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Axiomatic of the Shapley value of a game with a priori unions

Author

Listed:
  • J. Alonso-Meijide
  • B. Casas-Méndez
  • A. González-Rueda
  • S. Lorenzo-Freire

Abstract

In this paper, we define a modification of the Shapley value for the model of TU games with a priori unions. We provide two characterizations of this value and a new characterization of the Banzhaf–Owen coalitional value. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • J. Alonso-Meijide & B. Casas-Méndez & A. González-Rueda & S. Lorenzo-Freire, 2014. "Axiomatic of the Shapley value of a game with a priori unions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 749-770, July.
    • Handle: RePEc:spr:topjnl:v:22:y:2014:i:2:p:749-770
    DOI: 10.1007/s11750-013-0298-4
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    References listed on IDEAS

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    4. Andrzej S. Nowak, 1997. "note: On an Axiomatization of the Banzhaf Value without the Additivity Axiom," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 137-141.
    5. 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.
    6. Owen, Guillermo & Winter, Eyal, 1992. "The multilinear extension and the coalition structure value," Games and Economic Behavior, Elsevier, vol. 4(4), pages 582-587, October.
    7. Amer, Rafael & Carreras, Francese & Gimenez, Jose Miguel, 2002. "The modified Banzhaf value for games with coalition structure: an axiomatic characterization," Mathematical Social Sciences, Elsevier, vol. 43(1), pages 45-54, January.
    8. J. Alonso-Meijide & F. Carreras & M. Fiestras-Janeiro, 2005. "The Multilinear Extension and the Symmetric Coalition Banzhaf Value," Theory and Decision, Springer, vol. 59(2), pages 111-126, September.
    9. Álvarez-Mozos, M. & van den Brink, R. & van der Laan, G. & Tejada, O., 2013. "Share functions for cooperative games with levels structure of cooperation," European Journal of Operational Research, Elsevier, vol. 224(1), pages 167-179.
    10. Hamiache, Gerard, 1999. "A new axiomatization of the Owen value for games with coalition structures," Mathematical Social Sciences, Elsevier, vol. 37(3), pages 281-305, May.
    11. José Alonso-Meijide & M. Fiestras-Janeiro, 2002. "Modification of the Banzhaf Value for Games with a Coalition Structure," Annals of Operations Research, Springer, vol. 109(1), pages 213-227, January.
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    15. Francesc Carreras & M. Llongueras & Antonio Magaña, 2005. "On the Convenience to Form Coalitions or Partnerships in Simple Games," Annals of Operations Research, Springer, vol. 137(1), pages 67-89, July.
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    Citations

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    Cited by:

    1. André Casajus & Rodrigue Tido Takeng, 2022. "Second-order productivity, second-order payoffs, and the Owen value," Post-Print hal-03798448, HAL.
    2. Béal, Sylvain & Moyouwou, Issofa & Rémila, Eric & Solal, Philippe, 2020. "Cooperative games on intersection closed systems and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 104(C), pages 15-22.
    3. André Casajus & Rodrigue Tido Takeng, 2023. "Second-order productivity, second-order payoffs, and the Owen value," Annals of Operations Research, Springer, vol. 320(1), pages 1-13, January.
    4. J. M. Alonso-Meijide & J. Costa & I. García-Jurado & J. C. Gonçalves-Dosantos, 2020. "On egalitarian values for cooperative games with a priori unions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 672-688, October.
    5. Silvia Lorenzo-Freire, 2017. "New characterizations of the Owen and Banzhaf–Owen values using the intracoalitional balanced contributions property," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 579-600, October.
    6. Sylvain Béal & Issofa Moyouwou & Eric Rémila & Phillippe Solal, 2018. "Cooperative games on intersection closed systems and the Shapley value," Working Papers 2018-06, CRESE.

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