We propose a new 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 is characterized by 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.

I study a strategic-communication game between an informed sender and an uninformed receiver with partially aligned preferences. The receiver is endowed with the ability to probabilistically detect if the sender is lying. Specifically, if the sender is making a false claim about her type, with some commonly known probability p the receiver additionally observes a private signal indicating that the sender is lying. The main result is that the receiver's stochastic lie-detection ability makes fully revealing equilibria-the best outcome for the receiver-possible, even for small p (less than 1 2). Additionally, if the language consists of precise messages, fully revealing equilibria exist only for p = 1 and for a set of intermediate values of p that is bounded away from 0 and 1, making the maximal ex-ante expected equilibrium utility of the receiver non-monotone in p. If vague messages are allowed, full revelation can be supported for all large enough p, overturning the non-monotonicity and improving communication outcomes relative to the precise-language case.

We consider two natural notions of strategyproofness in random objectassignment mechanisms based on ordinal preferences. The two notions are stronger than weak strategyproofness but weaker than strategyproofness. We demonstrate that the two notions are equivalent, provide a geometric characterization of the new intermediate property which we call convex strategyproofness, and then show that the (generalized) probabilistic serial mechanism is, in fact, convexly strategyproof. We finish by showing that the property of weak envy-freeness of the random serial dictatorship can be strengthened in an analogous manner.

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We discuss the exclusion core, a solution concept for object-allocation and object-exchange problems. The exclusion core is based on the right of exclusion and is especially useful for the analysis of economies with complicated property arrangements, such as those with shared ownership. The exclusion core coincides with the (strong) core in classic settings, and is closely related to the celebrated Top Trading Cycles algorithm.