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An ordinal solution to bargaining problems with many players

  • Safra, Zvi
  • Samet, Dov

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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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 46 (2004)
Issue (Month): 1 (January)
Pages: 129-142

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Handle: RePEc:eee:gamebe:v:46:y:2004:i:1:p:129-142
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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