An ordinal solution to bargaining problems with many players

Zvi Safra and Dov Samet
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Zvi Safra: Facutly of Management Tel Aviv University
Dov Samet: Facutly of Management Tel Aviv University

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Abstract: 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.

Keywords: Bargaining problems; Ordinal utility; Bargaining solutions (search for similar items in EconPapers)
JEL-codes: C70 C71 C78 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth
Date: 2003-10-08
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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Persistent link: http://EconPapers.repec.org/RePEc:wpa:wuwpga:0310002

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