Competitive equilibrium in a coalition production economy or a club ec
onomy typically does not exist when there is free entry, for two reaso
ns. First, there may be an ''integer problem'', as is familiar from cl
ub theory with anonymous crowding. Second, ''optimal'' groups may have
different compositions from the population, and then even if there is
no integer problem, it may be impossible to partition the population
into optimal groups. I define a notion of approximate equilibrium and
show that such an equilibrium always exists in a sufficiently large ec
onomy. I focus on the optimal size of the economy rather than of clubs
.