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Minimum Cost Arborescences

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  • Dutta, Bhaskar
  • Mishra, Debasis

Abstract

In this paper, we analyze the cost allocation problem when a group of agents or nodes have to be connected to a source, and where the cost matrix describing the cost of connecting each pair of agents is not necessarily symmetric, thus extending the well-studied problem of minimum cost spanning tree games, where the costs are assumed to be symmetric. The focus is on rules which satisfy axioms representing incentive and fairness properties. We show that while some results are similar, there are also significant differences between the frameworks corresponding to symmetric and asymmetric cost matrices.

Suggested Citation

  • Dutta, Bhaskar & Mishra, Debasis, 2009. "Minimum Cost Arborescences," Economic Research Papers 271310, University of Warwick - Department of Economics.
    • Handle: RePEc:ags:uwarer:271310
    DOI: 10.22004/ag.econ.271310
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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. Tijs, S.H. & Moretti, S. & Brânzei, R. & Norde, H.W., 2005. "The Bird Core for Minimum Cost Spanning Tree problems Revisited : Monotonicity and Additivity Aspects," Discussion Paper 2005-3, Tilburg University, Center for Economic Research.
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    7. 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.
    8. 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.
    9. 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.
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    11. 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.
    12. 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.
    13. Norde, H.W. & Moretti, S. & Tijs, S.H., 2001. "Minimum Cost Spanning Tree Games and Population Monotonic Allocation Schemes," Other publications TiSEM 794e124d-6be4-494d-a14f-4, Tilburg University, School of Economics and Management.
    14. 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.
    15. Gustavo Bergantiños & Juan Vidal-Puga, 2007. "The optimistic TU game in minimum cost spanning tree problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 223-239, October.
    16. Anna Bogomolnaia & Ron Holzman & Hervé Moulin, 2010. "Sharing the Cost of a Capacity Network," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 173-192, February.
    17. Tijs, S.H. & Moretti, S. & Brânzei, R. & Norde, H.W., 2005. "The Bird Core for Minimum Cost Spanning Tree problems Revisited : Monotonicity and Additivity Aspects," Other publications TiSEM 530f2c60-024d-4f3e-b724-1, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Ruben Juarez & Michael Wu, 2019. "Routing-Proofness in Congestion-Prone Networks," Games, MDPI, vol. 10(2), pages 1-18, April.
    2. Streekstra, Leanne & Trudeau, Christian, 2020. "Stable source connection and assignment problems as multi-period shortest path problems," Discussion Papers on Economics 7/2020, University of Southern Denmark, Department of Economics.
    3. Kusunoki, Yoshifumi & Tanino, Tetsuzo, 2017. "Investigation on irreducible cost vectors in minimum cost arborescence problems," European Journal of Operational Research, Elsevier, vol. 261(1), pages 214-221.
    4. Eric Bahel & Christian Trudeau, 2017. "Minimum incoming cost rules for arborescences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(2), pages 287-314, August.
    5. Bahel, Eric & Gómez-Rúa, María & Vidal-Puga, Juan, 2020. "Stability in shortest path problems," MPRA Paper 98504, University Library of Munich, Germany.
    6. G. Bergantiños & J. Vidal-Puga, 2020. "One-way and two-way cost allocation in hub network problems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(1), pages 199-234, March.
    7. Bergantiños, Gustavo & Vidal-Puga, Juan, 2020. "Cooperative games for minimum cost spanning tree problems," MPRA Paper 104911, University Library of Munich, Germany.
    8. Hernández, Penélope & Peris, Josep E. & Silva-Reus, José A., 2016. "Strategic sharing of a costly network," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 72-82.
    9. Bergantiños, Gustavo & Martínez, Ricardo, 2014. "Cost allocation in asymmetric trees," European Journal of Operational Research, Elsevier, vol. 237(3), pages 975-987.
    10. Hernández, Penélope & Peris, Josep E. & Vidal-Puga, Juan, 2023. "A non-cooperative approach to the folk rule in minimum cost spanning tree problems," European Journal of Operational Research, Elsevier, vol. 307(2), pages 922-928.
    11. Bahel, Eric, 2021. "Hyperadditive games and applications to networks or matching problems," Journal of Economic Theory, Elsevier, vol. 191(C).
    12. Gustavo Bergantiños & Juan Vidal-Puga, 2021. "A review of cooperative rules and their associated algorithms for minimum-cost spanning tree problems," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 73-100, March.
    13. 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.
    14. Bahel, Eric & Trudeau, Christian, 2019. "Stability and fairness in the job scheduling problem," Games and Economic Behavior, Elsevier, vol. 117(C), pages 1-14.

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    More about this item

    Keywords

    Financial Economics;

    JEL classification:

    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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