A Second Remark on the Core of an Atomless Economy

Abstract

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,