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....

Discontinuous games, such as auctions, may require special tie-breaking rules to guarantee equilibrium existence. The best results available ensure equilibrium existence only in mixed strategy with endogenously defined tie-breaking rules and communication of private information. We show that an...