On the Shapley value of Minimum cost spanning tree problems

We associate to each minimum cost spanning tree problem a characteristic function v+ where v+ (S) denotes the cost of connecting agents in S to the source assuming that agents of N n S are already connected. We define the rule as the Shapley value of the game v+: We prove that coincides with a rule present in the literature under different names. We also present a new characterization of this rule using a property of equal contributions