This work deals with the possibility of coalitions to manipulate the competitive equilibrium allocation. The manipulation is made by reallocating the endowments of the coalition's members in such a way that in the resulting equilibrium the position of each one of them will be improved. The main task of this work is to answer (1) whether any economy possess manipulable states, or do the known examples represent an exceptional phenomenon? and (2) whether there is any condition that characterize the coalitions that are able to manipulate? The results are as follows: (a) If every allocation has a unique constant equilibrium price, then manipulation does not exist; for all the other cases: (b) any coalition that contains two members with different 'income effects' is able to manipulate; (c) there exists a set of manipulable states which has a positive measure; and (d) Pareto optimal allocations are not manipulable.