The Average Tree Solution for Cooperative Games with Communication Structure
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.
|Date of creation:||2008|
|Date of revision:|
|Contact details of provider:|| Postal: P.O. Box 616, 6200 MD Maastricht|
Phone: +31 (0)43 38 83 830
Web page: http://www.maastrichtuniversity.nl/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Le Breton, M. & Owen, G. & Weber, S., 1991. "Strongly Balanced Cooperative Games," G.R.E.Q.A.M. 91a09, Universite Aix-Marseille III.
- Le Breton, M. & Owen, G. & Weber, S., 1991. "Strongly Balanced Cooperative Games," Papers 92-3, York (Canada) - Department of Economics.
- Le Breton,Michel & Owen,Guillermo & Weber,Shlomo, 1991. "Strongly balanced cooperative games," Discussion Paper Serie A 338, University of Bonn, Germany.
- 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).
- Herings, P. Jean Jacques & van der Laan, Gerard & Talman, Dolf, 2008. "The average tree solution for cycle-free graph games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 77-92, January.
- Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2008. "The average tree solution for cycle-free graph games," Other publications TiSEM f243609c-2847-415f-ae52-1, Tilburg University, School of Economics and Management.
- 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.
- René 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.
- Demange, Gabrielle, 1994.
"Intermediate preferences and stable coalition structures,"
Journal of Mathematical Economics,
Elsevier, vol. 23(1), pages 45-58, January.
- Demange, G., 1991. "Intermediate Preferences and Stable Coalition Structures," DELTA Working Papers 91-16, DELTA (Ecole normale supérieure).
- Gabrielle Demange, 1994. "Intermediate Preferences and Stable Coalition Structures," Post-Print halshs-00670920, HAL.
- Mamoru Kaneko & Myrna Holtz Wooders, 1982.
"Cores of Partitioning Games,"
Cowles Foundation Discussion Papers
620, Cowles Foundation for Research in Economics, Yale University.
- Gabrielle Demange, 2004.
"On group stability in hierarchies and networks,"
- 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.
- Baron, Richard & Béal, Sylvain & Remila, Eric & Solal, Philippe, 2008.
"Average tree solutions for graph games,"
10189, University Library of Munich, Germany.
- 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.
- Talman, A.J.J. & Yamamoto, Y., 2007. "Games With Limited Communication Structure," Discussion Paper 2007-19, Tilburg University, Center for Economic Research.
When requesting a correction, please mention this item's handle: RePEc:unm:umamet:2008026. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Charles Bollen)
If references are entirely missing, you can add them using this form.