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Linking the Kar and Folk Solutions Through a Problem Separation Property

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  • Christian Trudeau

    () (Department of Economics, University of Windsor)

Abstract

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.

Suggested Citation

  • Christian Trudeau, 2013. "Linking the Kar and Folk Solutions Through a Problem Separation Property," Working Papers 1301, University of Windsor, Department of Economics.
  • Handle: RePEc:wis:wpaper:1301
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    File URL: http://web2.uwindsor.ca/economics/RePEc/wis/pdf/1301.pdf
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. repec:wsi:igtrxx:v:15:y:2013:i:02:n:s0219198913400033 is not listed on IDEAS
    5. 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.
    6. 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.
    7. Stefano Moretti & Rodica Branzei & Henk Norde & Stef Tijs, 2004. "The P-value for cost sharing in minimum," Theory and Decision, Springer, vol. 56(1), pages 47-61, April.
    8. 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.
    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. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    11. 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.
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    Cited by:

    1. repec:wsi:igtrxx:v:15:y:2013:i:02:n:s0219198913400033 is not listed on IDEAS
    2. Christian Trudeau, 2014. "Characterizations of the cycle-complete and folk solutions for minimum cost spanning tree problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 941-957, April.
    3. 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.

    More about this item

    Keywords

    Minimum cost spanning tree problems; folk solution; Kar solution; problem separability.;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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