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)

In this note, I provide an axiomatic characterization of the relative utilitarian bargaining solution to Nash bargaining problems. The solution is obtained when Nash’s independence of irrelevant alternatives axiom is replaced by the weak linearity axiom, while retaining the other three axioms. RU maximizes the sum of proportional gains, or, equivalently, minimizes the sum of proportional losses. RU is scale invariant and compared to the Nash and Kalai and Smorodinsky solutions, it is ex ante efficient when the bargaining problem is (...) considered as a lottery of future bargaining problems. (shrink)