On Unification of Solutions to the Bargaining Problem

Abstract

We establish axioms under which a bargaining solution can be found by the maximization of the CES function and is unique up to specifications of the distribution and elasticity parameters. This solution is referred to as the CES solution which includes the Nash and egalitarian solutions as special cases. Next, we consider a normalization of the CES function and establish axioms, under which a bargaining solution can be found by the maximization of the normalized CES function and is unique up to specifications of the distribution and substitution parameters. We refer to this solution as the normalized CES solution which includes the Nash and Kalai-Smorodinsky solutions as special cases. Our paper contributes to bargaining theory by establishing unified characterizations of existing as well as a great variety of new bargaining solutions.

Keywords: Bargaining problem, CES Function, Normalized CES Function, Nash solution, Kalai-Smorodinsky Solution, Egalitarian Solution

JEL Classification: C78, D21