On the sensitivity matrix of the Nash bargaining solution

Abstract

In this note we provide a characterization of a subclass of bargaining problems for which the Nash solution has the property of disagreement point monotonicity. While the original d-monotonicity axiom and its stronger notion, strong d-monotonicity, were introduced and discussed by Thomson (J Econ Theory, 42: 50-58, 1987), this paper introduces local strong d-monotonicity and derives a necessary and sufficient condition for the Nash solution to be locally strongly d-monotonic. This characterization is given by using the sensitivity matrix of the Nash bargaining solution w.r.t. the disagreement point d. Moverover, we present a sufficient condition for the Nash solution to be strong d-monotonic. © 2007 Springer-Verlag.