BEST-REPLY DYNAMICS IN LARGE ANONYMOUS GAMES By

We consider small-influence anonymous games with a large number of players n where every player has two actions. For this class of games we present a best-reply dynamic with the following two properties. First, the dynamic reaches Nash approximate equilibria fast (in at most cn logn steps for some constant c > 0). Second, Nash approximate equilibria are played by the dynamic with a limit frequency of at least 1− e−cn for some constant c′ > 0. ∗Center for the Study of Rationality, Institute of Mathematics, The Hebrew University of Jerusalem. e-mail:[email protected]. †This paper is part of the Ph.D. research of the author at the Hebrew University of Jerusalem. The author wishes to thank his supervisor, Sergiu Hart, for his support and guidance, and Itai Arieli for useful discussions and comments. The author would like to acknowledge financial support by ERC 030-7950-411 and ISF 039-7679-411.