Large games with transformed summary statistics

Summary. The existence of pure-strategy Nash equilibrium is shown for a non-cooperative game with a continuum of small players and a compact action space. The players payoffs depend on their own actions and the mean of the transformed strategy profiles. This covers the case when the payoffs depend on players own actions and finitely many summary statistics.Received: 24 November 2003, Revised: 29 March 2004, JEL Classification Numbers: C7, D4. Correspondence to: Haomiao YuThe authors are grateful to Yeneng Sun for his help and guidance. They also thank Ali Khan, Kali Rath, and an anonymous referee for useful comments.