An equivalence theorem for a bargaining set (Q1123107)

The author proposes a redefinition of the bargaining set concept as a solution concept for economies. Generally speaking, an allocation is said to belong to the bargaining set if for any objection against the allocation there exists a counterobjection to the objection. A so-called Walrasian allocation necessarily belongs to the bargaining set because there can be no objection to the Walrasian allocation. The aim of the paper is to show that the converse is also true with respect to the proposed modification of the bargaining set. To be exact, under certain standard conditions it is established that the modified bargaining set coincides with the set of Walrasian allocations. The standard conditions under which the equivalence theorem holds require strict monotonicity of preferences, strictly positive endowments and complete, transitive preferences.