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Defining Rules in Cost Spanning Tree Problems Through the Canonical Form

Author

Listed:
  • Juan J. Vidal-Puga

    (Departamento de Estatística, Universidade de Vigo)

  • Gustavo Bergantiños

    (Research Group in Economic Analysis, Universidade de Vigo)

Abstract

We define the canonical form of a cost spanning tree problem. The canonical form has the property that reducing the cost of any arc, the minimal cost of connecting agents to the source is also reduced. We argue that the canonical form is a relevant concept in this kind of problems and study a rule using it. This rule satisfies much more interesting properties than other rules in the literature. Furthermore we provide two characterizations. Finally, we present several approaches to this rule without using the canonical form.

Suggested Citation

  • Juan J. Vidal-Puga & Gustavo Bergantiños, 2004. "Defining Rules in Cost Spanning Tree Problems Through the Canonical Form," Working Papers 2004.97, Fondazione Eni Enrico Mattei.
    • Handle: RePEc:fem:femwpa:2004.97
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    References listed on IDEAS

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    7. Brânzei, R. & Moretti, S. & Norde, H.W. & Tijs, S.H., 2003. "The P-Value for Cost Sharing in Minimum Cost Spanning Tree Situations," Other publications TiSEM de0e437c-1588-469d-a2ff-a, Tilburg University, School of Economics and Management.
    8. Roger B. Myerson, 1978. "Conference Structures and Fair Allocation Rules," Discussion Papers 363, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    11. Daniel Granot & Michael Maschler, 1998. "Spanning network games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(4), pages 467-500.
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    Cited by:

    1. Gustavo Bergantiños & Juan Vidal-Puga, 2004. "Realizing efficient outcomes in cost spanning problems," Game Theory and Information 0403001, University Library of Munich, Germany.
    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.
    3. 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.
    4. Moretti, S. & Tijs, S.H. & Brânzei, R. & Norde, H.W., 2005. "Cost Monotonic "Cost and Charge" Rules for Connection Situations," Other publications TiSEM 52b2694e-5a67-4fec-a46b-1, Tilburg University, School of Economics and Management.
    5. 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.
    6. Moretti, S. & Tijs, S.H. & Brânzei, R. & Norde, H.W., 2005. "Cost Monotonic "Cost and Charge" Rules for Connection Situations," Discussion Paper 2005-104, Tilburg University, Center for Economic Research.

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    More about this item

    Keywords

    Cost spanning tree; Rules; Canonical form;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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