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.

Additional Metadata
Keywords Nash bargaining solution · d-monotonicity · Diagonally dominant, Stieltjes matrix
Persistent URL dx.doi.org/10.1007/s00182-007-0113-2, hdl.handle.net/1765/116044
Journal International Journal of Game Theory
Citation
Engwerda, J., & Douven, R.C.H.M. (2007). On the sensitivity matrix of the Nash bargaining solution. International Journal of Game Theory, 37(2), 265–279. doi:10.1007/s00182-007-0113-2