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The Average Tree Solution for Cooperative Games with Communication Structure

  • Herings P. Jean-Jacques
  • Laan Gerard van der
  • Talman Dolf
  • Yang Zaifu

    (METEOR)

We study cooperative games with communication structure, represented by an undirectedgraph. 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 ofgames. Given the graph structure we define a collection of spanning trees, where eachspanning 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 acomplete communication structure, then the proposed solution coincides with the Shapleyvalue, and that if the game has a cycle-free communication structure, it is the solutionproposed by Herings, van der Laan and Talman (2008). We introduce the notion of linkconvexity, 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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File URL: http://digitalarchive.maastrichtuniversity.nl/fedora/objects/guid:dc1c8518-5e42-4816-a3bf-9b055c5e638b/datastreams/ASSET1/content
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Paper provided by Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) in its series Research Memorandum with number 026.

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Date of creation: 2008
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Handle: RePEc:unm:umamet:2008026
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  1. 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.
  2. Le Breton, M & Owen, G & Weber, S, 1992. "Strongly Balanced Cooperative Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 419-27.
  3. HERINGS, P. Jean-Jacques & van der LAAN, Gerard & TALMAN, Dolf, . "The average tree solution for cycle-free graph games," CORE Discussion Papers RP 2155, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. René Brink & Gerard Laan & Vitaly Pruzhansky, 2011. "Harsanyi power solutions for graph-restricted games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 87-110, February.
  5. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
  6. Mamoru Kaneko & Myrna Holtz Wooders, 1982. "Cores of Partitioning Games," Cowles Foundation Discussion Papers 620, Cowles Foundation for Research in Economics, Yale University.
  7. Gabrielle Demange, 2004. "On group stability in hierarchies and networks," Post-Print halshs-00581662, HAL.
  8. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
  9. Baron, Richard & Béal, Sylvain & Remila, Eric & Solal, Philippe, 2008. "Average tree solutions for graph games," MPRA Paper 10189, University Library of Munich, Germany.
  10. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 505-514, November.
  11. Talman, A.J.J. & Yamamoto, Y., 2007. "Games With Limited Communication Structure," Discussion Paper 2007-19, Tilburg University, Center for Economic Research.
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