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Some Properties for Bisemivalues on Bicooperative Games

Author

Listed:
  • Margarita Domènech

    (Universitat Politècnica de Catalunya)

  • José Miguel Giménez

    (Universitat Politècnica de Catalunya)

  • María Albina Puente

    (Universitat Politècnica de Catalunya)

Abstract

In this work, we focus on bicooperative games, a variation of the classic cooperative games, and investigate the conditions for the coefficients of the bisemivalues—a generalization of semivalues for cooperative games—necessary and / or sufficient in order to satisfy some properties, including among others, desirability relation, balanced contributions, null player exclusion property and block property. Moreover, a computational procedure to calculate bisemivalues in terms of the multilinear extension of the game is given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:1:d:10.1007_s10957-020-01640-x
    DOI: 10.1007/s10957-020-01640-x
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    References listed on IDEAS

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    1. Carreras, Francesc & Freixas, Josep & Puente, Maria Albina, 2003. "Semivalues as power indices," European Journal of Operational Research, Elsevier, vol. 149(3), pages 676-687, September.
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    5. Carreras, Francesc & Giménez, José Miguel, 2011. "Power and potential maps induced by any semivalue: Some algebraic properties and computation by multilinear extensions," European Journal of Operational Research, Elsevier, vol. 211(1), pages 148-159, May.
    6. Josep Freixas & M. Puente, 2002. "Reliability Importance Measures of the Components in a System Based on Semivalues and Probabilistic Values," Annals of Operations Research, Springer, vol. 109(1), pages 331-342, January.
    7. 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.
    8. 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.
    9. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
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    Cited by:

    1. Margarita Domènech & José Miguel Giménez & María Albina Puente, 2022. "Weak null, necessary defender and necessary detractor players: characterizations of the Banzhaf and the Shapley bisemivalues," Annals of Operations Research, Springer, vol. 318(2), pages 889-910, November.

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