Strategy - Proofness , Core , and Sequential Trade ¤

We extend the Shapley-Scarf (1974) model-where a …nite number of indivisible objects is to be allocated among a …nite number of individuals-to the case where the primary endowment set of an individual may contain none, one, or several objects and where property rights may be transferred (objects inherited) as the allocation process unfolds, under the retained assumption that an individual consumes at most one object. In this environment we analyze the core of the economy and characterize the set of strategy-proof and Pareto e¢cient mechanisms. From a dual perspective, we consider property rights implicitly de…ned by a strategy-proof and Pareto e¢cient mechanism and show a core property for the mechanism-induced endowment rule.