A Robustness Result for Rationalizable Implementation

This paper investigates the extent to which rationalizable implementation depends on the implicit common knowledge restrictions of traditional models. Under general conditions such restrictions are without loss of generality: If a mechanism M implements a social choice function f on a type space X, then M implements f assuming only that agents’ k-order beliefs are among those described by an open set B containing X, while higher-order beliefs are unrestricted. The result is applied to direct implementation on payoff type spaces, and related to incentive compatible implementation.