Anonymous implementation

We consider Nash implementation under complete information with the additional feature that planners are restricted by anonymity when designing mechanisms and shaping individuals’ unilateral deviation opportunities. We identify the necessary and (almost) sufficient condition for (full) implementation of social choice correspondence. We show that there are collective goals that are implementable under anonymity but not in Nash equilibrium. Thus, our observations justify that anonymity provides society with additional decentralizable social choice correspondences that are otherwise not implementable. Unfortunately, anonymity imposes a heavy burden when implementing efficiency: The Pareto social choice correspondence is not implementable under anonymity in the full domain.