We identify particular exchange economies with asymmetric information in which the ex ante incentive compatible core is nonempty provided that coalitions can allocate goods by means of random mechanisms. Both the use of random mechanisms and the restriction to a specific class of economies are crucial for the result. Indeed, the ex ante incentive compatible core can be empty (i) in our class of economies if coalitions can only use deterministic mechanisms and (ii) outside this class, even if random mechanisms are allowed.