A Theory of Multidimensional Information Disclosure

Abstract

This paper studies the optimal disclosure policy of multidimensional information when the sender can commit ex ante to the policy. By controlling the information available to an uninformed receiver, the sender controls the distribution of the receiver’s posterior expectations. Assuming quadratic preferences, we derive an upper bound of the sender’s ex ante utility based on semidefinite programming, and show that a linear transformation of the state is optimal if it is normally distributed. In addition, we examine extensions in which the receiver has private information and there are multiple senders. Applications of our theory include information sharing in an oligopoly.