For every 2-person bargaining problem, the Nash bargaining solution selects a point that is “between” the relative utilitarian point and the relative egalitarian point. Also, it is “between” the 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.

We provide two alternative characterizations of the Nash bargaining solution. We introduce new simple axioms, strong undominatedness by the disagreement point, and egalitarian Pareto optimality. First, we prove that the Nash solution is characterized by symmetry, scale invariance, independence of irrelevant alternatives, and strong undominatedness by the disagreement point. Second, we replace the independence of irrelevant alternatives axiom with the sandwich axiom and egalitarian Pareto optimality. We then demonstrate that the Nash solution is characterized by symmetry, scale invariance, strong undominatedness (...) by the disagreement point, the sandwich axiom, and egalitarian Pareto optimality. (shrink)