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Coalition Formation Games: a Survey

In this paper we give an overview of various methods used to study cooperation within a set of players. Besides the classical games with transferable utility and games without transferable utility, recently new models have been proposed: the coalition formation games. In these, each player has his own preferences over coalitions to which he could belong and the quality of a coalition structure is evaluated according to its stability. We review various definitions of stability and restrictions of preferences ensuring the existence of a partition stable with respect to a particular stability definition. Further, we stress the importance of preferences over sets of players derived from preferences over individuals and review the known algorithmic results for special types of preferences derived from the best and/or the worst player of a coalition.