Continuous implementation with payoff knowledge

The literature on robust mechanism design assumes players' knowledge about a fixed payoff environment and investigates global robustness of optimal mechanisms to large changes in the information structure. Acknowledging global robustness as a demanding requirement, we propose continuous implementation as a notion of local robustness. Keeping the assumption of payoff knowledge, we say that an SCF is continuously implementable if there exists a mechanism which yields the outcome close to the desired one for all types close to the planner's initial model. We show that when a generic correlation condition is imposed on the class of interdependent-value environments, any (interim) incentive compatible SCF is continuously implementable with arbitrarily small transfers imposed on and off the equilibrium. This stands in stark contrast to Bergemann and Morris (2005), who show that their global robustness amounts to ex post incentive compatibility, as well as to Oury and Tercieux (2012), who show that continuous implementation without payoff knowledge generates a substantial restriction on the SCF, tightly connected to full implementation in rationalizable strategies.