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A note on the group bargaining solution

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  • Zhang, Xiaodong
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    Abstract

    The well known Nash's pure bargaining solution was generalized by the author [Zhang, X., 1995. The pure bargaining problem among coalitions. Asia-Pacific Journal of Operational Research 12, 1-15] for the bargaining problem with an exogenous coalition structure. Nash's axiom set was modified to develop a solution mapping for this new type of pure bargaining problem. Among other things, a similar solution concept for the same bargaining problem was given by [Chae, S., Heidhues, P., 2004. A group bargaining solution. Mathematical Social Sciences 48, 37-53]. Their solution's mathematical presentation is quite different from Zhang's solution. In this note, we present a proof to show that the two solutions are equivalent.

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    Bibliographic Info

    Article provided by Elsevier in its journal Mathematical Social Sciences.

    Volume (Year): 57 (2009)
    Issue (Month): 2 (March)
    Pages: 155-160

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    Handle: RePEc:eee:matsoc:v:57:y:2009:i:2:p:155-160

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    Web page: http://www.elsevier.com/locate/inca/505565

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    Keywords: Game theory Bargaining problem Coalition;

    References

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    1. Bergantinos, G. & Casas-Mendez, B. & Fiestras-Janeiro, M.G. & Vidal-Puga, J.J., 2007. "A solution for bargaining problems with coalition structure," Mathematical Social Sciences, Elsevier, vol. 54(1), pages 35-58, July.
    2. Juan Vidal-Puga, 2005. "A bargaining approach to the Owen value and the Nash solution with coalition structure," Economic Theory, Springer, vol. 25(3), pages 679-701, 04.
    3. McLean, Richard P, 1991. "Random Order Coalition Structure Values," International Journal of Game Theory, Springer, vol. 20(2), pages 109-27.
    4. Juan Vidal-Puga, 2005. "The Harsanyi paradox and the 'right to talk' in bargaining among coalitions," Game Theory and Information 0501005, EconWPA.
    5. Vidal-Puga, Juan & Bergantinos, Gustavo, 2003. "An implementation of the Owen value," Games and Economic Behavior, Elsevier, vol. 44(2), pages 412-427, August.
    6. Winter, Eyal, 1991. "On Non-transferable Utility Games with Coalition Structure," International Journal of Game Theory, Springer, vol. 20(1), pages 53-63.
    7. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    8. Chae, Suchan & Heidhues, Paul, 2004. "A group bargaining solution," Mathematical Social Sciences, Elsevier, vol. 48(1), pages 37-53, July.
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