Error message

Deprecated function: Array and string offset access syntax with curly braces is deprecated in include_once() (line 20 of /mnt/web104/a0/07/510451407/htdocs/includes/file.phar.inc).

The Average Tree Solution for Cooperative Games with Communication Structure

Printer-friendly version
Working paper
Author/s: 
P. Jean-Jacques Herings, Gerard van der Laan, Dolf Talman and Zaifu Yang
Issue number: 
RM/08/026
Publisher: 
Maastricht University
Year: 
2008
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 even weaker than convexity. For games with a cycle-free communication structure, link-convexity is even weaker than supper-additivity.
Developed by Paolo Gittoi