  In this paper, we consider a linear-quadratic-Gaussian defending assets
differential game (DADG) where the attacker and the defender do not know each
other's state information while they know the trajectory of a moving asset.
Both players can choose to observe the other player's state information by
paying a cost. The defender and the attacker have to craft both control
strategies and observation strategies. We obtain a closed-form feedback
solution that characterizes the Nash control strategies. We show that the
trajectory of the asset does not affect both players' observation choices.
Moreover, we show that the observation choices of the defender and the attacker
can be decoupled and the Nash observation strategies can be found by solving
two independent optimization problems. A set of necessary conditions is
developed to characterize the optimal observation instances. Based on the
necessary conditions, an effective algorithm is proposed to numerically compute
the optimal observation instances. A case study is presented to demonstrate the
effectiveness of the optimal observation instances.
