Step-by-step negotiations and utilitarianism

I characterize the individually-rational utilitarian bargaining solution by combining several classical axioms with a novel axiom, monotone step-by-step negotiations (monotone SSN). One of the axioms involved in the characterization is conflict freeness, which imposes Pareto optimality on problems that include their ideal point; when conflict freeness is replaced by weak Pareto optimality, only one additional solution becomes admissible—the egalitarian solution. I also show that in Kalai’s (Econometrica 45:1623–1630, 1977) SSN-based characterization of the proportional solutions, SSN can be weakened to monotone SSN if feasible set continuity is assumed.