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The average tree solution for cooperative games with communication structure

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  • Herings, P.J.J.
  • van der Laan, G.
  • Talman, A.J.J.
  • Yang, Z.

Abstract

We study cooperative games with communication structure, represented by an undirected graph. Players in the game are able to cooperate only if they can form a network in the graph. A single-valued solution, the average tree solution, is proposed for this class of games. The average tree solution is defined to be the average of all these payoff vectors. It is shown that if a game has a complete communication structure, then the proposed solution coincides with the Shapley value, and that if the game has a cycle-free communication structure, it is the solution proposed by Herings, van der Laan and Talman in 2008. We introduce the notion of link-convexity, under which the game is shown to have a non-empty core and the average tree solution lies in the core. In general, link-convexity is weaker than convexity. For games with a cycle-free communication structure, link-convexity is even weaker than super-additivity.

Suggested Citation

  • Herings, P.J.J. & van der Laan, G. & Talman, A.J.J. & Yang, Z., 2010. "The average tree solution for cooperative games with communication structure," Games and Economic Behavior, Elsevier, vol. 68(2), pages 626-633, March.
    • Handle: RePEc:eee:gamebe:v:68:y:2010:i:2:p:626-633
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    References listed on IDEAS

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    More about this item

    Keywords

    Cooperative game Graph structure Single-valued solution Core Convexity Spanning tree;

    JEL classification:

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

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