Obligation Rules for Minimum Cost Spanning Tree Situations and their Monotonicity Properties

We introduce the class of Obligation Rules for Minimum Cost Spanning Tree Situations. The main result of this paper is that such rules are cost monotonic and induce also population monotonic allocation schemes. Another characteristic of Obligation Rules is that they assign to a minimum cost spanning tree situation a vector of cost contributions which can be obtained as product of a double stochastic matrix with the cost vector of edges in the optimal tree provided by the Kruskal algorithm. It turns out that the Potters value (P-value) is an element of this class.