Reconciling Consistency and Continuity: A Bounded-Population Characterization of the Nash Bargaining Solution

This paper explores the robustness of a characterization of the Nash bargaining solution in a variable-population framework in which the population of players is bounded (Lensberg in J Econ Theory 45:330–341, 1988). A central axiom in this characterization is “consistency”, which says that the solution outcome of any problem should always be “confirmed” by the solution in the “reduced problem” that results after some players have left with their assigned payoffs. Another axiom in this characterization is the standard requirement of Hausdorff continuity. We advocate a weaker version of continuity, a version that is a better conceptual fit with consistency that Hausdorff-continuity, and show that the Nash solution still emerges as the only one to satisfy all of the axioms.