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Axiomatization and implementation of a class of solidarity values for TU-games

Author

Listed:
  • Sylvain Béal

    (Univ. Bourgogne Franche-Comté)

  • Eric Rémila

    (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne)

  • Philippe Solal

    (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne)

Abstract

A new class of values combining marginalistic and egalitarian principles is introduced for cooperative TU-games. It includes some modes of solidarity among the players by taking the collective contribution of some coalitions to the grand coalition into account. Relationships with other class of values such as the Egalitarian Shapley values and the Procedural values are discussed. We propose a strategic implementation of our class of values in subgame perfect Nash equilibrium. Two axiomatic characterizations are provided: one of the whole class of values, and one of each of its extreme points.

Suggested Citation

  • Sylvain Béal & Eric Rémila & Philippe Solal, 2017. "Axiomatization and implementation of a class of solidarity values for TU-games," Theory and Decision, Springer, vol. 83(1), pages 61-94, June.
    • Handle: RePEc:kap:theord:v:83:y:2017:i:1:d:10.1007_s11238-017-9586-z
    DOI: 10.1007/s11238-017-9586-z
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    Cited by:

    1. Dongshuang Hou & Aymeric Lardon & Panfei Sun & Hao Sun, 2019. "Procedural and optimization implementation of the weighted ENSC value," Theory and Decision, Springer, vol. 87(2), pages 171-182, September.
    2. Surajit Borkotokey & Loyimee Gogoi & Dhrubajit Choudhury & Rajnish Kumar, 2022. "Solidarity induced by group contributions: the MI $$^k$$ k -value for transferable utility games," Operational Research, Springer, vol. 22(2), pages 1267-1290, April.
    3. Xun-Feng Hu & Gen-Jiu Xu & Deng-Feng Li, 2019. "The Egalitarian Efficient Extension of the Aumann–Drèze Value," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 1033-1052, June.
    4. Sylvain Béal & Sylvain Ferrières & Eric Rémila & Philippe Solal, 2017. "Axiomatic and bargaining foundation of an allocation rule for ordered tree TU-games," Post-Print halshs-01644797, HAL.
    5. Borkotokey, Surajit & Choudhury, Dhrubajit & Kumar, Rajnish & Sarangi, Sudipta, 2020. "Consolidating Marginalism and Egalitarianism: A New Value for Transferable Utility Games," QBS Working Paper Series 2020/12, Queen's University Belfast, Queen's Business School.
    6. Sylvain Béal & Eric Rémila & Philippe Solal, 2019. "Coalitional desirability and the equal division value," Theory and Decision, Springer, vol. 86(1), pages 95-106, February.
    7. Emilio Calvo & Esther Gutiérrez-López, 2018. "Discounted Solidarity Values," Discussion Papers in Economic Behaviour 0418, University of Valencia, ERI-CES.
    8. Jun Su & Yuan Liang & Guangmin Wang & Genjiu Xu, 2020. "Characterizations, Potential, and an Implementation of the Shapley-Solidarity Value," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    9. Ben Dhaou Bourheneddine & Ziad Abderrahmane, 2023. "Free Solidarity Value," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 2023-07, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    10. Rong Zou & Wenzhong Li & Marc Uetz & Genjiu Xu, 2023. "Two-step Shapley-solidarity value for cooperative games with coalition structure," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(1), pages 1-25, March.
    11. Borkotokey, Surajit & Choudhury, Dhrubajit & Gogoi, Loyimee & Kumar, Rajnish, 2020. "Group contributions in TU-games: A class of k-lateral Shapley values," European Journal of Operational Research, Elsevier, vol. 286(2), pages 637-648.
    12. Gutiérrez-López, Esther, 2020. "Axiomatic characterizations of the egalitarian solidarity values," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 109-115.

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