Template-type: ReDif-Paper 1.0
Author-Name: Herings P. Jean-Jacques 
Author-Name: Laan Gerard van der
Author-Name: Talman Dolf 
Author-Name: Yang Zaifu 
Author-workplace-name: METEOR
Title: The Average Tree Solution for Cooperative Games with Communication Structure
Abstract: We study cooperative games with communication structure, represented by an undirectedgraph. 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 ofgames. Given the graph structure we define a collection of spanning trees, where eachspanning 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 acomplete communication structure, then the proposed solution coincides with the Shapleyvalue, and that if the game has a cycle-free communication structure, it is the solutionproposed by Herings, van der Laan and Talman (2008). We introduce the notion of linkconvexity, 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.
Keywords: operations research and management science; 
Series: Research Memoranda
Creation-Date: 2008
Number: 026
File-URL: http://digitalarchive.maastrichtuniversity.nl/fedora/objects/guid:dc1c8518-5e42-4816-a3bf-9b055c5e638b/datastreams/ASSET1/content
File-Format: application/pdf
File-Size: 193877
Handle: RePEc:unm:umamet:2008026