Axiomatizations of the Shapley value for cooperative games on antimatroids

Abstract.

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 rectricted games by antimatroids allows to unify criteria of various lines of research. The current paper establishes axioms that determine the restricted Shapley value on antimatroids by conditions on the cooperative game v and the structure determined by the antimatroid. This axiomatization generalizes the axiomatizations of both the conjunctive and disjunctive permission value for games with a permission structure. We also provide an axiomatization of the Shapley value restricted to the smaller class of poset antimatroids. Finally, we apply our model to auction situations.