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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
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  1. SPRUMONT, Yves, 1997. "A Note on Ordinally Equivalent Pareto Surfaces," Cahiers de recherche 9702, Universite de Montreal, Departement de sciences economiques.
  2. Thomson, W., 1989. "Cooperative Models Of Bargaining," RCER Working Papers 177, University of Rochester - Center for Economic Research (RCER).
  3. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-30, October.
  4. Barry O'Neill & Dov Samet & Zvi Wiener & Eyal Winter, 2001. "Bargaining with an Agenda," Game Theory and Information 0110004, EconWPA.
  5. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  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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