On the Informational Properties of the Nash Solution of LQG Dynamic Games

The M-person, N-stage discrete time LQG Nash game is considered. The players use strategies that are linear functions of the current estimate of the state generated by a Kalman filter. We study the impact of improvements of the information on the costs of the players. For certain classes of such problems, we show that better information is beneficial to all the players if the number of stages, or the number of players are larger than some bounds, which bounds are given explicitly in terms of the coefficient matrices. Conditions guaranteeing the uniform boundedness of the solutions of the coupled Riccati equations which arise in such games are also given.