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On the sensitivity matrix of the Nash bargaining solution

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  • Jacob Engwerda

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  • Rudy Douven

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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Suggested Citation

  • Jacob Engwerda & Rudy Douven, 2008. "On the sensitivity matrix of the Nash bargaining solution," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 265-279, June.
  • Handle: RePEc:spr:jogath:v:37:y:2008:i:2:p:265-279
    DOI: 10.1007/s00182-007-0113-2
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    References listed on IDEAS

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    1. Thomson,William & Lensberg,Terje, 2006. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521027038, April.
    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 612-636, October.
    3. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    4. Douven, R.C.M.H., 1995. "Policy coordination and convergence in the EU," Other publications TiSEM d4354b51-1c72-4109-9bde-e, Tilburg University, School of Economics and Management.
    5. 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.
    6. 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.
    7. 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.
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    Cited by:

    1. Michael R. Caputo, 2016. "Intrinsic Comparative Statics of a Nash Bargaining Solution," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-11, December.

    More about this item

    Keywords

    Nash bargaining solution; d-monotonicity; Diagonally dominant Stieltjes matrix;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - 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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