In this note we shall show that we can further restrict the coalitions that are allowed to form and still have the above identity. Let the commodity space be of finite dimension 1, and let a > 0. The result is that an allocation is a Walras allocation if and only if it cannot be blocked by a coalition which is the union of at most 1 + 1 coalitions, each of which has measure and diameter less than a. That a coalition has measure and diameter less than a intuitively means that the coalition consists of relatively few agents, and that the agents in the coalition resemble one another in chosen characteristics, e.g., initial allocation, production possibilities,

This paper defines a general equilibrium model with exchange and club formation. Agents trade multiple private goods widely in the market, can belong to several clubs, and care about the characteristics of the other members of 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 coincides with the set of equilibrium states. The central subtlety is in modeling club memberships and expressing the notion that membership choices are consistent across the population.