On the sensitivity matrix of the Nash bargaining solution
AbstractIn 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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Bibliographic InfoArticle provided by Springer in its journal International Journal of Game Theory.
Volume (Year): 37 (2008)
Issue (Month): 2 (June)
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Web page: http://link.springer.de/link/service/journals/00182/index.htm
Other versions of this item:
- Engwerda, J.C. & Douven, R.C.M.H., 2008. "On the sensitivity matrix of the Nash bargaining solution," Open Access publications from Tilburg University urn:nbn:nl:ui:12-364999, Tilburg University.
- Engwerda, J.C. & Douven, R.C.M.H., 2005. "On the Sensitivity Matrix of the Nash Bargaining Solution," Discussion Paper 2005-35, Tilburg University, Center for Economic Research.
- Engwerda, J.C., 2006. "On the Sensitivity Matrix of the Nash Bargaining Solution," Discussion Paper 2006-107, Tilburg University, Center for Economic Research.
- 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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- Zeeuw, A.J. de & Ploeg, F. van der, 1987.
"Difference games and policy evaluation: A conceptual framework,"
268, Tilburg University, Faculty of Economics and Business Administration.
- 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.
- Ploeg, F. van der & Zeeuw, A.J. de, 1991. "Difference games and policy evaluation: A conceptual framework," Open Access publications from Tilburg University urn:nbn:nl:ui:12-377519, Tilburg University.
- 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.
- 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.
- 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.
- 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.
- Thomson,William & Lensberg,Terje, 2006. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521027038.
- Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
- repec:cup:cbooks:9780521343831 is not listed on IDEAS
- Engwerda, J.C., 2005. "On the Matrix (I + X)-1 ," Discussion Paper 2005-120, Tilburg University, Center for Economic Research.
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