Static LQG teams with countably infinite players

In static LQG teams with finite number of players, there is no loss of optimality in restricting attention to affine control strategies. This result, in turn, implies that affine control strategies are globally optimal for finite horizon partially nested LQG teams. The standard proof of optimality of affine strategies does not generalize to the setting where the team has countably infinite players and the cost function is the average expected cost per player. Consequently, it is not clear whether affine control strategies are globally optimal for infinite horizon partially nested LQG teams. We identify sufficient conditions under which affine control strategies are globally optimal for static teams with countably infinite players. An example is included.