On unification of solutions to the bargaining problem

We establish axioms under which a bargaining solution can be found by the maximization of the CES function and is unique up to specification 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 and is unique up to the specifications of the distribution and its 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.