Continuous implementation with local payoff uncertainty

Following the notion of continuous implementation, we consider a situation where the social planner is not entirely sure of the validity of his model and thus wants the social choice function to be not only (partially) implemented at all types of the initial model, but also at all types “close” to those types. In addition, we assume that the social planner also has some doubts on the payoffs of the outcomes and thus wants his prediction to be robust when these payoffs are close but not exactly equal to those in the initial model. Under this local payoff uncertainty, the present paper establishes the following full characterization result for finite mechanisms: a social choice function is continuously implementable if and only if it is fully implementable in rationalizable strategies.