Refinements of the Nash equilibrium concept for bimatrix games

In the literature several refinements of the Nash equilibrium concept have been introduced. Among these there are: the essential equilibrium point [16], the quasi-strong equilibrium point [2], the perfect equilibrium point [15], and the proper equilibrium point [11]. In this paper bimatrix games are considered. For this class of games a new refinement of the equilibrium concept, called nondegenerate equilibrium point, is introduced. It is proved that nondegenerate equilibrium points are essential, quasi-strong, proper and perfect. Furthermore, it is shown that for almost all bimatrix games all equilibrium points are nondegenerate