Robust implementation in weakly perfect Bayesian strategies

We examine a strong form of robust implementation in dynamic mechanisms that is both belief- and belief-revision-free. Specifically, we characterize robust wPBE-implementation, that is, full implementation in weak Perfect Bayesian equilibrium across all type spaces. We introduce a dynamic robust monotonicity condition that is weaker than Bergemann and Morris' (2011) robust monotonicity condition and show that under a conditional no total indifference condition, ex-post incentive compatibility and dynamic robust monotonicity characterize robust wPBE-implementation in general dynamic mechanisms. We also introduce a notion of weakly rationalizable implementation (wr-implementation) and prove that it is equivalent to robust wPBE-implementation. Applied to static mechanisms, wr-implementation exactly characterizes a version of static belief-free implementation.