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Sharing a minimal cost spanning tree: Beyond the Folk solution

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  • Bogomolnaia, Anna
  • Moulin, Hervé

Abstract

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

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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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. Brânzei, R. & Moretti, S. & Norde, H.W. & Tijs, S.H., 2004. "The P-value for cost sharing in minimum cost spanning tree situations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-142598, Tilburg University.
  3. 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.
  4. 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.
  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. Gustavo Bergantiños & Juan Vidal-Puga, 2005. "A fair rule in minimum cost spanning tree problems," Game Theory and Information 0504001, EconWPA.
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Cited by:
  1. Dutta, Bhaskar & Mishra, Debasis, 2009. "Minimum Cost Arborescences," The Warwick Economics Research Paper Series (TWERPS) 889, University of Warwick, Department of Economics.
  2. Hougaard, Jens Leth & Tvede, Mich, 2012. "Truth-telling and Nash equilibria in minimum cost spanning tree models," European Journal of Operational Research, Elsevier, vol. 222(3), pages 566-570.
  3. Moulin, Hervé & Velez, Rodrigo A., 2013. "The price of imperfect competition for a spanning network," Games and Economic Behavior, Elsevier, vol. 81(C), pages 11-26.
  4. Trudeau, Christian, 2012. "A new stable and more responsive cost sharing solution for minimum cost spanning tree problems," Games and Economic Behavior, Elsevier, vol. 75(1), pages 402-412.
  5. Chun, Youngsub & Lee, Joosung, 2012. "Sequential contributions rules for minimum cost spanning tree problems," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 136-143.

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