Information Design in Games: Certification Approach

Several players participate in a game with a continuum of actions. A designer chooses an information structure - a joint distribution of a state and private signals - and evaluates it according to the expected designer's payoff in the induced Bayes Nash equilibrium. We show an information structure is designer-optimal whenever the equilibrium play it induces can also be induced in an auxiliary contracting problem. This finding gives rise to a tractable solution method, which we use to study two novel applications. In an investment game, an optimal structure fully informs a single investor while providing no information to others. This structure is robustly optimal, for any state distribution and number of investors. In a price competition game, an optimal structure is Gaussian and recommends prices linearly in the state. This structure is uniquely optimal.