Linear Quadratic Differential Games in a Hilbert Space

We consider linear quadratic games in a Hilbert space. The system equation is linear and involves an unbounded operator which generates a strongly continuous evolution operator (or semigroup). We show that the existence of a solution to a Riccati integral equation implies the existence of a saddle point for the closed-loop game, and that the former is guaranteed if there exists a unique open-loop saddle point. We also consider quadratic games on an infinite interval.