An ordinal solution to bargaining problems with many players
AbstractShapley proved the existence of an ordinal, symmetric and efficient solution for three-player bargaining problems. Ordinality refers to the covariance of the solution with respect to order-preserving transformations of utilities. The construction of this solution is based on a special feature of the three-player utility space: given a Pareto surface in this space, each utility vector is the ideal point of a unique utility vector, which we call a ground point for the ideal point. Here, we extend Shapley's solution to more than three players by proving first that for each utility vector there exists a ground point. Uniqueness, however, is not guaranteed for more than three players. We overcome this difficulty by the construction of a single point from the set of ground points, using minima and maxima of coordinates.
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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Games and Economic Behavior.
Volume (Year): 46 (2004)
Issue (Month): 1 (January)
Contact details of provider:
Web page: http://www.elsevier.com/locate/inca/622836
Other versions of this item:
- Zvi Safra & Dov Samet, 2003. "An ordinal solution to bargaining problems with many players," Game Theory and Information 0310002, EconWPA.
- C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
- 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
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.:
- Thomson, W., 1989.
"Cooperative Models Of Bargaining,"
RCER Working Papers
177, University of Rochester - Center for Economic Research (RCER).
- 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.
- SPRUMONT, Yves, 1997.
"A Note on Ordinally Equivalent Pareto Surfaces,"
Cahiers de recherche
9702, Universite de Montreal, Departement de sciences economiques.
- O'Neill, Barry & Samet, Dov & Wiener, Zvi & Winter, Eyal, 2004.
"Bargaining with an agenda,"
Games and Economic Behavior,
Elsevier, vol. 48(1), pages 139-153, July.
- Barry O'Neill & Dov Samet & Zvi Wiener & Eyal Winter, 2001. "Bargaining with an Agenda," Game Theory and Information 0110004, EconWPA.
- Barry O'Neill & Dov Samet & Zvi Wiener & Eyal Winter, 2002. "Bargaining with an Agenda," Discussion Paper Series dp315, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- Kalai, Ehud, 1977.
"Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons,"
Econometric Society, vol. 45(7), pages 1623-30, October.
- Ehud Kalai, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Discussion Papers 179, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
- Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
- Calvo, Emilio & Peters, Hans, 2005. "Bargaining with ordinal and cardinal players," Games and Economic Behavior, Elsevier, vol. 52(1), pages 20-33, July.
- Barry O'Neill & Dov Samet & Zvi Wiener & Eyal Winter, 2001.
"Bargaining with an Agenda,"
Game Theory and Information
- Geoffroy de Clippel, 2009. "Axiomatic Bargaining on Economic Enviornments with Lott," Working Papers 2009-5, Brown University, Department of Economics.
- repec:ebl:ecbull:v:3:y:2004:i:26:p:1-6 is not listed on IDEAS
- Samet, Dov & Safra, Zvi, 2005. "A family of ordinal solutions to bargaining problems with many players," Games and Economic Behavior, Elsevier, vol. 50(1), pages 89-106, January.
- David Perez-Castrillo & David Wettstein, 2004. "An Ordinal Shapley Value for Economic Environments (Revised Version)," UFAE and IAE Working Papers 634.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Özgür Kıbrıs, 2012. "Nash bargaining in ordinal environments," Review of Economic Design, Springer, vol. 16(4), pages 269-282, December.
- Jozsef Sakovics, 2004.
"A meaningful two-person bargaining solution based on ordinal preferences,"
AccessEcon, vol. 3(26), pages 1-6.
- Jozsef Sakovics, 2004. "A Meaningful Two-Person Bargaining Solution Based on Ordinal Preferences," ESE Discussion Papers 98, Edinburgh School of Economics, University of Edinburgh.
- John Conley & Simon Wilkie, 2012. "The ordinal egalitarian bargaining solution for finite choice sets," Social Choice and Welfare, Springer, vol. 38(1), pages 23-42, January.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.