  Information design in an incomplete information game includes a designer with
the goal of influencing players' actions through signals generated from a
designed probability distribution so that its objective function is optimized.
We consider a setting in which the designer has partial knowledge on agents'
utilities. We address the uncertainty about players' preferences by formulating
a robust information design problem against worst case payoffs. If the players
have quadratic payoffs that depend on the players' actions and an unknown
payoff-relevant state, and signals on the state that follow a Gaussian
distribution conditional on the state realization, then the information design
problem under quadratic design objectives is a semidefinite program (SDP).
Specifically, we consider ellipsoid perturbations over payoff coefficients in
linear-quadratic-Gaussian (LQG) games. We show that this leads to a tractable
robust SDP formulation. Numerical studies are carried out to identify the
relation between the perturbation levels and the optimal information
structures.
