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Intrinsic Comparative Statics of a Nash Bargaining Solution

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  • Michael R. Caputo

    (Department of Economics, University of Central Florida, P. O. Box 161400, Orlando, FL 32816-1400, USA)

Abstract

A generalization of the class of bargaining problems examined by Engwerda and Douven [(2008) On the sensitivity matrix of the Nash bargaining solution, Int. J. Game Theory 37, 265–279] is studied. The generalized class consists of nonconvex bargaining problems in which the feasible set satisfies the requirement that the set of weak Pareto-optimal solutions can be described by a smooth function. The intrinsic comparative statics of the aforesaid class are derived and shown to be characterized by a symmetric and positive semidefinite matrix, and an upper bound to the rank of the matrix is established. A corollary to this basic result is that a Nash bargaining solution is intrinsically a locally nondecreasing function of its own disagreement point. Other heretofore unknown results are similarly deduced from the basic result.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:igtrxx:v:18:y:2016:i:04:n:s0219198916500134
    DOI: 10.1142/S0219198916500134
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Engwerda, J.C. & Douven, R.C.M.H., 2008. "On the sensitivity matrix of the Nash bargaining solution," Other publications TiSEM 8661cd7e-15f7-4384-8d56-3, Tilburg University, School of Economics and Management.
    4. Xu, Yongsheng & Yoshihara, Naoki, 2006. "Alternative characterizations of three bargaining solutions for nonconvex problems," Games and Economic Behavior, Elsevier, vol. 57(1), pages 86-92, October.
    5. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    6. William Thomson, 2009. "Bargaining and the theory of cooperative games: John Nash and beyond," RCER Working Papers 554, University of Rochester - Center for Economic Research (RCER).
    7. M. Hossein Partovi & Michael R. Caputo, 2006. "A Complete Theory Of Comparative Statics For Differentiable Optimization Problems," Metroeconomica, Wiley Blackwell, vol. 57(1), pages 31-67, February.
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    More about this item

    Keywords

    Nash bargaining solution; disagreement point; comparative statics;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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