A monotonic and merge-proof rule in minimum cost spanning tree situations

We present a new model for cost sharing in minimum cost spanning tree problems to allow planners to identify how many agents merge. Under this new framework, in contrast to the traditional model, there are rules that satisfy the property of Merge-proofness. Furthermore, strengthening this property and adding some others, such as Population Monotonicity and Solidarity, makes it possible to define a unique rule that coincides with the weighted Shapley value of an associated cost game.