A parametric representation of totally mixed Nash equilibria

GABRIELA JERONIMO; DANIEL PERRUCCI; JUAN SABIA

COMPUTERS & MATHEMATICS WITH APPLICATIONS (1987)

Elsevier

Año: 2009 vol. 58 p. 1126 - 1141

0898-1221

We present an algorithm to compute a parametric description of thetotally mixed Nash equilibria of a generic game in normal form witha fixed structure. Using this representation, we also show analgorithm 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 isolatedtotally mixed Nash equilibria of an arbitrary game and to compute,under certain general assumptions, the exact number of theseequilibria. The complexity of all these algorithms is polynomial inthe number of players, the number of each player´s strategies andthe generic number of totally mixed Nash equilibria of a game withthe considered structure.