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Equal treatment, symmetry and Banzhaf value axiomatizations

Author

Listed:
  • Marcin Malawski

    (Instytut Podstaw Informatyki PAN, Ordona 21, PL 01-237 Warszawa, POLAND)

Abstract

The Banzhaf value is the only value satisfying the equal treatment, dummy player and marginal contributions conditions and neutrality of some linear operators on the spaces of games. Under some of these neutrality assumptions, equal treatment can be replaced by even weaker conditions. For linear values having the dummy player property, equal treatment is equivalent to symmetry. All these properties together imply the marginal contributions condition, but in some Banzhaf value axiomatizations marginal contributions cannot be a substitute for linearity.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jogath:v:31:y:2002:i:1:p:47-67
    Note: Received: December 1997/Revised version: May 2001
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    References listed on IDEAS

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    1. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
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    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.
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    Cited by:

    1. René van den Brink, 2017. "Games with a Permission Structure: a survey on generalizations and applications," Tinbergen Institute Discussion Papers 17-016/II, Tinbergen Institute.
    2. Anna A. Klis, 2019. "Identity and equal treatment in negative externality agreements," International Environmental Agreements: Politics, Law and Economics, Springer, vol. 19(6), pages 615-630, December.
    3. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "Axioms of invariance for TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 891-902, November.
    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. 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.
    6. van den Brink, René, 2012. "Efficiency and collusion neutrality in cooperative games and networks," Games and Economic Behavior, Elsevier, vol. 76(1), pages 344-348.
    7. Anna Khmelnitskaya & Gerard van der Laan & Dolf Talman, 2016. "Centrality Rewarding Shapley and Myerson Values for Undirected Graph Games," Tinbergen Institute Discussion Papers 16-070/II, Tinbergen Institute.
    8. Haimanko, Ori, 2018. "The axiom of equivalence to individual power and the Banzhaf index," Games and Economic Behavior, Elsevier, vol. 108(C), pages 391-400.
    9. 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.
    10. Sylvain Béal & Eric Rémila & Philippe Solal, 2014. "Decomposition of the space of TU-games, Strong Transfer Invariance and the Banzhaf value," Working Papers 2014-05, CRESE.
    11. McQuillin, Ben & Sugden, Robert, 2018. "Balanced externalities and the Shapley value," Games and Economic Behavior, Elsevier, vol. 108(C), pages 81-92.
    12. Norman Kleinberg & Jeffrey Weiss, 2013. "On membership and marginal values," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 357-373, May.
    13. M. Álvarez-Mozos & O. Tejada, 2015. "The Banzhaf value in the presence of externalities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 781-805, April.
    14. 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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