The Average Tree Solution for Cooperative Games with Communication Structure

P. Jean-Jacques Herings, Gerard van der Laan, Adolphus Talman and Zaifu Yang

No 08-083/1, Tinbergen Institute Discussion Papers from Tinbergen Institute

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.

Keywords: Cooperative game; graph structure; single-valued solution; core; convexity; spanning tree (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Date: 2008-09-04
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Related works:
Journal Article: The average tree solution for cooperative games with communication structure (2010)
Working Paper: The average tree solution for cooperative games with communication structure (2010)
Working Paper: The Average Tree Solution for Cooperative Games with Communication Structure (2008)
Working Paper: The Average Tree Solution for Cooperative Games with Communication Structure (2008)
Working Paper: The average tree solution for cooperative games with communication structure (2008)
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