Examples of well-behaved sequences of economies without monotonic preferences are constructed. These economies have core allocations that cannot be decentralized by prices, even in a weak sense. Relaxing the monotonicity assumption results in core allocations that are not uniformly integrable, breaking the connection between the continuum and the large finite model. If in addition preferences are nonconvex, even sequences of economies with uniformly bounded core allocations may fail to exhibit equivalence properties. Sufficient conditions to restore convergence are provided.