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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.

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File URL: http://hermes-ir.lib.hit-u.ac.jp/rs/bitstream/10086/19222/1/070ccesDP_42.pdf
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Bibliographic Info

Paper provided by Center for Research on Contemporary Economic Systems, Graduate School of Economics, Hitotsubashi University in its series CCES Discussion Paper Series with number 42.

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Length: 21 p.
Date of creation: Jul 2011
Date of revision:
Handle: RePEc:hit:ccesdp:42

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  1. Jose Apesteguia & Miguel A. Ballester, 2008. "A Characterization of Sequential Rationalizability," Working Papers 345, Barcelona Graduate School of Economics.
  2. Paola Manzini & Marco Mariotti, 2007. "Sequentially Rationalizable Choice," American Economic Review, American Economic Association, vol. 97(5), pages 1824-1839, December.
  3. 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.
  4. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  5. 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.
  6. Tadenuma, Koichi, 1998. "Efficiency First or Equity First?: Two Principles and Rationality of Social Choice," Discussion Papers 1998-01, Graduate School of Economics, Hitotsubashi University.
  7. Hammond, Peter J, 1976. "Equity, Arrow's Conditions, and Rawls' Difference Principle," Econometrica, Econometric Society, vol. 44(4), pages 793-804, July.
  8. Mariotti, Marco, 1999. "Fair Bargains: Distributive Justice and Nash Bargaining Theory," Review of Economic Studies, Wiley Blackwell, vol. 66(3), pages 733-41, July.
  9. 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.
  10. 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.
  11. Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, vol. 38(115), pages 307-17, July.
  12. 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.
  13. Paola Manzini & Marco Mariotti, 2006. "Two-stage Bargaining Solutions," Working Papers 572, Queen Mary, University of London, School of Economics and Finance.
  14. 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).
  15. Lin Zhou, 1997. "The Nash Bargaining Theory with Non-Convex Problems," Econometrica, Econometric Society, vol. 65(3), pages 681-686, May.
  16. Herrero, Maria Jose, 1989. "The nash program: Non-convex bargaining problems," Journal of Economic Theory, Elsevier, vol. 49(2), pages 266-277, December.
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