Efficiency and monotonicity of bargaining solutions

A continuity axiom for bargaining solutions is introduced, which is satisfied by all Pareto optimal and continuous (in the Hausdorff metric) solutions. It is shown by two examples how this axiom can be used to characterize solutions having certain kind of monotonicity properties. One of the solutions is the lexicographic maximin solution. The other is the lexicographic extension of the Kalai-Smorodinsky solution. The former is an efficient (Pareto optimal) extension of the symmetric proportional solution. The latter is an efficient extension of the Kalai-Smorodinsky solution.