The Communication Tree Value for TU-games with Graph Communication
AbstractAbstract: A new solution is presented for transferable utility games with graph communication where the cooperation possibilities are represented by a graph. Players are only able to cooperate and obtain some worth in a coalition if they form a connected set in the given graph. To determine the payoff for each player, a single-valued solution, the communication tree value, is proposed for this class of games. The idea is that to form the grand coalition of all players a player can join a set of players only if this player is connected in the graph to at least one of the players in the set. To a set of players, starting with an arbitrary single player, from each maximally connected subset of remaining players one player joins who is connected to one or more of the players in that set. In this way a (rooted) tree on the set of players is obtained, called a communication tree. For a given game each communication tree of the graph induces a marginal contribution vector, in which any player receives a payoff equal to what he contributes in worth when he joins his subordinates in the tree. The average payoff over all communication trees of the graph determines the value. In case the underlying graph is cycle-complete the value coincides with the average tree solution. When there is complete communication between all players, which is the special case of cycle-completeness, players join one by one, yielding the Shapley value. A weak form of convexity is introduced, under which the value is guaranteed to be an element of the core. For games with complete graph communication the condition coincides with convexity and in case the underlying graph is cycle-free it is weaker than super-additivity.
Download InfoIf 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.
Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2012-095.
Date of creation: 2012
Date of revision:
Contact details of provider:
Web page: http://center.uvt.nl
Cooperative game; communication structure; Myerson value; core stability; convexity; rooted tree;
Find related papers by JEL classification:
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-12-15 (All new papers)
- NEP-GTH-2012-12-15 (Game Theory)
- NEP-MIC-2012-12-15 (Microeconomics)
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.:
- Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2009.
"Average tree solutions and the distribution of Harsanyi dividends,"
17909, University Library of Munich, Germany.
- Richard Baron & Sylvain Béal & Eric Rémila & Philippe Solal, 2011. "Average tree solutions and the distribution of Harsanyi dividends," International Journal of Game Theory, Springer, vol. 40(2), pages 331-349, May.
- 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. & Laan, G. van der & Talman, A.J.J., 2008. "The average tree solution for cycle-free graph games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-377604, Tilburg University.
- Herings, P. Jean Jacques & Laan, Gerard van der & Talman, Dolf, 2008. "The average tree solution for cycle-free graph games," Open Access publications from Maastricht University urn:nbn:nl:ui:27-22849, Maastricht University.
- 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.J.J. & van der Laan, G. & Talman, A.J.J. & Yang, Z., 2010.
"The average tree solution for cooperative games with communication structure,"
Games and Economic Behavior,
Elsevier, vol. 68(2), pages 626-633, March.
- Herings, P.J.J. & Laan, G. van der & Talman, A.J.J. & Yang, Z.F., 2008. "The Average Tree Solution for Cooperative Games with Communication Structure," Discussion Paper 2008-73, Tilburg University, Center for Economic Research.
- Herings, P. Jean-Jacques & Laan, Gerard van der & Talman, Dolf & Yang, Zaifu, 2008. "The Average Tree Solution for Cooperative Games with Communication Structure," Research Memoranda 026, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
- Herings, P.J.J. & Laan, G. van der & Talman, A.J.J. & Yang, Z.F., 2010. "The average tree solution for cooperative games with communication structure," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3736837, Tilburg University.
- P. Jean-Jacques Herings & Gerard van der Laan & Dolf Talman & Zaifu Yang, 2008. "The Average Tree Solution for Cooperative Games with Communication Structure," Tinbergen Institute Discussion Papers 08-083/1, Tinbergen Institute.
- Gabrielle Demange, 2004.
"On Group Stability in Hierarchies and Networks,"
Journal of Political Economy,
University of Chicago Press, vol. 112(4), pages 754-778, August.
- Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer, vol. 33(4), pages 505-514, November.
- Koshevoy, G.A. & Talman, A.J.J., 2011. "Solution Concepts for Games with General Coalitional Structure (Replaces CentER DP 2011-025)," Discussion Paper 2011-119, Tilburg University, Center for Economic Research.
- Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154855, Tilburg University.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Richard Broekman).
If references are entirely missing, you can add them using this form.