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Simultaneity of Issues and Additivity in Bargaining

Hans Peters

Abstract

Simultaneous bargaining over more issues by two bargainers is treated by taking sums of bargaining games and requiring bargaining solutions to satisfy certain (super-) additivity axioms. A (new) characterization of a family of so-called proportional solutions is given with the aid of three axioms: (partial) superadditivity, homogeneity, and weak Pareto optimality. Requiring, besides individual rationality and Pareto continuity, the axioms of restricted additivity, scale transformation invariance, and Pareto optimality, yields an alternative characterization of a family of solutions consisting of all nonsymmetric extensions of Nash's solution. Also these solutions exhibit a (limited) proportionality property. Further, the relation with the Super-Additive solution of Perles and Maschler is discussed, and also the link with Myerson's results on proportional and utilitarian solutions.