We consider, in this paper, a class of hierarchical network games where there is a single service provider (leader, in a Stackelberg game framework) and multiple users (followers) which could be of different types. Depending on whether the type of a particular user is private information (only to that user), or public information (shared with all users as well as the service provider), or whether we have the intermediate case where this is common (shared) information among the users but not shared with the service provider, one can introduce and study the equilibria of different types of games, covering the entire gamut from complete information to incomplete information games. We undertake such a study in this paper, with general utility functions for the players and general distributions for user characteristics. We compare the performances of the leader and the followers under the different scenarios, and also study the asymptotic case as the user population grows. The study for the many-followers regime provides useful insight for communication network applications.