Bargaining under uncertainty and the monotone path solutions

Uncertainty with respect to the feasible set of utility vectors is introduced in an axiomatic bargaining model. Given a criterion for nonprobabilistic decision-making under uncertainty, a natural efficiency requirement can be imposed on a bargaining solution. Using the maximin ordering, the strictly monotone path solutions (generalizations of the egalitarian solution) to the bargaining problem are characterized as the only continuous solutions that satisfy this efficiency axiom. If the maximin criterion is replaced by the maximax ranking or a strict convex combination of the maximin and the maximax criterion, imposing our efficiency axiom and continuity leads to the dictatorial solutions. (C) 1996 Academic Press, Inc.