The maximal generic number of pure Nash equilibria

For finite pure strategy sets S-1,...,S-n if E subset of S = S-1 x ... x S-n is the set of pure strategy Nash equilibria for an open set of payoffs vectors, then #E less than or equal to #S/(max(i) #S-i). There is an open set of payoff vectors for which there are #S/(max(i) #S-i) pure Nash equilibria. (C) 1997 Academic Press.