The core of a continuum economy with widespread externalities and finite coalitions: From finite to continuum economies

When permissible coalitions in finite economies are constrained to be small relative to the player set, the continuum model with finite coalitions and its f-core are the limits of large finite economies and their ε-cores. We show convergence both of game-theoretic structures-relatively small coalitions in the finite economies converge to finite coalitions-and of solutions-ε-cores converge to the f-core. Our convergence is carried out in the context of exchange economies with widespread externalities where the requirement that coalitions be small is critical.