The Core in a Distributional Economy

TL;DR

This paper demonstrates that core analysis in large, negligible-agent economies can be conducted purely through distributional properties, without explicit agent specification.

Contribution

It provides a distributional proof of the core-equivalence theorem, extending core analysis to atomless economies and large matching markets.

Findings

Blocking coalitions can be identified distributionally.

Distributional core-equivalence theorem is established.

Methods apply to large matching markets and Shapley-value analogs.

Abstract

An economy, large or small, has traditionally been defined in terms of an explicit set of agents and an assignment of characteristics to each agent. But when individual agents are negligible, most economically relevant properties of an economy can be defined in terms of the distribution of characteristics alone. Agents need not be specified. It has been frequently asserted that the distributional description of an economy is too sparse for core analysis. Notions of coalitions and blocking require the individualistic description of agents. This paper shows that this is not so. The presence of blocking coalitions can be directly identified in terms of distributions alone. Indeed, we give a purely distributional proof of the classical core-equivalence theorem that delivers the core-equivalence theorem for individualistic economies as a corollary. Our methods have applications outside of general equilibrium theory. They apply to large matching markets and to analogs of the Shapley-value for atomless economies.