Non-optimal Nash bargaining solutions

Because Weak Pareto Optimality (WPO) only excludes the disagreement solution in the Nash (Econometrica, 1950, 18, 155–162) characterization, it is not possible to obtain ‘intermediate’ Nash Bargaining Solutions (NBS) by dropping WPO. We provide an axiomatic characterization of the following class α(·,·) of such intermediate solutions: for a bargaining problem (S,d), α(S,d) = (1−α)d + αν(S,d), where ν(·,·) denotes the NBS and α ε[0,1]. Relatedly, we provide a new characterization of the NBS in which the role of independence axioms is reduced and the role of WPO is extended to exclude exactly all these intermediate solutions.