The average tree solution for cooperative games with communication structure.

P.J.J. Herings; G. van der Laan; A.J.J. Talman; Z. Zang

doi:10.1016/j.geb.2009.10.002

The average tree solution for cooperative games with communication structure.

P.J.J. Herings, G. van der Laan, A.J.J. Talman, Z. Zang

Research output: Contribution to Journal › Article › Academic › peer-review

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. © 2009 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	626-633
Journal	Games and Economic Behavior
Volume	68
DOIs	https://doi.org/10.1016/j.geb.2009.10.002
Publication status	Published - 2010

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10.1016/j.geb.2009.10.002

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title = "The average tree solution for cooperative games with communication structure.",

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. {\textcopyright} 2009 Elsevier Inc. All rights reserved.",

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AU - Herings, P.J.J.

AU - van der Laan, G.

AU - Talman, A.J.J.

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N2 - 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. © 2009 Elsevier Inc. All rights reserved.

AB - 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. © 2009 Elsevier Inc. All rights reserved.

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DO - 10.1016/j.geb.2009.10.002

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JO - Games and Economic Behavior

JF - Games and Economic Behavior

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The average tree solution for cooperative games with communication structure.

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