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From spanning trees to arborescences: new and extended cost sharing solutions


  • Eric Bahel

    () (Department of Economics, Virginia Polytechnic Institute and State University)

  • Christian Trudeau

    () (Department of Economics, University of Windsor)


The paper examines minimal cost arborescence problems, which generalize the well-known minimal cost spanning tree (mcst) problems. We propose a new family of cost sharing methods that are easy to compute, as they closely relate to the network-building algorithm. These methods, called minimal incoming cost rules for arborescences (MICRAs), include as a particular case the extension of the folk solution introduced by Dutta and Mishra (2012). A simpler computational procedure thus obtains for this method. We also provide new axiomatizations of (a) the set of stable and symmetric MICRAs and (b) the folk solution. Finally, we closely examine two remarkable MICRAs. The first one relates to the cycle-complete rule for mcst problems introduced in Trudeau (2012). The second one contrasts with the folk rule by fully rewarding agents who help others connect to the source.

Suggested Citation

  • Eric Bahel & Christian Trudeau, 2016. "From spanning trees to arborescences: new and extended cost sharing solutions," Working Papers 1601, University of Windsor, Department of Economics.
  • Handle: RePEc:wis:wpaper:1601

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    References listed on IDEAS

    1. Bergantiños, Gustavo & Kar, Anirban, 2010. "On obligation rules for minimum cost spanning tree problems," Games and Economic Behavior, Elsevier, vol. 69(2), pages 224-237, July.
    2. 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.
    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. 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. Tijs, Stef & Branzei, Rodica & Moretti, Stefano & Norde, Henk, 2006. "Obligation rules for minimum cost spanning tree situations and their monotonicity properties," European Journal of Operational Research, Elsevier, vol. 175(1), pages 121-134, November.
    6. Eric Bahel, 2016. "On the core and bargaining set of a veto game," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(3), pages 543-566, August.
    7. Bahel, Eric & Trudeau, Christian, 2014. "Stable lexicographic rules for shortest path games," Economics Letters, Elsevier, vol. 125(2), pages 266-269.
    8. Dutta, Bhaskar & Mishra, Debasis, 2012. "Minimum cost arborescences," Games and Economic Behavior, Elsevier, vol. 74(1), pages 120-143.
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    More about this item


    arborescence problems; stable allocations; minimal incoming cost rules; leftover cost matrix;

    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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