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Alternative Characterizations of the Proportional Solution for Nonconvex Bargaining Problems with Claims

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  • Lombardi, Michele
  • Yoshihara, Naoki
  • 吉原, 直毅
  • ヨシハラ, ナオキ

Abstract

We provide three alternative characterizations of the proportional solution defined on compact and comprehensive bargaining problems with claims that are not necessarily convex. One characterization result is obtained by using, together with other standard axioms, two solidarity axioms. Another characterization theorem shows that the single-valuedness axiom is dispensable even within the class of nonconvex problems if the standard symmetry axiom is imposed.

Suggested Citation

  • Lombardi, Michele & Yoshihara, Naoki & 吉原, 直毅 & ヨシハラ, ナオキ, 2008. "Alternative Characterizations of the Proportional Solution for Nonconvex Bargaining Problems with Claims," Discussion Paper Series a501, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hit:hituec:a501
    Note: June, 2008
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    References listed on IDEAS

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    6. Yoshihara, Naoki, 2003. "Characterizations of bargaining solutions in production economies with unequal skills," Journal of Economic Theory, Elsevier, vol. 108(2), pages 256-285, February.
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    11. 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.
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    Cited by:

    1. Yongsheng Xu & Naoki Yoshihara, 2019. "An equitable Nash solution to nonconvex bargaining problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(3), pages 769-779, September.
    2. Albizuri, M.J. & Dietzenbacher, B.J. & Zarzuelo, J.M., 2020. "Bargaining with independence of higher or irrelevant claims," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 11-17.
    3. Xu, Yongsheng & Yoshihara, Naoki & 吉原, 直毅, 2011. "Proportional Nash solutions - A new and procedural analysis of nonconvex bargaining problems," CCES Discussion Paper Series 42, Center for Research on Contemporary Economic Systems, Graduate School of Economics, Hitotsubashi University.
    4. Gong, Doudou & Dietzenbacher, Bas & Peters, Hans, 2022. "A random arrival rule for NTU-bankruptcy problems," Economics Letters, Elsevier, vol. 218(C).
    5. 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

    Bargaining problems; claims point; proportional solution; nonconvexity; solidarity axioms;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D60 - Microeconomics - - Welfare Economics - - - General
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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