Rationality of bargaining solutions

Résumé

We analyze the rationality of two person bargaining solutions by considering conditions which are weaker than those used by Peters and Wakker (1991) or Bossert (1994). As a particular consequence of their results, the rationality of the Nash solution is obtained, although they can not be applied to other well known bargaining solutions. The aim of this paper is, on the one hand, lo prove that a choice function defined on the usual bargaining domain which satisfies Independence of Irrelevant Alternatives, Weak Pareto Optimality and Pareto Continuity is also rationalized by a preorder (reflexive, complete and transitive binary relation). Moreover, the representability of this relation is analyzed. These results can be applied, in particular, lo the Nash solution and moreover to the egalitarian (Kalai, 1977), monotone path solutions and their lexicographic extensions. On the other hand, and by substituting Pareto Continuity for Monotonicity assumptions, rationality IS al so analyzed. As a consequence, a result along the same lines as Bossert's (1994) is obtained.