Equilibria in data injection attacks

Data injection attacks are studied in a game theoretic setting. Assuming that the network operator acquires the state variables via generalized least squares (GLS) estimation, different attack performance metrics are proposed. The scenarios defined by the performance metrics are then analyzed. In particular, closed form expressions for best response functions and Nash equilibria (NEs) are given. First the case in which the attack vector can be constructed without energy constraints is studied. It is shown that for unconstrained attacks infinitely many optimal attack vectors exist and that the construction requires knowledge of the state variables in the grid. Alternatively, when energy constraints are included, the attack vector construction does not depend on the state variables. As a consequence, the optimal energy constrained attack strategy follows a correlated multivariate Gaussian distribution. It is shown that for unconstrained attacks infinitely many NEs exist and that in the constrained case at least one NE exists.