Pascoa (1993a) showed that the failure of the law of large numbers for a continuum of independent randomizatons implies that Schmeidler's (1973) concept of a measure-valued profile function in equilibrium might not coincide with the concept of mixed strategies equilibrium of a nonatomic game....

In this note we show that the fixed points of a continuous function (or of an upper semi-continuous correspondence, with non-empty and convex values) can be attained as Nash Equilibria of a game with finitely many players.