Mathematical Methods of Operations Research

, Volume 59, Issue 1, pp 147–166 | Cite as

An axiomatization of the Banzhaf value for cooperative games on antimatroids

  • 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.

Antimatroid Cooperative game Permission structure Banzhaf value 

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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  • E. Algaba
    • 1
  • J. M. Bilbao
    • 2
  • R. van den Brink
    • 3
  • A. Jiménez-Losada
    • 4
  1. 1.Matemática Aplicada IIEscuela Superior de IngenierosSevillaSpain
  2. 2.Matemática
  3. 3.Department of EconometricsFree UniversityAmsterdamThe Netherlands
  4. 4.Matemática

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