  In this manuscript, we define and study probabilistic values for cooperative
games on simplicial complexes. Inspired by the work of Weber "Probabilistic
values for games", we establish the new theory step by step, following the
classical axiomatization, i.e. using the linearity axiom, the dummy axiom, etc.
  Furthermore, we define Shapley values on simplicial complexes generalizing
the classical notion in literature. Remarkably, the traditional axiomatization
of Shapley values can be extended to this general setting for a rather
interesting class of complexes that generalize the notion of vertex-transitive
graphs and vertex-homogeneous simplicial complexes. These combinatorial objects
are very popular in the literature because of the study of Evasiveness
Conjecture in Complexity Theory.
