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The Shapley-Solidarity Value For Games With A Coalition Structure

Author

Listed:
  • EMILIO CALVO

    (Department of Economic Analysis and ERI-CES, Universitat de Valencia, Av. dels Tarongers, s/n, 46022 Valencia, Spain)

  • ESTHER GUTIÉRREZ

    (Departamento de Economía Aplicada IV., Universidad del País Vasco U. P. V./E. H. U, Av. Lehendakari aguirre, 83, 48015 Bilbao, Spain)

Abstract

A value for games with a coalition structure is introduced, where the rules guiding cooperation among the members of the same coalition are different from the interaction rules among coalitions. In particular, players inside a coalition exhibit a greater degree of solidarity than they are willing to use with players outside their coalition. The Shapley value is therefore used to compute the aggregate payoffs for the coalitions, and the solidarity value to obtain the payoffs for the players inside each coalition.

Suggested Citation

  • Emilio Calvo & Esther Gutiérrez, 2013. "The Shapley-Solidarity Value For Games With A Coalition Structure," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-24.
    • Handle: RePEc:wsi:igtrxx:v:15:y:2013:i:01:n:s0219198913500023
    DOI: 10.1142/S0219198913500023
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    References listed on IDEAS

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    1. Emilio Calvo & Esther Gutierrez, 2011. "A value for cooperative games with a coalition structure," Discussion Papers in Economic Behaviour 0311, University of Valencia, ERI-CES.
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    Citations

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    Cited by:

    1. Bourheneddine Ben Dhaou & Abderrahmane Ziad, 2015. "The Free Solidarity Value," Economics Working Paper Archive (University of Rennes & University of Caen) 201508, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    2. Álvarez-Mozos, Mikel & Hellman, Ziv & Winter, Eyal, 2013. "Spectrum value for coalitional games," Games and Economic Behavior, Elsevier, vol. 82(C), pages 132-142.
    3. Emilio Calvo & Esther Gutiérrez-López, 2018. "Discounted Solidarity Values," Discussion Papers in Economic Behaviour 0418, University of Valencia, ERI-CES.
    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. Emilio Calvo & Esther Gutiérrez-López, 2017. "Asymmetric players in the Solidarity and Shapley values," Discussion Papers in Economic Behaviour 0217, University of Valencia, ERI-CES.
    6. Xun-Feng Hu, 2021. "New axiomatizations of the Owen value," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 585-603, June.

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    1. Álvarez-Mozos, Mikel & Hellman, Ziv & Winter, Eyal, 2013. "Spectrum value for coalitional games," Games and Economic Behavior, Elsevier, vol. 82(C), pages 132-142.
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    More about this item

    Keywords

    Coalitional value; Shapley value; Owen value; Solidarity value; C71;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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