Coalition Formation in General Apex Games
We generalize the class of apex game by combining a winning coalition of symmetric minor players with a collection of apex sets which can form winning coalitions only together with a fixed quota of minor players. By applying power indices to these games and their subgames we generate players' preferences over coalitions which we use to define a coalition formation game. We focus on strongly monotonic power indices and investigate under which conditions on the initial general apex game there are core stable coalitions in the resulting coalition formation game. Besides several general results, we develop condition for the Shapley-Shubik index, the Banzhaf index, and the normalized Banzhaf index in particular. It turns out that many statements can be easily verified for arbitrary collections of apex sets. Nevertheless, we give some relations between the collection of apex sets and the set of core stable coalitions.
|Date of creation:||28 Oct 2013|
|Contact details of provider:|| Postal: Manor Rd. Building, Oxford, OX1 3UQ|
Web page: https://www.economics.ox.ac.uk/
More information through EDIRC
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.:
- Montero, Maria, 2002.
"Non-cooperative bargaining in apex games and the kernel,"
Games and Economic Behavior,
Elsevier, vol. 41(2), pages 309-321, November.
- Montero, M.P., 1999. "Noncooperative Bargaining in Apex Games and the Kernel," Discussion Paper 1999-61, Tilburg University, Center for Economic Research.
- Dimitrov, Dinko & Haake, Claus-Jochen, 2011.
"A note on the paradox of smaller coalitions,"
Center for Mathematical Economics Working Papers
386, Center for Mathematical Economics, Bielefeld University.
- Dinko Dimitrov & Claus-Jochen Haake, 2006.
"Government versus Opposition: Who Should be Who in the 16th German Bundestag?,"
Journal of Economics,
Springer, vol. 89(2), pages 115-128, November.
- Dimitrov, Dinko & Haake, Claus-Jochen, 2011. "Government versus opposition. Who should be who in the 16th German Bundestag?," Center for Mathematical Economics Working Papers 375, Center for Mathematical Economics, Bielefeld University.
- Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
- Sagonti, Emanuela, 1991. "On the Strong Monotonicity of Power Indices," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(1), pages 13-22.
- Dreze, J H & Greenberg, J, 1980.
"Hedonic Coalitions: Optimality and Stability,"
Econometric Society, vol. 48(4), pages 987-1003, May.
- Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
- repec:dau:papers:123456789/87 is not listed on IDEAS
- Dimitrov, Dinko & Haake, Claus-Jochen, 2008. "Stable governments and the semistrict core," Games and Economic Behavior, Elsevier, vol. 62(2), pages 460-475, March.
- Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
- Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001.
"Core in a simple coalition formation game,"
Social Choice and Welfare,
Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.
When requesting a correction, please mention this item's handle: RePEc:oxf:wpaper:680. 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: (Monica Birds)
If references are entirely missing, you can add them using this form.