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An Axiomatization of the Banzhaf Value for Cooperative Games on Antimatroids

Author

Listed:
  • E. Algaba

    (Matemática Aplicada II, Escuela Superior de Ingenieros, Sevilla, Spain)

  • J.M. Bilbao

    (Matemática Aplicada II, Escuela Superior de Ingenieros, Sevilla, Spain)

  • R. van den Brink

    (Faculty of Economics and Econometrics, Vrije Universiteit Amsterdam)

  • A. Jiménez-Losada

    (Matemática Aplicada II, Escuela Superior de Ingenieros, Sevilla, Spain)

Abstract

This discussion paper led to a publication in 'Mathematical Methods of Operations Research', 59, 147-166. Cooperative games on antimatroids are cooperative games restricted by a combinatorial structure which generalize the permission structure. So, cooperative games on antimatroids group several well-known families of games which have important applications in economics and politics. Therefore, the study of the restricted games by antimatroids allows to unify criteria of various lines of research. The current paper establishes axioms that determine the restricted Banzhaf value on antimatroids by conditions on the cooperative game and the structure determined by the antimatroid. The set of given axioms generalize 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.

Suggested Citation

  • E. Algaba & J.M. Bilbao & R. van den Brink & A. Jiménez-Losada, 2002. "An Axiomatization of the Banzhaf Value for Cooperative Games on Antimatroids," Tinbergen Institute Discussion Papers 02-110/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20020110
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    Cited by:

    1. 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.
    2. Conrado M. Manuel & Daniel Martín, 2021. "A Monotonic Weighted Banzhaf Value for Voting Games," Mathematics, MDPI, vol. 9(12), pages 1-23, June.
    3. 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.
    4. 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.
    5. 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.
    6. 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.

    More about this item

    Keywords

    Cooperative game; antimatroid; 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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