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An axiomatization of the Banzhaf value for cooperative games on antimatroids

Author

Listed:
  • E. Algaba
  • J. M. Bilbao
  • R. van den Brink
  • A. Jiménez-Losada

Abstract

Cooperative games on antimatroids are cooperative games in which coalition formation is restricted by a combinatorial structure which generalizes permission structures. These games group several well-known families of games which have important applications in economics and politics. The current paper establishes axioms that determine the restricted Banzhaf value for cooperative games on antimatroids. The set of given axioms generalizes the axiomatizations given for the Banzhaf permission values. We also give an axomatization of the restricted Banzhaf value for the smaller class of poset antimatroids. Finally, we apply the above results to auction situations. Copyright Springer-Verlag 2004

Suggested Citation

  • E. Algaba & J. M. Bilbao & R. van den Brink & A. Jiménez-Losada, 2004. "An axiomatization of the Banzhaf value for cooperative games on antimatroids," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(1), pages 147-166, February.
    • Handle: RePEc:spr:mathme:v:59:y:2004:i:1:p:147-166
    DOI: 10.1007/s001860300307
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    Citations

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    Cited by:

    1. René Brink & Chris Dietz, 2014. "Games with a local permission structure: separation of authority and value generation," Theory and Decision, Springer, vol. 76(3), pages 343-361, March.
    2. Kamijo, Yoshio & Kongo, Takumi, 2012. "Whose deletion does not affect your payoff? The difference between the Shapley value, the egalitarian value, the solidarity value, and the Banzhaf value," European Journal of Operational Research, Elsevier, vol. 216(3), pages 638-646.
    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. Conrado M. Manuel & Daniel Martín, 2021. "A Monotonic Weighted Banzhaf Value for Voting Games," Mathematics, MDPI, vol. 9(12), pages 1-23, June.
    5. Matthew Ryan, 2010. "Mixture sets on finite domains," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 33(2), pages 139-147, November.
    6. René Brink, 2010. "Axiomatizations of Banzhaf permission values for games with a permission structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 445-466, July.

    More about this item

    Keywords

    Antimatroid; Cooperative game; Permission structure; Banzhaf value;
    All these keywords.

    JEL classification:

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

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