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...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2009 |
| País: | Argentina |
| Recursos: | 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 |
| Acesso em linha: | http://hdl.handle.net/20.500.12110/paper_08981221_v58_n6_p1126_Jeronimo |
| Access Level: | acceso abierto |
| Palavra-chave: | Complexity Multihomogeneous resultants Nash equilibria Noncooperative game theory Polynomial equation solving Polynomials Game theory |
| Resumo: | 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. |
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