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

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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:wp632
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    File URL: http://www.econ.qmul.ac.uk/media/econ/research/workingpapers/archive/wp632.pdf
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    References listed on IDEAS

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    1. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    2. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    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. Chun, Youngsub & Thomson, William, 1992. "Bargaining problems with claims," Mathematical Social Sciences, Elsevier, vol. 24(1), pages 19-33, August.
    5. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    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.
    7. Yongsheng Xu & Naoki Yoshihara, 2008. "The Behaviour Of Solutions To Bargaining Problems On The Basis Of Solidarity," The Japanese Economic Review, Japanese Economic Association, vol. 59(1), pages 133-138.
    8. Thomson, William, 1994. "Cooperative models of bargaining," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 35, pages 1237-1284 Elsevier.
    9. Ross, Stephen A, 1973. "The Economic Theory of Agency: The Principal's Problem," American Economic Review, American Economic Association, vol. 63(2), pages 134-139, May.
    10. Marco Mariotti, 1998. "Nash bargaining theory when the number of alternatives can be finite," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(3), pages 413-421.
    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. Xu, Yongsheng & Yoshihara, Naoki, 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.

    More about this item

    Keywords

    Bargaining problems; Claims point; Proportional solution; Nonconvexity; Solidarity axioms;

    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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