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Collusion, quarrel, and the Banzhaf value

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  • André Casajus

Abstract

We provide new, concise characterizations of the Banzhaf value on a fixed player set employing just the standard dummy player property and one of the collusion properties suggested by Haller (Int J Game Theory 23:261–281, 1994 ) and Malawski (Int J Game Theory 31:47–67, 2002 ). Within these characterizations, any of the collusion properties can be replaced by additivity and the quarrel property due to the latter author. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • André Casajus, 2014. "Collusion, quarrel, and the Banzhaf value," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 1-11, February.
    • Handle: RePEc:spr:jogath:v:43:y:2014:i:1:p:1-11
    DOI: 10.1007/s00182-012-0364-4
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    References listed on IDEAS

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    1. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
    2. Annick Laruelle & Federico Valenciano, 2001. "Shapley-Shubik and Banzhaf Indices Revisited," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 89-104, February.
    3. 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.
    4. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 261-281.
    5. André Casajus, 2012. "Amalgamating players, symmetry, and the Banzhaf value," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 497-515, August.
    6. André Casajus, 2011. "Marginality, differential marginality, and the Banzhaf value," Theory and Decision, Springer, vol. 71(3), pages 365-372, September.
    7. 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.
    8. Dubey, Pradeep & Einy, Ezra & Haimanko, Ori, 2005. "Compound voting and the Banzhaf index," Games and Economic Behavior, Elsevier, vol. 51(1), pages 20-30, April.
    9. Marcin Malawski, 2002. "Equal treatment, symmetry and Banzhaf value axiomatizations," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 47-67.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. André Casajus & Frank Huettner, 2019. "The Coleman–Shapley index: being decisive within the coalition of the interested," Public Choice, Springer, vol. 181(3), pages 275-289, December.
    2. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2016. "Axiomatic characterizations under players nullification," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 47-57.
    3. Sylvain Béal & Eric Rémila & Philippe Solal, 2014. "Decomposition of the space of TU-games, Strong Transfer Invariance and the Banzhaf value," Working Papers hal-01377929, HAL.
    4. René Brink, 2017. "Games with a permission structure - A survey on generalizations and applications," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 1-33, April.
    5. Arash Abizadeh & Adrian Vetta, 2023. "The blocker postulates for measures of voting power," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(4), pages 595-623, May.

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    More about this item

    Keywords

    Banzhaf value; Symmetry; Collusion; Proxy; Association; Distrust; Quarrel; C71;
    All these keywords.

    JEL classification:

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

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