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Linking the Kar and Folk Solutions Through a Problem Separation Property

  • Christian Trudeau

    ()

    (Department of Economics, University of Windsor)

Minimum cost spanning tree problems connect agents efficiently to a source with the cost of using an edge fixed. We revisit the dispute between the Kar and folk solutions, two solution concepts to divide the common cost of connection based on the Shapley value. We introduce a property called Weak Problem Separation that allows, under conditions, to divide the problem in two: connecting an agent to the source and connecting agents to each other. It allows us to characterize the set of all affine combinations of the Kar and folk solutions.

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File URL: http://web2.uwindsor.ca/economics/RePEc/wis/pdf/1301.pdf
File Function: First version, 2013
Download Restriction: no

Paper provided by University of Windsor, Department of Economics in its series Working Papers with number 1301.

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Length: 19 pages
Date of creation: Jan 2013
Date of revision:
Handle: RePEc:wis:wpaper:1301
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  1. 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.
  2. Norde, H.W. & Moretti, S. & Tijs, S.H., 2001. "Minimum Cost Spanning Tree Games and Population Monotonic Allocation Schemes," Discussion Paper 2001-18, Tilburg University, Center for Economic Research.
  3. Christian Trudeau, 2013. "Characterizations Of The Kar And Folk Solutions For Minimum Cost Spanning Tree Problems," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1340003-1-1.
  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. Bogomolnaia, Anna & Moulin, Hervé, 2010. "Sharing a minimal cost spanning tree: Beyond the Folk solution," Games and Economic Behavior, Elsevier, vol. 69(2), pages 238-248, July.
  6. Bergantiños, Gustavo & Vidal-Puga, Juan, 2009. "Additivity in minimum cost spanning tree problems," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 38-42, January.
  7. repec:ner:tilbur:urn:nbn:nl:ui:12-123753 is not listed on IDEAS
  8. repec:ner:tilbur:urn:nbn:nl:ui:12-142598 is not listed on IDEAS
  9. 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.
  10. Bergantiños, Gustavo & Vidal-Puga, Juan, 2010. "Realizing fair outcomes in minimum cost spanning tree problems through non-cooperative mechanisms," European Journal of Operational Research, Elsevier, vol. 201(3), pages 811-820, March.
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