Equivalence of Nash implementability and robust implementability with incomplete information

This paper is concerned with the design of robust mechanisms which are applicable to a wide class of possible information structures of agents. We examine a society consisting of several groups such that (i) there are at least three agents in each group; and (ii) each agent knows the preferences of the agents in his group but has incomplete information about the preferences of the agents outside his group. We show that for a large class of information structures, a social choice set (SCS) is implementable for each possible information structure if and only if it is Nash implementable. In other words, the class of robustly implementable SCS's is identical to the class of implementable SCS's in the complete information setting.

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