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The Harsanyi paradox and the “right to talk” in bargaining among coalitions

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  • Vidal-Puga, Juan

Abstract

We describe a coalitional value from a non-cooperative point of view, assuming coalitions are formed for the purpose of bargaining. The idea is that all the players have the same chances to make proposals. This means that players maintain their own “right to talk” when joining a coalition. The resulting value coincides with the weighted Shapley value in the game between coalitions, with weights given by the size of the coalitions. Moreover, the Harsanyi paradox (forming a coalition may be disadvantageous) disappears for convex games.

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  • 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.
    • Handle: RePEc:eee:matsoc:v:64:y:2012:i:3:p:214-224
    DOI: 10.1016/j.mathsocsci.2012.05.002
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    1. Gómez-Rúa, María & Vidal-Puga, Juan, 2010. "The axiomatic approach to three values in games with coalition structure," European Journal of Operational Research, Elsevier, vol. 207(2), pages 795-806, December.
    2. Laruelle, Annick & Valenciano, Federico, 2008. "Noncooperative foundations of bargaining power in committees and the Shapley-Shubik index," Games and Economic Behavior, Elsevier, vol. 63(1), pages 341-353, May.
    3. María Gómez-Rúa & Juan Vidal-Puga, 2011. "Balanced per capita contributions and level structure of cooperation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 167-176, July.
    4. Xun-Feng Hu, 2020. "The weighted Shapley-egalitarian value for cooperative games with a coalition structure," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 193-212, April.
    5. Besner, Manfred, 2018. "The weighted Shapley support levels values," MPRA Paper 87617, University Library of Munich, Germany.
    6. Zhang, Xiaodong, 2009. "A note on the group bargaining solution," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 155-160, March.
    7. Calvo, Emilio & Gutiérrez, Esther, 2010. "Solidarity in games with a coalition structure," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 196-203, November.
    8. Besner, Manfred, 2018. "Two classes of weighted values for coalition structures with extensions to level structures," MPRA Paper 87742, University Library of Munich, Germany.
    9. Gustavo Bergantiños & Balbina Casas- Méndez & Gloria Fiestras- Janeiro & Juan Vidal-Puga, 2005. "A Focal-Point Solution for Bargaining Problems with Coalition Structure," Game Theory and Information 0511006, University Library of Munich, Germany.
    10. 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.
    11. Besner, Manfred, 2018. "Weighted Shapley hierarchy levels values," MPRA Paper 88160, University Library of Munich, Germany.
    12. María Gómez-Rúa & Juan Vidal-Puga, 2014. "Bargaining and membership," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 800-814, July.
    13. Besner, Manfred, 2021. "Disjointly productive players and the Shapley value," MPRA Paper 108241, University Library of Munich, Germany.
    14. Besner, Manfred, 2023. "The per capita Shapley support levels value," MPRA Paper 116457, University Library of Munich, Germany.
    15. Besner, Manfred, 2017. "Weighted Shapley levels values," MPRA Paper 82978, University Library of Munich, Germany.
    16. Besner, Manfred, 2021. "Disjointly and jointly productive players and the Shapley value," MPRA Paper 108511, University Library of Munich, Germany.

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    More about this item

    JEL classification:

    • 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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