A parametric representation of totally mixed Nash equilibria

Authors:
Gabriela Jeronimo;Daniel Perrucci;Juan Sabia
Affiliations:
Departamento de Matemática, FCEN, Universidad de Buenos Aires, Ciudad Universitaria, (1428) Buenos Aires, Argentina and CONICET, Argentina;Departamento de Matemática, FCEN, Universidad de Buenos Aires, Ciudad Universitaria, (1428) Buenos Aires, Argentina;Departamento de Matemática, FCEN, Universidad de Buenos Aires, Ciudad Universitaria, (1428) Buenos Aires, Argentina and Departamento de Ciencias Exactas, CBC, Universidad de Buenos Aires, Ciu ...
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

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.