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Centrality Rewarding Shapley and Myerson Values for Undirected Graph Games

Author

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  • Khmelnitskaya, A.
  • van der Laan, G.
  • Talman, Dolf

    (Tilburg University, Center For Economic Research)

Abstract

In this paper we introduce two values for cooperative games with communication graph structure. For cooperative games the shapley value distributes the worth of the grand coalition amongst the players by taking into account the worths that can be obtained by any coalition of players, but does not take into account the role of the players when communication between players is restricted. Existing values for communication graph games as the Myerson value and the average tree solution only consider the worths of connected coalitions and respect only in this way the communication restrictions. The two values take into account the position of a player in the graph. The rst one respects centrality, but not the communication abilities of any player. The second value reflects both centrality and the commu- nication ability of each player. That implies that in unanimity games players that do not generate worth but are needed to connect worth generating players are treated as those latter players, and simultaneously players that are more central in the graph get bigger shares in the worth than players that are less central. For both values an axiomatic characterization is given on the class of connected cycle-free graph games.

Suggested Citation

  • Khmelnitskaya, A. & van der Laan, G. & Talman, Dolf, 2016. "Centrality Rewarding Shapley and Myerson Values for Undirected Graph Games," Discussion Paper 2016-035, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:f449b907-5e19-4702-b48e-a1c812747507
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    References listed on IDEAS

    as
    1. René Brink & P. Herings & Gerard Laan & A. Talman, 2015. "The Average Tree permission value for games with a permission tree," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 99-123, January.
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    Cited by:

    1. Krishna Khatri, 2017. "The Shapley Value of Digraph Games," Papers 1701.01677, arXiv.org, revised Jun 2017.

    More about this item

    Keywords

    cooperative game; Shapley value; communication graph; restricted cooperation; Centrality;

    JEL classification:

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

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