This paper defines a general equilibrium model with exchange and club forma
tion. Agents trade multiple private goods widely in the market, can belong
to several clubs, and care about the characteristics of the other members o
f their clubs. The space of agents is a continuum, but clubs are finite. It
is shown that (i) competitive equilibria exist, and (ii) the core coincide
s with the set of equilibrium states. The central subtlety is in modeling c
lub memberships and expressing the notion that membership choices are consi
stent across the population.