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On the Shapley value of a minimum cost spanning tree problem

Author

Listed:
  • Gustavo Bergantiños

    (Universidade de Vigo)

  • Juan Vidal-Puga

    (Universidade de Vigo)

Abstract

We associate an optimistic coalitional game with each minimum cost spanning tree problem. We define the worth of a coalition as the cost of connection assuming that the rest of the agents are already connected. We define a cost sharing rule as the Shapley value of this optimistic game. We prove that this rule coincides with a rule present in the literature under different names. We also introduce a new characterization using a property of equal contributions.

Suggested Citation

  • Gustavo Bergantiños & Juan Vidal-Puga, 2005. "On the Shapley value of a minimum cost spanning tree problem," Game Theory and Information 0509001, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:0509001
    Note: Type of Document - pdf; pages: 17
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0509/0509001.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    minimum cost spanning tree problems Shapley value;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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