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An ordinal solution to bargaining problems with many players

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  • Safra, Zvi
  • Samet, Dov

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

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

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Thomson, W., 1989. "Cooperative Models Of Bargaining," RCER Working Papers 177, University of Rochester - Center for Economic Research (RCER).
  2. SPRUMONT, Yves, 1997. "A Note on Ordinally Equivalent Pareto Surfaces," Cahiers de recherche 9702, Universite de Montreal, Departement de sciences economiques.
  3. 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.
  4. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-30, October.
  5. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
  6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
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Cited by:
  1. Calvo, Emilio & Peters, Hans, 2005. "Bargaining with ordinal and cardinal players," Games and Economic Behavior, Elsevier, vol. 52(1), pages 20-33, July.
  2. Barry O'Neill & Dov Samet & Zvi Wiener & Eyal Winter, 2001. "Bargaining with an Agenda," Game Theory and Information 0110004, EconWPA.
  3. Geoffroy de Clippel, 2009. "Axiomatic Bargaining on Economic Enviornments with Lott," Working Papers 2009-5, Brown University, Department of Economics.
  4. repec:ebl:ecbull:v:3:y:2004:i:26:p:1-6 is not listed on IDEAS
  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. 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).
  7. Özgür Kıbrıs, 2012. "Nash bargaining in ordinal environments," Review of Economic Design, Springer, vol. 16(4), pages 269-282, December.
  8. Jozsef Sakovics, 2004. "A meaningful two-person bargaining solution based on ordinal preferences," Economics Bulletin, AccessEcon, vol. 3(26), pages 1-6.
  9. 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.

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