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An ordinal solution to bargaining problems with many players

  • Zvi Safra

    (Facutly of Management Tel Aviv University)

  • Dov Samet

    (Facutly of Management Tel Aviv University)

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.

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Paper provided by EconWPA in its series Game Theory and Information with number 0310002.

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Length: 12 pages
Date of creation: 08 Oct 2003
Date of revision:
Handle: RePEc:wpa:wuwpga:0310002
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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  1. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  2. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-30, October.
  3. Thomson, W., 1989. "Cooperative Models Of Bargaining," RCER Working Papers 177, University of Rochester - Center for Economic Research (RCER).
  4. SPRUMONT, Yves, 1997. "A Note on Ordinally Equivalent Pareto Surfaces," Cahiers de recherche 9702, Universite de Montreal, Departement de sciences economiques.
  5. 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.
  6. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
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