Implementation with a sympathizer

This paper studies Nash implementation under complete information with the distinctive feature that the planner does not know individuals' state-contingent preferences and is completely ignorant of how individuals' payoff-relevant characteristics correspond to the states of the economy, on which the social goal depends. Our main question is whether or not the planner can learn individuals' underlying preferences and simultaneously implement the given social goal. In economic environments with at least three individuals, we show that the planner may Nash implement a social goal while extracting the desired information about individuals' state-contingent preferences from the society whenever this goal has standard monotonicity properties and one of the individuals, whose identity is not necessarily known to the planner and the other individuals, is a sympathizer. Vaguely put, such an agent is inclined toward the truthful revelation of how states of the economy are associated with individuals' preferences, while he is not inclined to reveal the realized "true" state of the economy. Then, in every Nash equilibrium of the mechanism we design, all individuals truthfully reveal the same information about individuals' choices.