Anonymous implementation

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We consider Nash implementation under complete information with the additional feature that planners have to obey anonymity when designing mechanisms and shaping individuals’ unilateral deviation opportunities. Our notion of full implementation, anonymous implementation, demands the following: First, any socially optimal alternative at any one of the given states is attainable via a Nash equilibrium (NE) at that state, which provides the same opportunity set for all individuals. Second, any such NE at any one of the states must be socially optimal at that state. We identify the necessary and (almost) sufficient condition for anonymous implementation of social choice correspondences. Further, we show that there are collective goals that are anonymously implementable but fail to be Nash implementable. Therefore, anonymity provides society with additional decentralizable social choice rules that are otherwise not Nash implementable. Unfortunately, anonymity imposes a heavy burden when implementing efficiency: The Pareto social choice correspondence is not anonymously implementable in the full domain.