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It is well known that any decision efficient, budget balanced, and envy-free mechanism for allocating a single object with transfers is vulnerable to manipulation. In this paper we examine whether the possible manipulations can have a serious impact on the outcome. Specifically, we examine which allocations are realized in the direct revelation game of any rule satisfying certain normative properties. For this class of rules we show that decision efficient, budget balanced, and envy-free allocations are the only ones realized through an ɛ-Nash equilibrium for any sufficiently small ɛ > 0. [ABSTRACT FROM AUTHOR]