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.
A general model of a coalition production economy allowing set-up costs, indivisibilities, and non-convexities is developed. It is shown that for all sufficiently large replications, approximate cores of the economy are non-empty.
A generalization of assignment games, called partitioning games, is introduced. Given a finite set N of players, there is an a priori given subset pi of coalitions of N and only coalitions in pi play an essential role. Necessary and sufficient conditions for the non-emptiness of the cores of all games with essential coalitions pi are developed. These conditions appear extremely restrictive. However, when N is “large,” there are relatively few “types” of players, and members of pi are “small” and defined in terms of numbers of players of each type contained in subsets, then approximate cores are non-empty.
Sufficient conditions are demonstrated for the non-emptiness of asymptotic cores of sequences of replica games, i.e., for all sufficiently large replications, the games have non-empty approximate cores and the approximation can be made arbitrarily “good”. The conditions are simply that the games are superadditive and satisfy a very non-restrictive “per-capita” boundedness assumption (these properties are satisfied by games derived from well-known models of replica economies). It is argued that the results can be applied to a broad class of games derived from economic models, including ones with external economies and diseconomies, indivisibilities and non-convexities. To support this claim, in Part I applications to an economy with local public goods are provided and in Part II, to a general model of a coalition production economy with remarkably few restrictions on production technology sets and with (possibly) indivisibilities in consumption. Additional examples in Part I illustrate the generality of the result.