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A note on the group bargaining solution

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  • Zhang, Xiaodong

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.

Suggested Citation

  • Zhang, Xiaodong, 2009. "A note on the group bargaining solution," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 155-160, March.
    • Handle: RePEc:eee:matsoc:v:57:y:2009:i:2:p:155-160
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    References listed on IDEAS

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    1. McLean, Richard P, 1991. "Random Order Coalition Structure Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 109-127.
    2. Vidal-Puga, Juan & Bergantinos, Gustavo, 2003. "An implementation of the Owen value," Games and Economic Behavior, Elsevier, vol. 44(2), pages 412-427, August.
    3. Vidal-Puga, Juan, 2012. "The Harsanyi paradox and the “right to talk” in bargaining among coalitions," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 214-224.
    4. Winter, Eyal, 1991. "On Non-transferable Utility Games with Coalition Structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(1), pages 53-63.
    5. Juan Vidal-Puga, 2005. "A bargaining approach to the Owen value and the Nash solution with coalition structure," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 679-701, April.
    6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    7. 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.
    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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