Definition

Let $\{ J;\Gamma^{i},i\in\mathcal{N} \}$ be a standard quadratic team. If $\xi$ is a Gaussian random vector and $r_{i}(\xi)=Q_{i}\xi$, $\eta^{i}(\xi)=H^{i}\xi$, $i\in\mathcal{N}$, for some deterministic matrices $Q_{i},H^{i},i\in\mathcal{N}$, the decision problem is a quadratic-Gaussian team.