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Sharing a minimal cost spanning tree: Beyond the Folk solution

  • Bogomolnaia, Anna
  • Moulin, Hervé

Several authors recently proposed an elegant construction to divide the minimal cost of connecting a given set of users to a source. This folk solution applies the Shapley value to the largest reduction of the cost matrix that does not affect the efficient cost. It is also obtained by the linear decomposition of the cost matrix in the canonical basis. Because it relies on the irreducible cost matrix, the folk solution ignores interpersonal differences in relevant connecting costs. We propose alternative solutions, some of them arbitrarily close to the folk solution, to resolve this difficulty.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 69 (2010)
Issue (Month): 2 (July)
Pages: 238-248

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Handle: RePEc:eee:gamebe:v:69:y:2010:i:2:p:238-248
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Bhaskar Dutta & Anirban Kar, 2002. "Cost monotonicity, consistency and minimum cost spanning tree games," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 02-04, Indian Statistical Institute, New Delhi, India.
  2. Norde, Henk & Moretti, Stefano & Tijs, Stef, 2004. "Minimum cost spanning tree games and population monotonic allocation schemes," European Journal of Operational Research, Elsevier, vol. 154(1), pages 84-97, April.
  3. Bergantinos, Gustavo & Vidal-Puga, Juan J., 2007. "A fair rule in minimum cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 326-352, November.
  4. Brânzei, R. & Moretti, S. & Norde, H.W. & Tijs, S.H., 2003. "The P-Value for Cost Sharing in Minimum Cost Spanning Tree Situations," Discussion Paper 2003-129, Tilburg University, Center for Economic Research.
  5. Kar, Anirban, 2002. "Axiomatization of the Shapley Value on Minimum Cost Spanning Tree Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 265-277, February.
  6. Feltkamp, V. & Tijs, S.H. & Muto, S., 1994. "On the irreducible core and the equal remaining obligations rule of minimum cost spanning extension problems," Discussion Paper 1994-106, Tilburg University, Center for Economic Research.
  7. Sharkey, W.W., 1991. "Network Models in Economics," Papers 69, Bell Communications - Economic Research Group.
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