A mass-economy is one with many, many agents where each agent is negligible and each trading group is also negligible with respect to the mass-economy. Feasible allocations are those which are virtually attainable by trades only among members of coalitions contained in feasible (“measure-consistent”) partitions of the agent set. A feasible allocation is in the core, called the f -core, if it cannot be improved upon by any ﬁnite coalition. We show that in a private goods economy with indivisibilities and without externalities, the f -core, the A -core (Aumann’s core concept) and the Walrasian allocations coincide. In the presence of widespread externalities, the f -core and the Walrasian allocations coincide but the deﬁnition of the A -core is problematic. The conceptual signiﬁcance of these results will be discussed.
Hammond, Peter J.; Kaneko, Mamoru; and Wooders, Myrna Holtz, "-Core Approach" (1985). Cowles Foundation Discussion Papers. 993.