A characterization of Kruskal sharing rules for minimum cost spanning tree problems

Abstract

In Tijs et al. (2006) a new family of cost allocation rules is introduced. In this paper we provide the first characterization of this family by means of population monotonicity and a property of additivity in the context of cost spanning tree problems.

On obligation rules for minimum cost spanning tree problems

“…Some papers have also used them in mcstp context, such as, Vidal-Puga (2009), Bergantiños et al (2010), Bogomolnaia and Moulin (2008), Lorenzo and Lorenzo-Freire (2009 (CSEC). Let …”

“…In recent years a number of papers have appeared proposing different allocation methods. Whereas some of them, like Granot and Huberman (1984), Kar (2002), Vidal-Puga (2007a, 2007b) and Lorenzo-Freire (2008a, 2008b) have proposed allocations based on the marginality principle, some others, including Tijs et al (2006), Dutta and Kar (2004), Lorenzo and Lorenzo-Freire (2009), Bogomolnaia and Moulin (2008) have taken non-marginalistic approaches. As mentioned previously, until now, obligation rules were thought to be a part of the latter category.…”

A monotonic and merge-proof rule in minimum cost spanning tree situations

“…A stronger version of core selection is population monotonicity, which requires that the cost allocated to any agent will not decrease if new agents join the society. Population monotonicity in mcst problems has been studied by Bergantiños and Gómez-Rúa (2010), Vidal-Puga (2007a, 2009), Bogomolnaia and Moulin (2010), Lorenzo-Freire (2009), andNorde et al (2004).…”

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

“…Separability allows this as soon as the (stand-alone) costs to connect S and N \S to the source sum to the total cost c Piecewise Linearity is labeled Cone-wise positive linearity in Bergantinos and Vidal-Puga (2009a) and Bergantinos and Kar (2010). d Restricted Addivity is called Constrained Additivity in Lorenzo and Lorenzo-Freire (2009 …”