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On the sensitivity matrix of the Nash bargaining solution

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Author Info
Engwerda, Jacob (Tilburg University, Center for Economic Research)

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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 [15], this paper introduces local strong d-monotonicity and derives a necessary and sufficient condition for the Nash solution to be locally strong 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.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 107.

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Date of creation: 2006
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Handle: RePEc:dgr:kubcen:2006107

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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  1. Douven, R. C. & Engwerda, J. C., 1995. "Is there room for convergence in the E.C.?," European Journal of Political Economy, Elsevier, vol. 11(1), pages 113-130, March. [Downloadable!] (restricted)
  2. de Zeeuw, A J & van der Ploeg, F, 1991. "Difference Games and Policy Evaluation: A Conceptual Framework," Oxford Economic Papers, Oxford University Press, vol. 43(4), pages 612-36, October. [Downloadable!] (restricted)
  3. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April. [Downloadable!] (restricted)
  4. Engwerda, Jacob C. & van Aarle, Bas & Plasmans, Joseph E. J., 2002. "Cooperative and non-cooperative fiscal stabilization policies in the EMU," Journal of Economic Dynamics and Control, Elsevier, vol. 26(3), pages 451-481, March. [Downloadable!] (restricted)
  5. Thomson, William, 1987. "Monotonicity of bargaining solutions with respect to the disagreement point," Journal of Economic Theory, Elsevier, vol. 42(1), pages 50-58, June. [Downloadable!] (restricted)
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  1. Engwerda, Jacob, 2005. "On the matrix (I + X) -1 <= I," Discussion Paper 120, Tilburg University, Center for Economic Research. [Downloadable!]
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