Egalitarian–utilitarian bounds in Nash’s bargaining problem

Abstract

For every 2-person bargaining problem, the Nash bargaining solution selects a point that is “between” the relative (or normalized) utilitarian point and the relative egalitarian (i.e., Kalai–Smorodinsky) point. Also, it is “between” the (non-normalized) utilitarian and egalitarian points. I improve these bounds. I also derive a new characterization of the Nash solution which combines a bounds property together with strong individual rationality and an axiom which is new to Nash’s bargaining model, the sandwich axiom. The sandwich axiom is a weakening of Nash’s IIA.