Template-Type: ReDIF-Paper 1.0 Series: Tinbergen Institute Discussion Papers Creation-Date: 2008-09-04 Number: 08-083/1 Author-Name: P. Jean-Jacques Herings Author-Email: P.Herings@algec.unimaas.nl Author-Workplace-Name: Maastricht University Author-Name: Gerard van der Laan Author-Email: glaan@feweb.vu.nl Author-Workplace-Name: VU University Amsterdam Author-Name: Dolf Talman Author-Email: talman@uvt.nl Author-Workplace-Name: Tilburg University Author-Name: Zaifu Yang Author-Email: yang@ynu.ac.jp Author-Workplace-Name: Yokohama National University Title: The Average Tree Solution for Cooperative Games with Communication Structure 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. Classification-JEL: C71 Keywords: Cooperative game, graph structure, single-valued solution, core, convexity, spanning tree File-Url: https://papers.tinbergen.nl/08083.pdf File-Format: application/pdf File-Size: 235437 bytes Handle: RePEc:tin:wpaper:20080083