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|
|Date of revision:|
|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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- Sprumont, Yves, 2000.
"A note on ordinally equivalent Pareto surfaces,"
Journal of Mathematical Economics,
Elsevier, vol. 34(1), pages 27-38, August.
- 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.
- Ehud Kalai, 1977.
"Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons,"
179, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-30, October.
- Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
- 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
- Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
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