Continuous Implementation with Small Transfers

The robust mechanism design literature investigates the global robustness of op-timal mechanisms to large changes in the environment. Acknowledging the global robustness as an overly demanding requirement, we propose continuous implementa-tion as a local robustness of optimal mechanisms to small changes in the environment. We say that a social choice function is continuously implementable “with small trans-fers” if there exists a mechanism which yields the outcome close to the desired one for all types close to the designer’s initial model. We show that when a generic cor-relation condition is imposed on the class of interdependent values environments, any incentive compatible social choice function is continuously implementable with small transfers. This exhibits a stark contrast with Bergemann and Morris (2005) who show that their global robustness amounts to ex post incentive compatibility as well as Oury and Tercieux (2012) who show that continuous implementation generates a substantial restriction, tightly connected to full implementation in rationalizable strategies.