Non-optimal Nash bargaining solutions

Because Weak Pareto Optimally (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 φα(·, ·) of such intermediate solutions: for a bargaining problem (S, d), φα(S, d) = (1 - α)d + αv(S, d), where v(·, ·) denotes the NBS and α ∈ [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.