We study a notion of locally robust implementation that captures the idea that the planner may know agentsʼ beliefs well, but not perfectly. Locally robust implementation is a weaker concept than ex-post implementation, but we show that no regular allocation function is locally robust...

We show that a mechanism that robustly implements optimal outcomes in a one-dimensional supermodular environment continues to robustly implement ε-optimal outcomes in all close-by environments. Robust implementation of ε-optimal outcomes is thus robust to small perturbations of the...