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Symmetric Coalitional Binomial Semivalues

Author

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  • Francesc Carreras

    (Technical University of Catalonia)

  • María Albina Puente

    (Technical University of Catalonia)

Abstract

We introduce here a family of mixed coalitional values. They extend the binomial semivalues to games endowed with a coalition structure, satisfy the property of symmetry in the quotient game and the quotient game property, generalize the symmetric coalitional Banzhaf value introduced by Alonso and Fiestras and link and merge the Shapley value and the binomial semivalues. A computational procedure in terms of the multilinear extension of the original game is also provided and an application to political science is sketched.

Suggested Citation

  • Francesc Carreras & María Albina Puente, 2012. "Symmetric Coalitional Binomial Semivalues," Group Decision and Negotiation, Springer, vol. 21(5), pages 637-662, September.
    • Handle: RePEc:spr:grdene:v:21:y:2012:i:5:d:10.1007_s10726-011-9239-5
    DOI: 10.1007/s10726-011-9239-5
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    Cited by:

    1. Conrado M. Manuel & Daniel Martín, 2020. "A Monotonic Weighted Shapley Value," Group Decision and Negotiation, Springer, vol. 29(4), pages 627-654, August.
    2. Antonio Magaña & Francesc Carreras, 2018. "Coalition Formation and Stability," Group Decision and Negotiation, Springer, vol. 27(3), pages 467-502, June.
    3. Francesc Carreras & María Albina Puente, 2018. "A note on multinomial probabilistic values," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 164-186, April.
    4. Maurice Koster & Sascha Kurz & Ines Lindner & Stefan Napel, 2017. "The prediction value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 433-460, February.
    5. Oğuzhan Ahmet Arık & Erkan Köse & Jeffrey Yi-Lin Forrest, 2019. "Project Staff Scheduling with Theory of Coalition," Group Decision and Negotiation, Springer, vol. 28(4), pages 827-847, August.
    6. Francesc Carreras & María Albina Puente, 2022. "On the axiomatic characterization of the coalitional multinomial probabilistic values," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 119-151, April.
    7. Francesc Carreras & María Albina Puente, 2015. "Multinomial Probabilistic Values," Group Decision and Negotiation, Springer, vol. 24(6), pages 981-991, November.

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