Implementation with a sympathizer

We study Nash implementation under complete information with the distinctive feature that the planner knows neither individuals’ state-contingent preferences (payoff states) nor how they correspond to the states of the economy on which the social goal depends. Our main question is whether or not the planner can extract only the essential information about individuals’ underlying preferences and simultaneously implement the given social goal. Our setup is especially relevant when the planner cannot use mechanisms asking for the full revelation of the payoffs states due to privacy and political correctness concerns or non-disclosure and confidentiality agreements. In economic environments with at least three individuals, we show that the planner may Nash implement a social goal while extracting only the essential information about the payoff states 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 the essential information about 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 disclose the same essential information about the payoff states.