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A Constructive Proof of the Nash Bargaining Solution

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  • Luís Carvalho

Abstract

This paper o ers a constructive proof of the Nash Bargaining solution. We start by proving that Nashs solution is representable based on its continuity. This property along with the linearity of the choice function will then allow us to identify the function representing Nashs bargaining choice. Finally, supported on the result for two players, we will generalize it to n-players.

Suggested Citation

  • Luís Carvalho, 2014. "A Constructive Proof of the Nash Bargaining Solution," Working Papers Series 2 14-01, ISCTE-IUL, Business Research Unit (BRU-IUL).
  • Handle: RePEc:isc:iscwp2:bruwp1401
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    File URL: http://bru-unide.iscte.pt/RePEc/pdfs/14-01.pdf
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    References listed on IDEAS

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    1. Hans Peters & Dries Vermeulen, 2012. "WPO, COV and IIA bargaining solutions for non-convex bargaining problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 851-884, November.
    2. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    3. Marco Mariotti, 1999. "Fair Bargains: Distributive Justice and Nash Bargaining Theory," Review of Economic Studies, Oxford University Press, vol. 66(3), pages 733-741.
    4. Lin Zhou, 1997. "The Nash Bargaining Theory with Non-Convex Problems," Econometrica, Econometric Society, vol. 65(3), pages 681-686, May.
    5. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    6. Conley, John P. & Wilkie, Simon, 1996. "An Extension of the Nash Bargaining Solution to Nonconvex Problems," Games and Economic Behavior, Elsevier, vol. 13(1), pages 26-38, March.
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    More about this item

    Keywords

    Nash Bargaining; Constructive Proof;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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