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On the sensitivity matrix of the Nash bargaining solution

  • Jacob Engwerda

    ()

  • Rudy Douven

In this note we derive the sensitivity matrix of the Nash bargaining solution w.r.t. the disagreement point d.This first order derivative is completely specified in terms of the Pareto frontier function.We show that whenever one player increases his threatpoint always at least one player will loose utility: i.e. the dual result of Pareto optimality.Furthermore,the dmonotonicity property is easily re-established from this matrix.This matrix also enables us to consider the concept of local strong d-monotonicity.That is,under which conditions on the Pareto frontier function . an infinitesimal increase of di,while for each j = i, dj remains constant,it happens that agent i is the only one who s payoff increases.We show that for the Nash bargaining solution this question is closely related to non-negativity of the Hamiltonian matrix of . at the solution.

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File URL: http://hdl.handle.net/10.1007/s00182-007-0113-2
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Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 37 (2008)
Issue (Month): 2 (June)
Pages: 265-279

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Handle: RePEc:spr:jogath:v:37:y:2008:i:2:p:265-279
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  1. Douven, R.C.M.H. & Engwerda, J.C., 1995. "Is there room for convergence in the E.C.?," Other publications TiSEM 36d97fd3-a495-4c2e-b800-0, Tilburg University, School of Economics and Management.
  2. repec:cup:cbooks:9780521027038 is not listed on IDEAS
  3. 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.
  4. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  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.
  6. de Zeeuw, A.J. & van der Ploeg, F., 1987. "Difference games and policy evaluation : A conceptual framework," Research Memorandum FEW 268, Tilburg University, School of Economics and Management.
  7. 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.
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