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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 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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Bibliographic Info

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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Related research

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

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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.
  2. 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.
  3. Zeeuw, A.J. de & Ploeg, F. van der, 1987. "Difference games and policy evaluation: A conceptual framework," Research Memorandum 268, Tilburg University, Faculty of Economics and Business Administration.
  4. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  5. Thomson,William & Lensberg,Terje, 1989. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521343831, December.
  6. Engwerda, J.C. & Aarle, B. van & Plasmans, J.E.J., 2002. "Cooperative and non-cooperative fiscal stabilization policies in the EMU," Open Access publications from Tilburg University urn:nbn:nl:ui:12-88304, Tilburg University.
  7. Thomson,William & Lensberg,Terje, 2006. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521027038, November.
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Cited by:
  1. Engwerda, J.C., 2005. "On the Matrix (I + X)-1 ," Discussion Paper 2005-120, Tilburg University, Center for Economic Research.

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