An effectivity function describes the blocking power of coalitions on subsets of alternatives. Given a preference profile, if any coalition blocks an alternative whenever it can, using its own power, make all of its members better off, only alternatives in the core can be reached. In this paper we study the incentives of the coalitions to use this power truthfully, i.e. to not manipulate. Some well known cores, among them the core of an exchange economy, are manipulable. We give sufficient conditions on an effectivity function that assure its core is nonmanipulable.