  We study information design in games in which each player has a continuum of
actions. We show that an information structure is designer-optimal whenever the
equilibrium play it induces can also be implemented in a principal-agent
contracting problem. We use this observation to solve three novel applications.
In an investment game, the optimal structure fully informs a single investor
while providing no information to others. In an expectation polarization game,
the optimal structure fully informs half of the players while providing no
information to the other half. In a price competition game, the optimal
structure is noise-free Gaussian and recommends prices linearly in the states.
Our analysis further informs on the robustness and uniqueness of the optimal
information structures.
