Characterizations of the Kar and Folk Solutions for Minimum Cost Spanning Tree Problems

Abstract

A review of the literature on cost sharing solutions for the minimum cost spanning tree problem is proposed, with a particular focus on the folk and Kar solutions. We compare the characterizations proposed, helped by some equivalencies between sets of properties.

On the set of extreme core allocations for minimal cost spanning tree problems

“…While most of the literature uses the private version of the game, the distinction between the two games has been noted in Bogomolnaia and Moulin (2010) and Trudeau (2013). We obtain the following result.…”

“…In Trudeau (2013), it was already noted that the folk solution was axiomatized by properties that fit better with the interpretation of the public game. Our result clearly shows why.…”

A review of cooperative rules and their associated algorithms for minimum-cost spanning tree problems

“…The public game has not received much attention in the literature, and it has been limited to the contrast with the private game (Trudeau 2013;Vidal-Puga 2017, 2019). A possible reason for this lack of attention is that the private game is more tractable.…”

“…Many papers have followed addressing the cost allocation problem arising from mcst p. Early works and reviews are due to Aarts (1994), Feltkamp (1995), Curiel (1997), Borm et al (2001). Trudeau (2013) reviews some cost sharing rules focusing on two rules (to be addressed below): the folk rule and the Kar's rule, comparing several axiomatic characterizations. Trudeau and Vidal-Puga (2019) review the main axiomatic characterizations of the rules based on the Shapley value in mcst p.…”

Linking the Kar and folk solutions through a problem separation property

“…The literature on cost sharing solutions to the mcst problem is well established (see Trudeau (2012a)). The two main cost sharing solutions are built around the familiar Shapley value.…”