The Component Fairness Solution for Cycle-free Graph Games
AbstractIn this paper we study cooperative games with limited cooperation possibilities, represented by an undirected cycle-free communication graph. Players in the game can cooperate if and only if they are connected in the graph, i.e. they can communicate with one another. We introduce a new single-valued solution concept, the component fairness solution. Our solution is characterized by component efficiency and component fairness. The interpretation of component fairness is that deleting a link between two players yields for both resulting components the same average change in payoff, where the average is taken over the players in the component. Component fairness replaces the axiom of fairness characterizing the Myerson value, where the players whose link is deleted face the same loss in payoff. The component fairness solution is always in the core of the restricted game in case the game is superadditive and can be easily computed as the average of n specific marginal vectors, where n is the number of players. We also show that the component fairness solution can be generated by a specific distribution of the Harsanyi-dividends.
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 Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 05-114/1.
Date of creation: 12 Dec 2005
Date of revision:
Contact details of provider:
Web page: http://www.tinbergen.nl
TU-game; communication structure; Myerson value; fairness; marginal vector;
Other versions of this item:
- Herings,P. Jean-Jacques & Laan,Gerard,van der & Talman,Dolf, 2005. "The Component Fairness Solution for Cycle- Free Graph Games," Research Memoranda 056, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
- Herings, P.J.J. & Laan, G. van der & Talman, A.J.J., 2005. "The Component Fairness Solution for Cycle-Free Graph Games," Discussion Paper 2005-127, Tilburg University, Center for Economic Research.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-01-24 (All new papers)
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.:
- Kaneko, Mamoru & Wooders, Myrna Holtz, 1982.
"Cores of partitioning games,"
Mathematical Social Sciences,
Elsevier, vol. 3(4), pages 313-327, December.
- René Brink & Gerard Laan & Vitaly Pruzhansky, 2011.
"Harsanyi power solutions for graph-restricted games,"
International Journal of Game Theory,
Springer, 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.
- Le Breton, M. & Owen, G. & Weber, S., 1991.
"Strongly Balanced Cooperative Games,"
91a09, Universite Aix-Marseille III.
- 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.
- Roger B. Myerson, 1978. "Conference Structures and Fair Allocation Rules," Discussion Papers 363, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer, vol. 33(4), pages 505-514, November.
- Demange, G., 1991.
"Intermediate Preferences and Stable Coalition Structures,"
DELTA Working Papers
91-16, DELTA (Ecole normale supérieure).
- Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
- 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.
- Roger B. Myerson, 1976. "Graphs and Cooperation in Games," Discussion Papers 246, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- María Gómez-Rúa & Juan Vidal-Puga, 2011.
"Balanced per capita contributions and level structure of cooperation,"
TOP: An Official Journal of the Spanish Society of Statistics and Operations Research,
Springer, vol. 19(1), pages 167-176, July.
- Gómez-Rúa, María & Vidal-Puga, Juan, 2008. "Balanced per capita contributions and levels structure of cooperation," MPRA Paper 8208, University Library of Munich, Germany.
- Talman, A.J.J. & Yamamoto, Y., 2007. "Games With Limited Communication Structure," Discussion Paper 2007-19, Tilburg University, Center for Economic Research.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Antoine Maartens (+31 626 - 160 892)).
If references are entirely missing, you can add them using this form.