This paper studies the security choices of identical plant- controller systems, when their security is interdependent due the exposure to network induced risks. Each plant is modeled by a discrete-time stochastic linear system, which is sensed and controlled over a communication network. We model security decisions of the individual systems (also called players) as a game. We consider a two-stage game, in which first, the players choose whether to invest in security or not; and thereafter, choose control inputs to minimize the average operational costs. We fully characterize equilibria of the game, which give us the individually optimal security choices. We also find the socially optimal choices. The presence of security interdependence creates a negative externality, and results in a gap between the individual and the socially optimal security choices for a wide range of security costs. Due to the negative externality, the individual players tend to under invest in security.