Linking the Kar and Folk Solutions Through a Problem Separation Property

Minimum cost spanning tree problems connect agents efficiently to a source with the cost of using an edge fixed. We revisit the dispute between the Kar and folk solutions, two solution concepts to divide the common cost of connection based on the Shapley value. We introduce a property called Weak Problem Separation that allows, under conditions, to divide the problem in two: connecting an agent to the source and connecting agents to each other. It allows us to characterize the set of all affine combinations of the Kar and folk solutions.