Robust Implementation: The Role of Large Type Spaces
A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with a social choice function. 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. It requires that there not be too much interdependence of types. We characterize robust monotonicity for some interesting economic environments. We identify conditions where, if robust implementation is possible, it is possible in a direct mechanism. We identify conditions where, if robust implementation is not possible, virtual robust implementation is not possible either.
Bergemann, Dirk and Morris, Stephen, "Robust Implementation: The Role of Large Type Spaces" (2005). Cowles Foundation Discussion Papers. 1803.