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Herings, P. Jean-Jacques
van der Laan, Gerard
Talman, Dolf
Yang, Zaifu
Year of Publication: 
Series/Report no.: 
Tinbergen Institute Discussion Paper 08-083/1
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.
Cooperative game
graph structure
single-valued solution
spanning tree
Document Type: 
Working Paper

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