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.
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