Sequential contributions rules for minimum cost spanning tree problems

We introduce a family of sequential contributions rules for minimum cost spanning tree problems. Each member of the family assigns an agent part of the cost of connecting him to his immediate predecessor, and all of his followers are equally responsible for the remaining part. We characterize the family by imposing the axioms of efficiency, non-negativity, independence of following costs, group independence, and weak first-link consistency. The Bird and the sequential equal contributions rules are two distinguished members of the family. The Bird rule is obtained by requiring an agent to pay the entire cost of connecting him to his immediate predecessor, and the sequential equal contributions rule is obtained by requiring an agent and each of his followers to be equally responsible for this cost. We show how each of these two rules can be singled out from the family.