Almost-dominant strategy implementation: exchange economies

We relax strategy-proofness (a form of dominant strategy implementation) by allowing “small” gains from manipulation. In 2-agent exchange economies, this relaxation is shown to have a discontinuous effect on the range of efficient rules, demonstrating a type of nonrobustness in previous impossibility results. When gains are measured with respect to a single good and preferences are linear, we characterize a particular rule as being the most equitable among all efficient rules satisfying the relaxation.