The objective of this paper is to study stable coalition structures in symmetric majority games. We assume that players deviate from a coalition structure to another to maximize their power given by the Owen power index. We introduce three myopic core concepts and one farsighted stability concept, the farsighted vNM stable set. Our main result is that the pessimistic core, the largest myopic core, coincides with some farsighted vNM stable set for any number of players. Moreover, we show that a (...) coalition structure belongs to the pessimistic core and the farsighted vNM stable set if and only if it contains an exact majority coalition. (shrink)