We propose a new cooperative solution for discrete exchange economies and resource allocation problems, the exclusion core. The exclusion core rests upon a foundational idea in the legal understanding of property, the right to exclude others. By reinterpreting endowments as a distribution of exclusion rights, rather than as bundles of goods, our analysis extends to economies with qualified property rights, joint ownership, and social hierarchies. The exclusion core characterizes a generalized top trading cycle algorithm in a large class of economies, including those featuring private, public, and mixed ownership; it is neither weaker nor stronger than the (strong) core.