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An Equitable Nash Solution to Nonconvex Bargaining Problems

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  • Xu, Yongsheng
  • Yoshihara, Naoki

Abstract

This paper studies the Nash solution to non-convex bargaining problems. Given the multiplicity of the Nash solution in this context, we refine the Nash solution by incorporating an equity consideration. The proposed refinement is defined as the composition of the Nash solution and a variant of the Kalai-Smorodinsky solution. We then present an axiomatic characterization of the new solution.

Suggested Citation

  • Xu, Yongsheng & Yoshihara, Naoki, 2018. "An Equitable Nash Solution to Nonconvex Bargaining Problems," Discussion Paper Series 680, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hit:hituec:680
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    File URL: https://hermes-ir.lib.hit-u.ac.jp/hermes/ir/re/29632/DP680.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.
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    18. 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.
    19. Tadenuma, Koichi, 2002. "Efficiency First or Equity First? Two Principles and Rationality of Social Choice," Journal of Economic Theory, Elsevier, vol. 104(2), pages 462-472, June.
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    Cited by:

    1. Yongsheng Xu & Naoki Yoshihara, 2020. "Nonconvex Bargaining Problems: Some Recent Developments," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 37(1), pages 7-41, November.
    2. William Thomson, 2022. "On the axiomatic theory of bargaining: a survey of recent results," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 491-542, December.

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    More about this item

    Keywords

    non-convex bargaining problem; Nash solution; equitable Nash solution; equity principle; binary weak axiom of revealed preference;
    All these keywords.

    JEL classification:

    • 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
    • D6 - Microeconomics - - Welfare Economics
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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