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An equitable Nash solution to nonconvex bargaining problems

Author

Listed:
  • Yongsheng Xu

    (Georgia State University)

  • Naoki Yoshihara

    (School of Economics and Management, Kochi University of Technology)

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

  • Yongsheng Xu & Naoki Yoshihara, 2018. "An equitable Nash solution to nonconvex bargaining problems," Working Papers SDES-2018-11, Kochi University of Technology, School of Economics and Management, revised Oct 2018.
    • Handle: RePEc:kch:wpaper:sdes-2018-11
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    File URL: http://www.souken.kochi-tech.ac.jp/seido/wp/SDES-2018-11.pdf
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    References listed on IDEAS

    as
    1. Conley, John P. & Wilkie, Simon, 1991. "The bargaining problem without convexity : Extending the egalitarian and Kalai-Smorodinsky solutions," Economics Letters, Elsevier, vol. 36(4), pages 365-369, August.
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    6. Xu, Yongsheng & Yoshihara, Naoki, 2013. "Rationality and solutions to nonconvex bargaining problems: Rationalizability and Nash solutions," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 66-70.
    7. Lombardi, Michele & Yoshihara, Naoki, 2010. "Alternative characterizations of the proportional solution for nonconvex bargaining problems with claims," Economics Letters, Elsevier, vol. 108(2), pages 229-232, August.
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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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