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

Author

Listed:
  • Eric Bahel

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

  • Christian Trudeau

    (Department of Economics, University of Windsor)

Abstract

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

    as
    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," Other publications TiSEM 56ea8c64-a05f-4b3f-ab61-9, Tilburg University, School of Economics and Management.
    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. Dutta, Bhaskar & Mishra, Debasis, 2012. "Minimum cost arborescences," Games and Economic Behavior, Elsevier, vol. 74(1), pages 120-143.
    5. Feltkamp, V. & Tijs, S.H. & Muto, S., 1994. "Minimum cost spanning extension problems : The proportional rule and the decentralized rule," Other publications TiSEM 2c6cd46b-7e72-4262-a479-3, Tilburg University, School of Economics and Management.
    6. 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.
    7. 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.
    8. Bahel, Eric & Trudeau, Christian, 2014. "Stable lexicographic rules for shortest path games," Economics Letters, Elsevier, vol. 125(2), pages 266-269.
    9. Eric Bahel, 2014. "On the core and bargaining set of a veto game," Working Papers e07-48, Virginia Polytechnic Institute and State University, Department of Economics.
    10. 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.
    11. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    arborescence problems; stable allocations; minimal incoming cost rules; leftover cost matrix;
    All these keywords.

    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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