Proportional Nash solutions - A new and procedural analysis of nonconvex bargaining problems
AbstractThis 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Institute of Economic Research, Hitotsubashi University in its series Discussion Paper Series with number 552.
Length: 21 p.
Date of creation: Jun 2011
Date of revision:
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.
Contact details of provider:
Postal: 2-1 Naka, Kunitachi City, Tokyo 186
Web page: http://www.ier.hit-u.ac.jp/
More information through EDIRC
Other versions of this item:
- 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.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-07-13 (All new papers)
- NEP-GTH-2011-07-13 (Game Theory)
- NEP-MIC-2011-07-13 (Microeconomics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Herrero, Maria Jose, 1989. "The nash program: Non-convex bargaining problems," Journal of Economic Theory, Elsevier, vol. 49(2), pages 266-277, December.
- Lin Zhou, 1997. "The Nash Bargaining Theory with Non-Convex Problems," Econometrica, Econometric Society, vol. 65(3), pages 681-686, May.
- Paola Manzini & Marco Mariotti, 2007. "Sequentially Rationalizable Choice," American Economic Review, American Economic Association, vol. 97(5), pages 1824-1839, December.
- 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.
- 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.
- 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.
- 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.
- Paola Manzini & Marco Mariotti, 2006. "Two-stage Bargaining Solutions," Working Papers 572, Queen Mary, University of London, School of Economics and Finance.
- Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
- Lombardi, Michele & Yoshihara, Naoki, 2010.
"Alternative characterizations of the proportional solution for nonconvex bargaining problems with claims,"
Elsevier, vol. 108(2), pages 229-232, August.
- Lombardi, Michele & Yoshihara, Naoki, 2008. "Alternative Characterizations of the Proportional Solution for Nonconvex Bargaining Problems with Claims," Discussion Paper Series a501, Institute of Economic Research, Hitotsubashi University.
- 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.
- 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.
- Jose Apesteguia & Miguel A. Ballester, 2008.
"A Characterization of Sequential Rationalizability,"
345, Barcelona Graduate School of Economics.
- Jose Apesteguia & Miguel A. Ballester, 2008. "A characterization of sequential rationalizability," Economics Working Papers 1089, Department of Economics and Business, Universitat Pompeu Fabra.
- Hammond, Peter J, 1976. "Equity, Arrow's Conditions, and Rawls' Difference Principle," Econometrica, Econometric Society, vol. 44(4), pages 793-804, July.
- Mariotti, Marco, 1999.
"Fair Bargains: Distributive Justice and Nash Bargaining Theory,"
Review of Economic Studies,
Wiley Blackwell, vol. 66(3), pages 733-41, July.
- Marco Mariotti, 1998. "Fair Bargains: Distributive Justice and Nash Bargaining Theory," Royal Holloway, University of London: Discussion Papers in Economics 98/16, Department of Economics, Royal Holloway University of London, revised Feb 1998.
- Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, vol. 38(115), pages 307-17, July.
- Peters, Hans & Vermeulen, Dries, 2006.
"WPO, COV and IIA bargaining solutions,"
021, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Hiromichi Miyake).
If references are entirely missing, you can add them using this form.