Implementation with a sympathizer

This paper considers the Nash implementation problem in which the planner does not know individuals' state-contingent choices that may involve violations of rationality. In economic environments with at least three individuals, we show that the planner may Nash implement a social choice correspondence while extracting information about individuals' state-contingent choices from the society whenever one of the individuals, whose identity is not necessarily known to the planner and the other individuals, is a weak sympathizer. Such an agent is weakly inclined toward the truthful revelation of individuals' state-contingent choices but not the \true" state. Then, in every Nash equilibrium of the mechanism we design, all individuals except one truthfully reveal the same information about individuals' choices.