Stable partitions with W-preferences Original Research Article

Suppose that in a coalition formation game each participant has a preference list of the other participants and she prefers a set S to a set T if and only if she prefers the worst participant of S to the worst participant of T. We consider three definitions of stability. In the case of no indifferences stable partitions cannot contain very large sets and their existence can be decided polynomially. However, in the presence of ties one of the existence problems is NP-complete, the other is polynomial and the existence of a polynomial algorithm for the third one is still open.