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An ordinal solution to bargaining problems with many players

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  • Zvi Safra

    (Facutly of Management Tel Aviv University)

  • Dov Samet

    (Facutly of Management Tel Aviv University)

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.

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Bibliographic Info

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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Keywords: Bargaining problems; Ordinal utility; Bargaining solutions;

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References

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  1. Ehud Kalai, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Discussion Papers 179, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Barry O'Neill & Dov Samet & Zvi Wiener & Eyal Winter, 2001. "Bargaining with an Agenda," Game Theory and Information 0110004, EconWPA.
  3. Thomson, W., 1989. "Cooperative Models Of Bargaining," RCER Working Papers 177, University of Rochester - Center for Economic Research (RCER).
  4. Sprumont, Yves, 2000. "A note on ordinally equivalent Pareto surfaces," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 27-38, August.
  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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Citations

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Cited by:
  1. Barry O'Neill & Dov Samet & Zvi Wiener & Eyal Winter, 2002. "Bargaining with an Agenda," Discussion Paper Series dp315, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. Calvo, Emilio & Peters, Hans, 2005. "Bargaining with ordinal and cardinal players," Games and Economic Behavior, Elsevier, vol. 52(1), pages 20-33, July.
  3. Özgür Kıbrıs, 2012. "Nash bargaining in ordinal environments," Review of Economic Design, Springer, vol. 16(4), pages 269-282, December.
  4. Jozsef Sakovics, 2004. "A meaningful two-person bargaining solution based on ordinal preferences," Economics Bulletin, AccessEcon, vol. 3(26), pages 1-6.
  5. Samet, Dov & Safra, Zvi, 2005. "A family of ordinal solutions to bargaining problems with many players," Games and Economic Behavior, Elsevier, vol. 50(1), pages 89-106, January.
  6. repec:ebl:ecbull:v:3:y:2004:i:26:p:1-6 is not listed on IDEAS
  7. John Conley & Simon Wilkie, 2012. "The ordinal egalitarian bargaining solution for finite choice sets," Social Choice and Welfare, Springer, vol. 38(1), pages 23-42, January.
  8. Geoffroy de Clippel, 2009. "Axiomatic Bargaining on Economic Enviornments with Lott," Working Papers 2009-5, Brown University, Department of Economics.
  9. David Perez-Castrillo & David Wettstein, 2004. "An Ordinal Shapley Value for Economic Environments (Revised Version)," UFAE and IAE Working Papers 634.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).

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