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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Berman A and Plemmons RJ (1994). Nonnegative matrices in the mathematical sciences. SIAM, Philadelphia
Carlson D and Markham T (1979). Schur complements of diagonally dominant matrices. Czech Math J 29: 246–251
Zeeuw AJ and Ploeg F (1991). Difference games and policy evaluation: a conceptual framework. Oxf Econ Pap 43: 612–636
Douven RC and Engwerda JC (1995). Is there room for convergence in the E.C.?. Eur J Polit Econ 11: 113–130
Douven RC (1995) Policy coordination and convergence in the EU. PhD. Thesis Tilburg University
Engwerda JC (2005). Linear quadratic dynamic optimization and differential games. Wiley, Chichester
Ghosh AR and Masson PR (1994). Economic cooperation in an uncertain world. Blackwell, Oxford
Lei T-G, Woo C-W, Liu J-Z, Zhang F (2003) On the Schur complement of diagonally dominant matrices. In: Proceedings of the SIAM conference on applied linear algebra. July 2003, Williamsburg, CP 13
Nabben R and Varga RS (1994). A linear algebraic proof that the inverse of a strictly ultrametric matrix is a strictly diagonally dominant Stieltjes matrix. SIAM J Matrix Anal Appl 15: 107–113
Nabben R (2000). A class of inverse M-matrices. Electron J Linear Algebra 7: 53–58
Nash JF (1950). The bargaining problem. Econometrica 18: 155–162
Peters HJM (1992). Axiomatic bargaining game theory. Kluwer, Dordrecht
Petit ML (1990). Control theory and dynamic games in economic policy analysis. Cambridge University Press, Cambridge
Plasmans J and Engwerda J (2006). Dynamic modeling of monetary and fiscal policy cooperation among nations. Springer, Berlin
Thomson W (1987). Monotonicity of bargaining solutions with respect to the disagreement Point. J Econ Theory 42: 50–58
Thomson W and Lensberg T (1989). Axiomatic theory of bargaining with a variable number of players. Cambridge University Press, Cambridge
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Engwerda, J.C., Douven, R.C. On the sensitivity matrix of the Nash bargaining solution. Int J Game Theory 37, 265–279 (2008). https://doi.org/10.1007/s00182-007-0113-2
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00182-007-0113-2