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Coalition Formation in Generalized Apex Games

The class of games with one apex player is generalized to the class of games with a collection of apex sets. These simple games, together with a power index, canonically induce a hedonic coalition formation game. A monotonicity property of solutions is introduced and its meaning for the induced hedonic game is analyzed. Necessary and sufficient conditions for the existence of core stable partitions are stated and core stable partitions are characterized.