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The Average Tree Solution for Cooperative Games with Communication Structure

Author

Listed:
  • P. Jean-Jacques Herings

    (Maastricht University)

  • Gerard van der Laan

    (VU University Amsterdam)

  • Dolf Talman

    (Tilburg University)

  • Zaifu Yang

    (Yokohama National University)

Abstract

This discussion paper resulted in a publication in 'Games and Economic Behavior', 2010, 68, 626-633. 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. Given the graph structure we define a collection of spanning trees, where each spanning tree specifies a particular way by which players communicate and determines a payoff vector of marginal contributions of all the players. 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 (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

  • P. Jean-Jacques Herings & Gerard van der Laan & Dolf Talman & Zaifu Yang, 2008. "The Average Tree Solution for Cooperative Games with Communication Structure," Tinbergen Institute Discussion Papers 08-083/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20080083
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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;
    All these keywords.

    JEL classification:

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

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