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The Banzhaf value for generalized probabilistic communication situations

Author

Listed:
  • Jilei Shi

    (Shanghai University
    Ningbo University of Finance and Economics)

  • Erfang Shan

    (Shanghai University)

Abstract

In this paper we generalize the graph Banzhaf value, proposed by Alonso-Meijide and Fiestras-Janeiro (Naval Res Logist 53(3):198–203, 2006) in the deterministic communication situations, to the generalized probabilistic communication situations. This new value is called the probabilistic Banzhaf value. We provide two axiomatic characterizations of the value by the probabilistic versions of component total power, fairness and balanced contributions. Furthermore, we give an alternative characterization of the value by using the probabilistic player potential function.

Suggested Citation

  • Jilei Shi & Erfang Shan, 2021. "The Banzhaf value for generalized probabilistic communication situations," Annals of Operations Research, Springer, vol. 301(1), pages 225-244, June.
    • Handle: RePEc:spr:annopr:v:301:y:2021:i:1:d:10.1007_s10479-020-03914-z
    DOI: 10.1007/s10479-020-03914-z
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    References listed on IDEAS

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    1. Mustapha Ridaoui & Michel Grabisch & Christophe Labreuche, 2018. "An axiomatisation of the Banzhaf value and interaction index for multichoice games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02381119, HAL.
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    3. Dragan, Irinel, 1996. "New mathematical properties of the Banzhaf value," European Journal of Operational Research, Elsevier, vol. 95(2), pages 451-463, December.
    4. Guillermo Owen, 1975. "Multilinear extensions and the banzhaf value," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 22(4), pages 741-750, December.
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    6. Feltkamp, Vincent, 1995. "Alternative Axiomatic Characterizations of the Shapley and Banzhaf Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(2), pages 179-186.
    7. A. Ghintran & E. González-Arangüena & C. Manuel, 2012. "A probabilistic position value," Annals of Operations Research, Springer, vol. 201(1), pages 183-196, December.
    8. Ori Haimanko, 2019. "Composition independence in compound games: a characterization of the Banzhaf power index and the Banzhaf value," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(3), pages 755-768, September.
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    10. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    11. 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.
    12. Calvo, Emilio & Lasaga, Javier & van den Nouweland, Anne, 1999. "Values of games with probabilistic graphs," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 79-95, January.
    13. Gómez, D. & González-Arangüena, E. & Manuel, C. & Owen, G., 2008. "A value for generalized probabilistic communication situations," European Journal of Operational Research, Elsevier, vol. 190(2), pages 539-556, October.
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    Cited by:

    1. Josep Freixas & Montserrat Pons, 2022. "A critical analysis on the notion of power," Annals of Operations Research, Springer, vol. 318(2), pages 911-933, November.

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    More about this item

    Keywords

    TU-game; Banzhaf value; Probabilistic communication situations; Graph Banzhaf value;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D60 - Microeconomics - - Welfare Economics - - - General

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