It is well-known that mechanism design literature makes many simplifying infor- mational assumptions in particular in terms of common knowledge of the environment among players. In this paper, we introduce a notion of continuous implementation and characterize when a social choice function is continuously implementable. More specif- ically, we say that a social choice function is continuously (partially) implementable if it is (partially) implementable for types in the model under study and it continues to be (partially) implementable for types "close" to this initial model. We ?rst show that if the model is of complete information a social choice function is continuously (partially) implementable only if it satis?es Maskin?s monotonicity. We then extend this result to general incomplete information settings and show that a social choice function is continuously (partially) implementable only if it is fully implementable in iterative dominance. For ?nite mechanisms, this condition is also su¢ cient. We also discuss implications of this characterization for the virtual implementation approach.
