Coincidence of the Mas-Colell bargaining set and the set of competitive equilibria in a continuum coalition production economy

Abstract

Mas-Colell (J Math Econ 18:129–139, 1989) proved that the bargaining set and the set of competitive allocations coincide in an exchange economy with a continuum of traders under some standard assumptions. We extend this result to continuum coalition production economies and prove that the bargaining set and the set of competitive allocations coincide in a coalition production economy with a continuum of traders under some standard assumptions. As a consequence, we obtain a coincidence theorem for the core and the set of competitive allocations in a coalition production economy which extends the well-known coincidence theorem by Aumann (Econometrica 32:39–50, 1964).