GENERALIZED GINIS AND COOPERATIVE BARGAINING SOLUTIONS

This paper introduces and characterizes a new class of solutions to co operative bargaining problems that can be rationalized by generalized Gini orderings defined on the agents' utility gains. Generalized Ginis are orderings which can be represented by quasi-concave, nondecreasin g functions that are linear in rank-ordered subspaces of Euclidean n-s pace. Our characterization of (multi-valued) generalized Gini bargaini ng solutions is based on a linear invariance requirement in addition t o some standard conditions. Linear invariance requires that if the fea sible set is changed by adding a constant to one agent's component of each vector of the feasible set (without changing the agent's rank ord er), the solution responds by adding the same constant to the correspo nding agent's utility in the outcome of the problem. Weak linear invar iance requires the solution to change in a parallel way if a constant is added to all components of each vector of the feasible set. In the two-person case, the generalized Gini bargaining solutions can be char acterized by imposing weak linear invariance, whereas, for n greater-t han-or-equal-to 3 agents, linear invariance is required. As a by-produ ct of our main result, we show that the egalitarian bargaining solutio n is characterized if single-valuedness is required together with some of our axioms. The main focus of cooperative bargaining theory has be en the characterization of single-valued solutions. The results of thi s paper demonstrate that relaxing this assumption enlarges the class o f solutions considerably. Hence, single-valuedness is not merely an as sumption of convenience but, rather, an assumption of substance.