Monotonicity properties

Abstract

Both foregoing chapters dealt with solutions depending on only local properties of the Pareto optimal subset of a bargaining game. Chapter 2 extensively discussed nonsymmetric Nash bargaining solutions, and chapter 3 led us to conclude that, at least for the case of two players and in the presence of Pareto optimality and (feasible set) continuity, the independence of irrelevant alternatives axiom implies the maximization of a strongly monotonic, strongly quasiconcave function (corollary 3.21, lemma 3.18): again a quite local phenomenon. The localization axiom (LOC) explicitly expresses this solution property (see section 2.5). As remarked at the end of subsection 2.5.2, feasible set continuity of a solution suffices to imply the equivalence of IIA and LOC. Thus, it is not surprising that the critical discussion in the literature has focussed on this localization property of the symmetric Nash bargaining solution, and on the IIA axiom.