Gradual negotiations and proportional solutions

I characterize the proportional N -person bargaining solutions by individual rationality, translation invariance, feasible set continuity, and a new axiom— interim improvement. The latter says that if the disagreement point d is known, but the feasible set is not—it may be either S or T , where S ⊂ T—then there exists a point d′ ∈ S, d′ > d, such that replacing d with d′ as the disagreement point would not change the final bargaining outcome, no matter which feasible set will be realized, S or T . In words, if there is uncertainty regarding a possible expansion of the feasible set, the players can wait until it is resolved; in the meantime, they can find a Pareto improving interim outcome to commit to—a commitment that has no effect in case negotiations succeed, but promises higher disagreement payoffs to all in case negotiations fail prior to the resolution of uncertainty.