Characterizing the Nash Bargaining Solution with Continuity and Almost No Individual Rationality

In the classical bargaining problems, 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 the disagreement point. This paper shows that the Nash solution (Nash, 1950) is characterized by Possibility of Utility Gain and continuity with respect to feasible sets or disagreement points together with Nash’s axioms except Weak Pareto Optimality. We also provide alternative and unified proofs for other efficiency-free characterizations of the Nash solution