Robust Implementation in General Mechanisms
A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with it. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) suﬀicient for robust implementation. Robust monotonicity is strictly stronger than both Maskin monotonicity (necessary and almost suﬀicient for complete information implementation) and ex post monotonicity (necessary and almost suﬀicient for ex post implementation). It is equivalent to Bayesian monotonicity on all type spaces.
Bergemann, Dirk and Morris, Stephen, "Robust Implementation in General Mechanisms" (2008). Cowles Foundation Discussion Papers. 1972.