Sharing a minimal cost spanning tree: Beyond the Folk solution

Several authors recently proposed an elegant construction to divide the minimal cost of connecting a given set of users to a source. This folk solution applies the Shapley value to the largest reduction of the cost matrix that does not affect the efficient cost. It is also obtained by the linear decomposition of the cost matrix in the canonical basis. Because it relies on the irreducible cost matrix, the folk solution ignores interpersonal differences in relevant connecting costs. We propose alternative solutions, some of them arbitrarily close to the folk solution, to resolve this difficulty.