Location of Repository

An ordinal solution to bargaining problems with many players

By Zvi Safra and Dov Samet

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.Bargaining problems; Ordinal utility; Bargaining solutions

OAI identifier:

Suggested articles

Preview

Citations

  1. (2000). A note on ordinally equivalent Pareto surfaces,
  2. (2001). Bargaining with an agenda, forthcoming in Games and Economic Behavior.
  3. (1994). Cooperative models of bargaining.
  4. (1957). Elementary Proof of the Essentiality of the Identical Mapping of a Simplex. Uspekhi Mat.
  5. (1982). Game Theory in the Social Sciences: Concepts and Solutions,
  6. (2001). Ordinal Solutions to Bargaining Problems.
  7. (1975). Other Solutions to the Nash Bargaining Problem,
  8. (1977). Proportional Solutions to Bargaining Situations:
  9. (1950). The Bargaining Problem,
  10. (1990). Theorems on Closed Coverings of a Simplex and Their Applications to Cooperative Game Theory.
  11. (1969). Utility Comparison and the Theory of Games,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.