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An Axiomatization of the Banzhaf Value for Cooperative Games on Antimatroids


Author Info

  • E. Algaba

    (Matem�tica Aplicada II, Escuela Superior de Ingenieros, Sevilla, Spain)

  • J.M. Bilbao

    (Matem�tica Aplicada II, Escuela Superior de Ingenieros, Sevilla, Spain)

  • R. van den Brink

    (Faculty of Economics and Econometrics, Vrije Universiteit Amsterdam)

  • A. Jim�nez-Losada

    (Matem�tica Aplicada II, Escuela Superior de Ingenieros, Sevilla, Spain)


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.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 02-110/1.

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Date of creation: 30 Oct 2002
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Handle: RePEc:dgr:uvatin:20020110

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Keywords: Cooperative game; antimatroid; permission structure; Banzhaf value.;

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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, Elsevier, vol. 216(3), pages 638-646.
  2. Rene van den Brink & Chris Dietz, 2012. "Games with a Local Permission Structure: Separation of Authority and Value Generation," Tinbergen Institute Discussion Papers, Tinbergen Institute 12-126/II, Tinbergen Institute.
  3. René Brink, 2010. "Axiomatizations of Banzhaf permission values for games with a permission structure," International Journal of Game Theory, Springer, Springer, vol. 39(3), pages 445-466, July.
  4. Matthew Ryan, 2010. "Mixture sets on finite domains," Decisions in Economics and Finance, Springer, Springer, vol. 33(2), pages 139-147, November.


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