The folk rule through a painting procedure for minimum cost spanning tree problems with multiple sources

Abstract

We consider minimum cost spanning tree problems with multiple sources. We propose a cost allocation rule based on a painting procedure. Agents paint the edges on the paths connecting them to the sources. We prove that the painting rule coincides with the folk rule. Finally, we provide an axiomatic characterization.

A characterization of the folk rule for multi-source minimal cost spanning tree problems

“…Bergantiños et al [5] extend the definition of the folk rule following four definitions and present some axiomatic characterizations. Bergantiños and Navarro-Ramos [2] extend the definition of the painting rule to the case of multiple sources and prove that it also coincides with the extension of folk rule. Bergantiños and Lorenzo [1] consider several family of rules obtained through Kruskal's algorithm.…”

“…Bergantiños and Navarro-Ramos [2] show that this definition does not depends on t and t * . Moreover, f P,t and f CW coincide for every (N, M, C) and the allocation they give is the folk rule.…”

“…Bergantiños and Navarro-Ramos [2] extend the definition of the painting rule to problems with multiple sources. They also prove that it coincides with the folk rule in the multi-source problem.…”