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The average covering tree value for directed graph games

Author

Listed:
  • Khmelnitskaya, Anna
  • Selcuktu, Ozer
  • Talman, A.J.J.

    (Tilburg University, School of Economics and Management)

Abstract

We introduce a single-valued solution concept, the so-called average covering tree value, for the class of transferable utility games with limited communication structure represented by a directed graph. The solution is the average of the marginal contribution vectors corresponding to all covering trees of the directed graph. The covering trees of a directed graph are those (rooted) trees on the set of players that preserve the dominance relations between the players prescribed by the directed graph. The average covering tree value is component efficient, and under a particular convexity-type condition it is stable. For transferable utility games with complete communication structure the average covering tree value equals to the Shapley value of the game. If the graph is the directed analog of an undirected graph the average covering tree value coincides with the gravity center solution.
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Suggested Citation

  • Khmelnitskaya, Anna & Selcuktu, Ozer & Talman, A.J.J., 2020. "The average covering tree value for directed graph games," Other publications TiSEM df006318-c4d7-4ab2-ab07-a, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:df006318-c4d7-4ab2-ab07-a9c8a90a4b3a
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    Cited by:

    1. is not listed on IDEAS
    2. Koshevoy, G.A. & Suzuki, T. & Talman, A.J.J., 2013. "Solutions For Games With General Coalitional Structure And Choice Sets," Other publications TiSEM a831011f-430e-4e82-b6f6-5, Tilburg University, School of Economics and Management.
    3. Khmelnitskaya, A. & Selçuk, O. & Talman, A.J.J., 2014. "The Shapley Value for Directed Graph Games," Discussion Paper 2014-064, Tilburg University, Center for Economic Research.

    More about this item

    JEL classification:

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

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