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The Bird Core for Minimum Cost Spanning Tree Problems Revisited: Monotonicity and Additivity Aspects

In: Recent Advances in Optimization

Author

Listed:
  • Stef Tijs

    (University of Genoa
    Tilburg University)

  • Stefano Moretti

    (University of Genoa
    National Cancer Research Institute of Genoa)

  • Rodica Branzei

    (“Alexandru Ioan Cuza” University)

  • Henk Norde

    (Tilburg University)

Abstract

Summary A new way is presented to define for minimum cost spanning tree (mcst) games the irreducible core, which is introduced by Bird in 1976. The Bird core correspondence turns out to have interesting monotonicity and additivity properties and each stable cost monotonic allocation rule for mcst-problems is a selection of the Bird core correspondence. Using the additivity property an axiomatic characterization of the Bird core correspondence is obtained.

Suggested Citation

  • Stef Tijs & Stefano Moretti & Rodica Branzei & Henk Norde, 2006. "The Bird Core for Minimum Cost Spanning Tree Problems Revisited: Monotonicity and Additivity Aspects," Lecture Notes in Economics and Mathematical Systems, in: Alberto Seeger (ed.), Recent Advances in Optimization, pages 305-322, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-28258-7_19
    DOI: 10.1007/3-540-28258-0_19
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    Citations

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    Cited by:

    1. Davila-Pena, Laura & Borm, Peter & Garcia-Jurado, Ignacio & Schouten, Jop, 2023. "An Allocation Rule for Graph Machine Scheduling Problems," Other publications TiSEM 17013f33-1d65-4294-802c-b, Tilburg University, School of Economics and Management.
    2. Bergantiños, Gustavo & Vidal-Puga, Juan, 2020. "Cooperative games for minimum cost spanning tree problems," MPRA Paper 104911, University Library of Munich, Germany.
    3. Davila-Pena, Laura & Borm, Peter & Garcia-Jurado, Ignacio & Schouten, Jop, 2023. "An Allocation Rule for Graph Machine Scheduling Problems," Discussion Paper 2023-009, Tilburg University, Center for Economic Research.
    4. María Gómez-Rúa & Juan Vidal-Puga, 2017. "A monotonic and merge-proof rule in minimum cost spanning tree situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 813-826, March.
    5. 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.
    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.

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