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|
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- Montero, Maria, 2002.
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- 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.
- 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. Full references (including those not matched with items on IDEAS)
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