On the redundancy of the implicit welfarist axiom in bargaining theory

It has long been argued that there is a mismatch between the general motivation provided for Nash’s (1950) axioms and their actual mathematical content because they are phrased in the space of joint (Bernoulli) utilities. Alternatively, it is easy to rephrase these axioms in an economic environment so as to match their intuitive meaning, but Nash’s proof then applies only if one adds a cardinal welfarist axiom requiring that the solution of two problems that happen to have the same image in the space of joint utilities for some linear representation of von Neumann/Morgenstern preferences, must coincide in that space. Attemps so far at recovering Nash’s uniqueness result without the cardinal welfarist axiom have not been successful, in that they all rely on the introduction of a non-straightforward axiom. The purpose of this paper is to show that the straightforward formulation of the arguments underlying Nash’s axioms does in fact characterize his solution on a natural economic domain. A similar result holds for Kalai and Smorodinsky’s (1975) characterization of their solution if and only if the domain contains multiple goods. The non-welfarist characterization of the Nash solution is shown to extend to a larger class of preferences that accommodate some forms of non-expected utility.