The Shapley value for games on matroids: The static model

In the classical model of cooperative games, it is considered that each coalition of players can form and cooperate to obtain its worth. However, we can think that in some situations this assumption is not real, that is, all the coalitions are not feasible. This suggests that it is necessary to raise the whole question of generalizing the concept of cooperative game, and therefore to introduce appropriate solution concepts. We propose a model for games on a matroid, based in several important properties of this combinatorial structure and we introduce the probabilistic Shapley value for games on matroids.