The average tree solution for cooperative games with communication structure
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
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.:
- 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.
- 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.
- Le Breton,Michel & Owen,Guillermo & Weber,Shlomo, 1991.
"Strongly balanced cooperative games,"
Discussion Paper Serie A
338, University of Bonn, Germany.
- Mamoru Kaneko & Myrna Holtz Wooders, 1982.
"Cores of Partitioning Games,"
Cowles Foundation Discussion Papers
620, Cowles Foundation for Research in Economics, Yale University.
- 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.
- 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.
- 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.
- 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. 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).
- Demange, Gabrielle, 1994.
"Intermediate preferences and stable coalition structures,"
Journal of Mathematical Economics,
Elsevier, vol. 23(1), pages 45-58, January.
- Gabrielle Demange, 1994. "Intermediate Preferences and Stable Coalition Structures," Post-Print halshs-00670920, HAL.
- Demange, G., 1991. "Intermediate Preferences and Stable Coalition Structures," DELTA Working Papers 91-16, DELTA (Ecole normale supérieure).
- Richard Baron & Sylvain Béal & Éric Rémila & Philippe Solal, 2008.
"Average tree solutions for graph games,"
- Baron, Richard & Béal, Sylvain & Remila, Eric & Solal, Philippe, 2008. "Average tree solutions for graph games," MPRA Paper 10189, University Library of Munich, Germany.
- Richard Baron & Sylvain Béal & Philippe Solal & Éric Rémila, 2008. "Average tree solution for graph games," Post-Print hal-00332537, HAL.
- 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.
- 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:eee:gamebe:v:68:y:2010:i:2:p:626-633. 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: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.