This paper studies resource-allocation mechanisms by using a reduced-form notion of mechanism. We formulate a mechanism by specifying the state space of the mechanism, the set of outcomes that agents can induce in a given state, and the set of admissible outcomes in each state. This notion of mechanism includes the Walrasian mechanism and majority voting as well as all game forms. With this notion, monotonicity is not only necessary but sufficient for a social choice correspondence to be implementable. Our main result is that in the context of exchange economies, if a mechanism implements a sub-correspondence of the Pareto correspondence and satisfies localness (one's "budget set" in a given state is independent of other agents' endowments), then the mechanism necessarily implements a sub-correspondence of the core correspondence. If the mechanism also satisfies anonymity, then it actually implements a sub-correspondence of the Walrasian equilibrium correspondence.
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