  File-sharing systems, like many online and traditional information sharing
communities (e.g. newsgroups, BBS, forums, interest clubs), are dynamical
systems in nature. As peers get in and out of the system, the information
content made available by the prevailing membership varies continually in
amount as well as composition, which in turn affects all peers' join/leave
decisions. As a result, the dynamics of membership and information content are
strongly coupled, suggesting interesting issues about growth, sustenance and
stability.
  In this paper, we propose to study such communities with a simple statistical
model of an information sharing club. Carrying their private payloads of
information goods as potential supply to the club, peers join or leave on the
basis of whether the information they demand is currently available.
Information goods are chunked and typed, as in a file sharing system where
peers contribute different files, or a forum where messages are grouped by
topics or threads. Peers' demand and supply are then characterized by
statistical distributions over the type domain.
  This model reveals interesting critical behaviour with multiple equilibria. A
sharp growth threshold is derived: the club may grow towards a sustainable
equilibrium only if the value of an order parameter is above the threshold, or
shrink to emptiness otherwise. The order parameter is composite and comprises
the peer population size, the level of their contributed supply, the club's
efficiency in information search, the spread of supply and demand over the type
domain, as well as the goodness of match between them.
