Introduction

The focus of this chapter is on the Nash solution. We offer a new characterization of this solution based on several standard axioms already introduced and discussed in previous chapters and a new axiom, similar to the Population Monotonicity axiom, that concerns the behavior of solutions across cardinalities. Loosely speaking, this axiom says that the outcome selected for a particular problem should be best not only for that problem but also for the subproblem faced by any subgroup, consisting of all the feasible alternatives at which the utilities of all the agents not in the subgroup are kept at the levels specified by the proposed outcome.

The characterization offered here differs from the classic characterization of the Nash solution (see Chapter 2) in that no use is made of the axiom of Independence of Irrelevant Alternatives, whose role is played by this new axiom.

The characterization of the two-person Nash solution, given by Nash in his original paper, has indeed been criticized for its reliance on the independence axiom. Although there are good reasons why one may want to impose it (recall our discussion of the axiom in Chapter 4), it would be of interest to develop results that do not rely on it. It is in that spirit that another axiom will be used instead. This axiom will turn out to play a role very similar to that played by the independence axiom, but its normative significance is quite different.