Abstract

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.