An ordinal solution to bargaining problems with many players
Shapley 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.
|Date of creation:||08 Oct 2003|
|Note:||Type of Document - ; pages: 12 . A PowerPoint presentation of the paper is available at http://www.tau.ac.il/~samet/safra-samet-1.pps|
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- Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
- Kalai, Ehud, 1977.
"Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons,"
Econometric Society, vol. 45(7), pages 1623-1630, 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.
- Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
- Sprumont, Yves, 2000. "A note on ordinally equivalent Pareto surfaces," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 27-38, August.
- SPRUMONT, Yves, 1997. "A Note on Ordinally Equivalent Pareto Surfaces," Cahiers de recherche 9702, Universite de Montreal, Departement de sciences economiques.
- 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.
- Thomson, W., 1989. "Cooperative Models Of Bargaining," RCER Working Papers 177, University of Rochester - Center for Economic Research (RCER).
- 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 Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.