Annals of Operations Research

, Volume 225, Issue 1, pp 45–63

# An axiomatic approach in minimum cost spanning tree problems with groups

Article

## Abstract

We study minimum cost spanning tree problems with groups, where agents are located in different villages, cities, etc. The groups are formed by agents living in the same village. In Bergantiños and Gómez-Rúa (Economic Theory 43:227–262, 2010) we define the rule F as the Owen value of the irreducible game with groups and we prove that F generalizes the folk rule of minimum cost spanning tree problems. Bergantiños and Vidal-Puga (Journal of Economic Theory 137:326–352, 2007a) give two characterizations of the folk rule. In the first one they characterize it as the unique rule satisfying cost monotonicity, population monotonicity and equal share of extra costs. In the second characterization of the folk rule they replace cost monotonicity by independence of irrelevant trees and population monotonicity by separability. In this paper we extend such characterizations to our setting. Some of the properties are the same (cost monotonicity and independence of irrelevant trees) and the other need to be adapted. In general, we do it by claiming the property twice: once among the groups and the other among the agents inside the same group.

## Keywords

Minimum cost spanning tree problems Folk rule Cost sharing Axiomatization

## Notes

### Acknowledgements

Financial support from Ministerio de Ciencia y Tecnología and FEDER through grants ECO2008-03484-C02-01/ECON and ECO2011-23460 and from Xunta de Galicia through grants PGIDIT06PXIB362390PR, INCITE08PXIB300005PR and 10 PXIB 362 299 PR is gratefully acknowledged.

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