C-complete sets for compromise stable games
The core cover of a TU-game is a superset of the core and equals the convex hull of its larginal vectors. A larginal vector corresponds to an ordering of the players and describes the efficient payoff vector giving the first players in the ordering their utopia demand as long as it is still possible to assign the remaining players at least their minimum right. A game is called compromise stable if the core is equal to the core cover, i.e. the core is the convex hull of the larginal vectors. This paper analyzes the structure of orderings corresponding to larginal vectors of the core cover and conditions ensuring equality between core cover and core. We introduce compromise complete (or c-complete) sets that satisfy the condition that if every larginal vector corresponding to an ordering of the set is a core element, then the game is compromise stable. We use combinatorial arguments to give a complete characterization of these sets. More specifically, we find c-complete sets of minimum cardinality and a closed formula for the minimum number of orderings in c-complete sets.
|Date of creation:||03 Dec 2012|
|Contact details of provider:|| Postal: Department of Business and Economics, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark|
Phone: 65 50 32 33
Fax: 65 50 32 37
Web page: http://www.sdu.dk/ivoe
More information through EDIRC
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.:
- Muto, S. & Nakayama, M. & Potters, J.A.M. & Tijs, S.H., 1988. "On big boss games," Other publications TiSEM 488a314a-179c-4628-91e6-7, Tilburg University, School of Economics and Management.
- Rafels, Carles & Ybern, Neus, 1995. "Even and Odd Marginal Worth Vectors, Owen's Multilinear Extension and Convex Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(2), pages 113-126.
- repec:spr:compst:v:76:y:2012:i:3:p:343-359 is not listed on IDEAS
- Marieke Quant & Peter Borm & Hans Reijnierse & Bas van Velzen, 2005.
"The core cover in relation to the nucleolus and the Weber set,"
International Journal of Game Theory,
Springer;Game Theory Society, vol. 33(4), pages 491-503, November.
- Quant, M. & Borm, P.E.M. & Reijnierse, J.H. & van Velzen, S., 2005. "The core cover in relation to the nucleolus and the Weber set," Other publications TiSEM 9723cee6-92c9-49a2-90d3-9, Tilburg University, School of Economics and Management.
- van Velzen, S. & Hamers, H.J.M. & Norde, H.W., 2002. "Convexity and Marginal Vectors," Discussion Paper 2002-53, Tilburg University, Center for Economic Research.
- Potters, Jos & Poos, Rene & Tijs, Stef & Muto, Shigeo, 1989. "Clan games," Games and Economic Behavior, Elsevier, vol. 1(3), pages 275-293, September.
- A. Estévez-Fernández & M. Fiestras-Janeiro & M. Mosquera & E. Sánchez-Rodríguez, 2012. "A bankruptcy approach to the core cover," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(3), pages 343-359, December.
- Arantza Estévez-Fernández & María Gloria Fiestras-Janeiro & Manuel Alfredo Mosquera & Estela Sánchez- Rodríguez, 2012. "A Bankruptcy Approach to the Core Cover," Tinbergen Institute Discussion Papers 12-012/1, Tinbergen Institute.
- Potters, J.A.M. & Poos, R. & Tijs, S.H. & Muto, S., 1989. "Clan games," Other publications TiSEM 1855e4e3-7392-4ef0-a073-8, Tilburg University, School of Economics and Management.
- Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:hhs:sdueko:2012_025. 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: (Lene Holbæk)
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.