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.
Let N be a finite set of players and let ρ be a class of coalitions of N. We consider games with and without sidepayments such that only the coalitions in pi play essential roles but not the others. For an arbitrary ρ, we get the class of all such games. The purpose of this note is to provide a necessary and sufficient condition with respect to pi for the nonemptiness of the cores of all games in the class.