The average tree solution for cooperative games with communication structure

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

Games and Economic Behavior, 2010, vol. 68, issue 2, 626-633

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. 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 in 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)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (52)

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Related works:
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)
Working Paper: The average tree solution for cooperative games with communication structure (2008)
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