WHEN ARE NONANONYMOUS PLAYERS NEGLIGIBLE

We examine games played by a single large player and a large number of opponents who are small, but not anonymous. if the Flay of the small players is observed with noise, and if the number of actions the large player controls is bounded as the number of small players grows, the equilibrium set converges to that of the grime where there is a contin uum of small players. This paper extends previous work on the negligib ility of small players by dropping the assumption that small players' actions are ''anonymous.'' That is, we allow each small player's actio ns to be observed separately, instead of supposing that the small play ers' actions are only observed through their effect on an aggregate st atistic. (C) 1998 Academic Press.