Optimal distributed detection in the presence of Byzantines

This paper considers the problem of optimal distributed detection with independent identical sensors in the presence of Byzantine attacks. By considering the attacker to be strategic in nature, we address the issue of designing the optimal fusion rule and the local sensor thresholds that minimize the probability of error at the fusion center (FC).We first consider the problem of finding the optimal fusion rule under the constraint of fixed local sensor thresholds and fixed Byzantine strategy. Next, we consider the problem of joint optimization of the fusion rule and local sensor thresholds for a fixed Byzantine strategy. Then we extend these results to the scenario where both the FC and the Byzantine attacker act in a strategic manner to optimize their own utilities. We model the strategic behavior of the FC and the attacker using game theory and show the existence of Nash Equilibrium. We also provide numerical results to gain insights into the solution.