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

Author

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  • Michele Lombardi

    (Queen Mary, University of London)

  • Naoki Yoshihara

    (Hitotsubashi University)

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

  • Michele Lombardi & Naoki Yoshihara, 2008. "Alternative Characterizations of the Proportional Solution for Nonconvex Bargaining Problems with Claims," Working Papers 632, Queen Mary University of London, School of Economics and Finance.
    • Handle: RePEc:qmw:qmwecw:632
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    References listed on IDEAS

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    Cited by:

    1. 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.
    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.
    3. Gong, Doudou & Dietzenbacher, Bas & Peters, Hans, 2022. "A random arrival rule for NTU-bankruptcy problems," Economics Letters, Elsevier, vol. 218(C).
    4. Xu, Yongsheng & Yoshihara, Naoki, 2011. "Proportional Nash solutions - A new and procedural analysis of nonconvex bargaining problems," Discussion Paper Series 552, Institute of Economic Research, Hitotsubashi University.
    5. 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.

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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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