An extension of Radner's theorem

Radner's theorem states that the optimal solution for a static linear quadratic Gaussian (LQG) team is linear. In this paper, we find the optimal solution for a static LQG team in which each player knows which observations he has, but in which the observation set that a player receives (how many, which measuring device,etc.) is random before the team acts. Via the concept of nesting, the result extends to the dynamic case and includes teams in which the order of play of the team members as well as their sets of data are random. We also include random changes in the cost function which depend on the randomness of the observation system but are independent of the stochastic process that the team is observing and controlling.