Equivalence of the Aubin bargaining set and the set of competitive equilibria in a finite coalition production economy

Mas-Colell (Mas-Colell, 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. In the case of pure exchange economies with a finite number of traders it is well-known that the set of competitive allocations could be a strict subset of the core which can also be a strict subset of the bargaining set. In this paper, we show that the Aubin bargaining set (or fuzzy bargaining set) and the set of competitive allocations coincide in a finite coalition production economy under some standard assumptions. We also show that the (Mas-Colell) bargaining set shrinks to the set of competitive allocations in a finite coalition production economy 8 under some standard conditions when e is replicated. As a consequence, the existence of competitive equilibrium in a finite coalition production economy implies the nonemptiness of Aubin bargaining sets. (C) 2016 Elsevier B.V. All rights reserved.