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Proportional Nash solutions - A new and procedural analysis of nonconvex bargaining problems

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  • Xu, Yongsheng
  • Yoshihara, Naoki

Abstract

This paper studies the Nash solution to nonconvex bargaining problems. The Nash solution in such a context is typically multi-valued. We introduce a procedure to exclude some options recommended by the Nash solution. The procedure is based on the idea of the Kalai-Smorodinsky solution which has the same informational requirement on individual utilities as the Nash solution does and has an equity consideration as well. We then use this procedure to introduce two new solutions to nonconvex bargaining problems and study them axiomatically.

Suggested Citation

  • 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.
  • Handle: RePEc:hit:hituec:552
    Note: This Version: 23 June 2011, An earlier version of the paper was presented at the SEA meetings in Atlanta, Georgia, November 2010 and at the CEPET meeting in Udine, Italy, June 2011.
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    References listed on IDEAS

    as
    1. 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.
    2. Paola Manzini & Marco Mariotti, 2007. "Sequentially Rationalizable Choice," American Economic Review, American Economic Association, vol. 97(5), pages 1824-1839, December.
    3. Jose Apesteguia & Miguel A. Ballester, 2008. "A characterization of sequential rationalizability," Economics Working Papers 1089, Department of Economics and Business, Universitat Pompeu Fabra.
    4. Herrero, Maria Jose, 1989. "The nash program: Non-convex bargaining problems," Journal of Economic Theory, Elsevier, vol. 49(2), pages 266-277, December.
    5. 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.
    6. Makoto Tanaka & Ryo-ichi Nagahisa, 2002. "An axiomatization of the Kalai-Smorodinsky solution when the feasible sets can be finite," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 751-761.
    7. Marco Mariotti, 1999. "Fair Bargains: Distributive Justice and Nash Bargaining Theory," Review of Economic Studies, Oxford University Press, vol. 66(3), pages 733-741.
    8. Lin Zhou, 1997. "The Nash Bargaining Theory with Non-Convex Problems," Econometrica, Econometric Society, vol. 65(3), pages 681-686, May.
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    10. 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.
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    13. Paola Manzini & Marco Mariotti, 2006. "Two-stage Bargaining Solutions," Working Papers 572, Queen Mary University of London, School of Economics and Finance.
    14. 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.
    15. Peters Hans & Vermeulen Dries, 2006. "WPO, COV and IIA bargaining solutions," Research Memorandum 021, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    16. Amartya K. Sen, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Oxford University Press, vol. 38(3), pages 307-317.
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    More about this item

    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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