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The average tree solution for cooperative games with communication structure

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

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.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 68 (2010)
Issue (Month): 2 (March)
Pages: 626-633

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Handle: RePEc:eee:gamebe:v:68:y:2010:i:2:p:626-633
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  2. Baron, Richard & Béal, Sylvain & Remila, Eric & Solal, Philippe, 2008. "Average tree solutions for graph games," MPRA Paper 10189, University Library of Munich, Germany.
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  14. Ren� van den Brink & Gerard van der Laan & Vitaly Pruzhansky, 2004. "Harsanyi Power Solutions for Graph-restricted Games," Tinbergen Institute Discussion Papers 04-095/1, Tinbergen Institute.
  15. Talman, A.J.J. & Yamamoto, Y., 2008. "Average tree solution and subcore for acyclic graph games," Other publications TiSEM 47c15bd0-3911-429c-8952-7, Tilburg University, School of Economics and Management.
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  17. Ren� van den Brink & Gerard van der Laan & Vitaly Pruzhansky, 2004. "Harsanyi Power Solutions for Graph-restricted Games," Tinbergen Institute Discussion Papers 04-095/1, Tinbergen Institute.
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