The average tree solution for cooperative games with communication structure

P.J.J. Herings*, G. van der Laan, A.J.J. Talman, S. Yang

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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 showed 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. 

Original languageEnglish
Pages (from-to)626-633
Number of pages8
JournalGames and Economic Behavior
Issue number2
Publication statusPublished - Mar 2010


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

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