Bargaining with reasonable aspirations (Q1342394)

This paper determines a unique solution to a two-player bargaining problem in which player aspirations are assumed to dominate a strongly Pareto-optimal point of the decision set but nevertheless are realistic, insofar as outcomes exist to satisfy the aspirations of both players (though not necessarily simultaneously). Aspirations need not be symmetric when the bargaining set is symmetric. The author does not require invariance with respect to individual transformations of utilities, but instead invokes either restricted homogeneity or relative monotonicity (together with other standard conditions): either axiom yields the unique solution. The result is extended to an arbitrary number of players by requiring comprehensiveness of the decision set; then the first assumption can be relaxed so that player aspirations dominate only a weakly Pareto-optimal point.