An apex game consists of one apex player and a set of minor players. We identify two key properties of apex games and use them to introduce the class of general apex games. We derive players' preferences over winning coalitions by applying strongly monotonic power indices on such a game and all...

We consider a hedonic coalition formation game in which a coalition chooses for each partition of the player set the probability with which it forms and thereby destroys the current partition. These probabilities are commonly known so that farsighted players know at every partition what future...