An axiomatization of the Banzhaf value for cooperative games on antimatroids

An axiomatization of the Banzhaf value for cooperative games on antimatroids

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Article ID: iaor20051021
Country: Germany
Volume: 59
Issue: 1
Start Page Number: 147
End Page Number: 166
Publication Date: Jan 2004
Journal: Mathematical Methods of Operations Research (Heidelberg)
Authors: , , ,
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 axiomatization 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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