Anonymity in Nonatomic Games

This paper purpose is twofold. First, it offers a critical review of the proofs of existence of pure strategy Nash Equilibria in nonatomic games. In particular, it focuses on the alternative ways of formalizing the critical assumption of anonymity. Second, the paper proves the existence of pure strategy Nash Equilibria by relaxing anonymity and allowing instead for \u201climited anonymity\u201d (i.e. players\u2019 decisions depend on the average strategy of a finite number of players\u2019 subsets and not on the average strategy of the whole set of players)