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The -person, -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, is larger than some bounds, and which bounds are given explicitly in terms of the coefficient matrices. Related properties of the two-person zero-sum game are also investigated. It is shown that under certain conditions, better information is beneficial to the player who has better maneuverability while the saddle-point cost is independent of the information if both players have the same maneuverability. Conditions guaranteeing the uniform boundedness of the solutions of the coupled Riccati equations which arise in such games are also given.