58Accesses
7Citations
Abstract
A partnership in a cooperative game is a coalition that possesses an internal structure and, simultaneously, behaves as an individual member. Forming partnerships leads to a modification of the original game which differs from the quotient game that arises when one or more coalitions are actually formed.
In this paper, the Shapley value is used to discuss the convenience to form either coalitions or partnerships. To this end, the difference between the additive Shapley value of the partnership in the partnership game and the Shapley alliance value of the coalition, and also between the corresponding value of the internal and external players, are analysed. Simple games are especially considered.
This is a preview of subscription content,log in via an institution to check access.
Access this article
Subscribe and save
- Get 10 units per month
- Download Article/Chapter or eBook
- 1 Unit = 1 Article or 1 Chapter
- Cancel anytime
Buy Now
Price includes VAT (Japan)
Instant access to the full article PDF.
Similar content being viewed by others
References
Carreras, F. (1996). “On the Existence and Formation of Partnerships in a Game.”Games and EconomicBehavior 12, 54–67.
Kalai, E. and D. Samet. (1987). “On Weighted Shapley Values.”International Journal of Game Theory 16, 205–222.
Magaña, A. (1996). “Coalition Formation in Cooperative Games and Games with Multiple Alternatives” (in Spanish). Ph.D. Thesis. Departmentof Applied Mathematics II, Polytechnic University of Catalonia, Spain.
Owen, G. (1977). “Values of Games with a Priori Unions.” In R. Henn and O. Moeschlin (Eds.),Mathematical Economics and Game Theory.Essays in Honor of Oskar Morgenstern. Springer-Verlag, pp. 76–88.
Owen, G. and E. Winter. (1992). “Multilinear Extensions and the Coalition Value.”Games and EconomicBehavior 4, 582–587.
Shapley, L.S. (1953). “A Value forn—Person Games.” In H.W. Kuhn and A.W. Tucker (Eds.),Contributions to the Theory of Games II. Princeton University Press, pp. 307–317.
Author information
Authors and Affiliations
Department of Applied Mathematics II and Industrial Engineering School of Terrassa, Polytechnic University of Catalonia, Spain
Francesc Carreras, M. Dolors Llongueras & Antonio Magaña
- Francesc Carreras
You can also search for this author inPubMed Google Scholar
- M. Dolors Llongueras
You can also search for this author inPubMed Google Scholar
- Antonio Magaña
You can also search for this author inPubMed Google Scholar
Additional information
Research partially supported by Grant BFM 2003-01314 of the Science and Technology Spanish Ministry and the European Regional Development Fund.
Rights and permissions
About this article
Cite this article
Carreras, F., Llongueras, M.D. & Magaña, A. On the Convenience to Form Coalitions or Partnerships in Simple Games.Ann Oper Res137, 67–89 (2005). https://doi.org/10.1007/s10479-005-2245-8
Share this article
Anyone you share the following link with will be able to read this content:
Sorry, a shareable link is not currently available for this article.
Provided by the Springer Nature SharedIt content-sharing initiative