A robustness result for rationalizable implementation

This paper investigates the extent to which rationalizable implementation depends on the implicit common knowledge restrictions usually embodied in traditional models. It is shown that under fairly general conditions such restrictions are without loss of generality in the following sense: If a mechanism implements a social choice function f on a type space X, then implements f assuming only that the agents' k-order beliefs are among those described by an open set B containing X, while higher-order beliefs are completely unrestricted. The result is applied to direct implementation on payoff type spaces, and related to the weak (incentive compatible) implementation problem.