The Folk Rule for Minimum Cost Spanning Tree Problems with Multiple Sources

Abstract

In this paper, we introduce minimum cost spanning tree problems with multiple sources. This new setting is an extension of the classical model where there is a single source. We extend several definitions of the folk rule, the most prominent rule in the classical model, to this new context: first as the Shapley value of the irreducible game; second as an obligation rule; third as a partition rule and finally through a cone-wise decomposition. We prove that all the definitions provide the same cost allocation and present two axiomatic characterizations.