria
Noncooperative game theory
Polynomial equation solving
Polynomials
Game theory
Descripción
Sumario: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.