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The Shapley value for bicooperative games

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Abstract

The aim of the present paper is to study a one-point solution concept for bicooperative games. For these games introduced by Bilbao (2000), we define a one-point solution called the Shapley value, since this value can be interpreted in a similar way to the classical Shapley value for cooperative games. The main result of the paper is an axiomatic characterization of this value.

Suggested Citation

  • Jesús Mario Bilbao & Julio R. Fernández & Nieves Jiménez & Jorge Jesús López, 2004. "The Shapley value for bicooperative games," Economic Working Papers at Centro de Estudios Andaluces E2004/56, Centro de Estudios Andaluces.
    • Handle: RePEc:cea:doctra:e2004_56
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    1. Jesús Mario Bilbao & Julio R. Fernández & Nieves Jiménez & Jorge Jesús López, 2004. "Probabilistic values for bicooperative games," Economic Working Papers at Centro de Estudios Andaluces E2004/54, Centro de Estudios Andaluces.
    2. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation for Research in Economics, Yale University.
    3. MoshÊ Machover & Dan S. Felsenthal, 1997. "Ternary Voting Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 335-351.
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    Cited by:

    1. René Brink, 2012. "On hierarchies and communication," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 721-735, October.
    2. Michel Grabisch, 2011. "Ensuring the boundedness of the core of games with restricted cooperation," Annals of Operations Research, Springer, vol. 191(1), pages 137-154, November.
    3. René van den Brink & Simin He & Jia-Ping Huang, 2015. "Polluted River Problems and Games with a Permission Structure," Tinbergen Institute Discussion Papers 15-108/II, Tinbergen Institute.
    4. Navarro, Florian, 2020. "The center value: A sharing rule for cooperative games on acyclic graphs," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 1-13.
    5. C. Manuel & E. González-Arangüena & R. Brink, 2013. "Players indifferent to cooperate and characterizations of the Shapley value," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 1-14, February.
    6. Michel Grabisch & Christophe Labreuche, 2010. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," Annals of Operations Research, Springer, vol. 175(1), pages 247-286, March.
    7. Mihai Daniel Roman & Diana Mihaela Stanculescu, 2021. "An Analysis of Countries’ Bargaining Power Derived from the Natural Gas Transportation System Using a Cooperative Game Theory Model," Energies, MDPI, vol. 14(12), pages 1-13, June.
    8. Margarita Domènech & José Miguel Giménez & María Albina Puente, 2020. "Some Properties for Bisemivalues on Bicooperative Games," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 270-288, April.
    9. Selcuk, O. & Talman, A.J.J., 2013. "Games With General Coalitional Structure," Other publications TiSEM 8d356e38-cdce-41e0-b3dd-a, Tilburg University, School of Economics and Management.
    10. Conrado M. Manuel & Daniel Martín, 2021. "A Monotonic Weighted Banzhaf Value for Voting Games," Mathematics, MDPI, vol. 9(12), pages 1-23, June.
    11. Encarnacion Algaba & René van den Brink & Chris Dietz, 2015. "Power Measures and Solutions for Games under Precedence Constraints," Tinbergen Institute Discussion Papers 15-007/II, Tinbergen Institute.
    12. Fabien Lange & Michel Grabisch, 2011. "New axiomatizations of the Shapley interaction index for bi-capacities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00625355, HAL.
    13. García-Martínez, Jose A. & Mayor-Serra, Antonio J. & Meca, Ana, 2020. "Efficient Effort Equilibrium in Cooperation with Pairwise Cost Reduction," MPRA Paper 105604, University Library of Munich, Germany.
    14. Encarnación Algaba & Rene van den Brink & Chris Dietz, 2013. "Cooperative Games on Accessible Union Stable Systems," Tinbergen Institute Discussion Papers 13-207/II, Tinbergen Institute.
    15. Bilbao, J.M. & Jiménez, N. & López, J.J., 2010. "The selectope for bicooperative games," European Journal of Operational Research, Elsevier, vol. 204(3), pages 522-532, August.
    16. van den Brink, René & González-Arangüena, Enrique & Manuel, Conrado & del Pozo, Mónica, 2014. "Order monotonic solutions for generalized characteristic functions," European Journal of Operational Research, Elsevier, vol. 238(3), pages 786-796.
    17. Selcuk, O. & Talman, A.J.J., 2013. "Games With General Coalitional Structure," Discussion Paper 2013-002, Tilburg University, Center for Economic Research.
    18. van den Brink, René & He, Simin & Huang, Jia-Ping, 2018. "Polluted river problems and games with a permission structure," Games and Economic Behavior, Elsevier, vol. 108(C), pages 182-205.

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    More about this item

    Keywords

    Bicooperative games; Shapley value.;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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