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

  • Xu, Yongsheng
  • Yoshihara, Naoki

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.

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File URL: http://hermes-ir.lib.hit-u.ac.jp/rs/bitstream/10086/19213/1/DP552.pdf
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Paper provided by Institute of Economic Research, Hitotsubashi University in its series Discussion Paper Series with number 552.

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Length: 21 p.
Date of creation: Jun 2011
Date of revision:
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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  1. Hammond, Peter J, 1976. "Equity, Arrow's Conditions, and Rawls' Difference Principle," Econometrica, Econometric Society, vol. 44(4), pages 793-804, July.
  2. Tadenuma, Koichi, 2002. "Efficiency First or Equity First? Two Principles and Rationality of Social Choice," Journal of Economic Theory, Elsevier, vol. 104(2), pages 462-472, June.
  3. 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.
  4. 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.
  5. Marco Mariotti, 1998. "Nash bargaining theory when the number of alternatives can be finite," Social Choice and Welfare, Springer, vol. 15(3), pages 413-421.
  6. Lin Zhou, 1997. "The Nash Bargaining Theory with Non-Convex Problems," Econometrica, Econometric Society, vol. 65(3), pages 681-686, May.
  7. 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.
  8. Herrero, Maria Jose, 1989. "The nash program: Non-convex bargaining problems," Journal of Economic Theory, Elsevier, vol. 49(2), pages 266-277, December.
  9. Paola Manzini & Marco Mariotti, 2007. "Sequentially Rationalizable Choice," American Economic Review, American Economic Association, vol. 97(5), pages 1824-1839, December.
  10. 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, vol. 19(4), pages 751-761.
  11. Mariotti, Marco, 1999. "Fair Bargains: Distributive Justice and Nash Bargaining Theory," Review of Economic Studies, Wiley Blackwell, vol. 66(3), pages 733-41, July.
  12. Paola Manzini & Marco Mariotti, 2006. "Two-stage Bargaining Solutions," Working Papers 572, Queen Mary University of London, School of Economics and Finance.
  13. Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, vol. 38(115), pages 307-17, July.
  14. Jose Apesteguia & Miguel A. Ballester, 2008. "A characterization of sequential rationalizability," Economics Working Papers 1089, Department of Economics and Business, Universitat Pompeu Fabra.
  15. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  16. 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).
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