A new rule for source connection problems

In this paper we study situations where a group of agents require a service that can only be provided from a source, the so‐called source connection problems. These problems contain the standard fixed tree, the classical minimum spanning tree and some other related problems such as the k‐hop, the degree constrained and the generalized minimum spanning tree problems among others. Our goal is to divide the cost of a network among the agents. To this end, we introduce a rule which will be referred to as a painting rule because it can be interpreted by means of a story about painting. Some meaningful properties in this context and a characterization of the rule are provided.