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An ordinal solution to bargaining problems with many players

Author

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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.

Suggested Citation

  • Zvi Safra & Dov Samet, 2003. "An ordinal solution to bargaining problems with many players," Game Theory and Information 0310002, University Library of Munich, Germany.
    • 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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    References listed on IDEAS

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    7. 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.
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    Cited by:

    1. 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.
    2. Jozsef Sakovics, 2004. "A meaningful two-person bargaining solution based on ordinal preferences," Economics Bulletin, AccessEcon, vol. 3(26), pages 1-6.
    3. Eric van Damme & Xu Lang, 2022. "Two-Person Bargaining when the Disagreement Point is Private Information," Papers 2211.06830, arXiv.org, revised Jan 2024.
    4. Perez-Castrillo, David & Wettstein, David, 2006. "An ordinal Shapley value for economic environments," Journal of Economic Theory, Elsevier, vol. 127(1), pages 296-308, March.
    5. Vidal-Puga, Juan, 2015. "A non-cooperative approach to the ordinal Shapley–Shubik rule," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 111-118.
    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. Geoffroy de Clippel, 2009. "Axiomatic Bargaining on Economic Enviornments with Lott," Working Papers 2009-5, Brown University, Department of Economics.
    8. Vidal-Puga, Juan, 2013. "A non-cooperative approach to the ordinal Shapley rule," MPRA Paper 43790, University Library of Munich, Germany.
    9. 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.
    10. Alon, Shiri & Lehrer, Ehud, 2019. "Competitive equilibrium as a bargaining solution: An axiomatic approach," Games and Economic Behavior, Elsevier, vol. 118(C), pages 60-71.
    11. Calvo, Emilio & Peters, Hans, 2005. "Bargaining with ordinal and cardinal players," Games and Economic Behavior, Elsevier, vol. 52(1), pages 20-33, July.
    12. Özgür Kıbrıs, 2012. "Nash bargaining in ordinal environments," Review of Economic Design, Springer;Society for Economic Design, vol. 16(4), pages 269-282, December.
    13. repec:ebl:ecbull:v:3:y:2004:i:26:p:1-6 is not listed on IDEAS
    14. John Conley & Simon Wilkie, 2012. "The ordinal egalitarian bargaining solution for finite choice sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(1), pages 23-42, January.

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    More about this item

    Keywords

    Bargaining problems; Ordinal utility; Bargaining solutions;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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