We study a situation with n retailers, each of them facing a news-vendor problem, i.e., selling to customers over a finite period of time (product with a short life cycle, such as fashion). Groups of retailers might improve their expected joint profit by coordinating their orders, followed by transshipments after demand realization is known. We analyze these situations by defining a cooperative game, called a general news-vendor game, for such a situation with n retailers. We concentrate on whether it makes sense to cooperate by studying properties of general news-vendor games. Our main result states that general news-vendor games have non-empty cores.