Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/86885 
Year of Publication: 
2008
Series/Report no.: 
Tinbergen Institute Discussion Paper No. 08-083/1
Publisher: 
Tinbergen Institute, Amsterdam and Rotterdam
Abstract: 
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.
Subjects: 
Cooperative game
graph structure
single-valued solution
core
convexity
spanning tree
JEL: 
C71
Document Type: 
Working Paper

Files in This Item:
File
Size
229.92 kB





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.