Robust Implementation in Weakly Rationalizable Strategies

Weakly rationalizable implementation represents a generalization of robust implementation to dynamic mechanisms. It is so conservative that virtual implementation in weakly rationalizable strategies is characterized by the same conditions as robust virtual implementation by static mechanisms. We show that despite that, (exact) weakly rationalizable implementation is more permissive than (exact) robust implementation in general static mechanisms. We introduce a dynamic robust monotonicity condition that is weaker than Bergemann and Morris’ (2011) robust monotonicity condition and prove that it is necessary, and together with weak extra assumptions sufficient for weakly rationalizable implementation in general dynamic mechanisms. We demonstrate that sometimes even weakly rationalizable implementation in finite dynamic mechanisms is more permissive than robust implementation in general static mechanisms.