Collective or individual rationality in the Nash bargaining solution: efficiency-free characterizations

Abstract

In the classical bargaining problem, we propose a very mild axiom of individual rationality, which we call possibility of utility gain. This requires that for at least one bargaining problem, there exists at least one player who reaches a higher utility level than their disagreement utility. This paper shows that the Nash solution (Nash in Econometrica 18(2):155–162, 1950) is characterized by possibility of utility gain and continuity with respect to feasible sets together with Nash’s axioms except weak Pareto optimality. We also show that in Nash’s theorem, weak Pareto optimality can be replaced by conflict-freeness (introduced by Rachmilevitch in Math Soc Sci 76(C):107–109, 2015). This demands that when the agreement most preferred by all players is feasible, this should be chosen. Furthermore, we provide alternative and unified proofs for other efficiency-free characterizations of the Nash solution. This clarifies the role of each axiom in the related results.