An axiomatization of the Banzhaf value for cooperative games on antimatroids

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.