A Game of Age of Incorrect Information Against an Adversary Injecting False Data

Remote sensing enables fast and cost-effective data collection and monitoring, but can be subject to the injection of false data by adversaries. We consider a remote transmitter that is sending status updates about a process to a receiver, incurring a cost when doing so. The system is modeled as transiting between two conditions, implying that the receiver may start with correct knowledge about the process, but this information may become obsolete due to a natural drift of the process toward another regime and the lack of updates by the transmitter. In normal conditions, the transmitter would estimate the age of incorrect information (AoII), a metric proposed in the literature to quantify the time elapsed from the last instant in which the receiver had correct knowledge about the process, to determine the required frequency of updates, balancing it with the transmission cost. We assume the presence of an adversary that may increase the process drift, also incurring its own cost when doing so. The resulting interaction can be analyzed through game theory, with the transmitter and the adversary as strategic players. We present an analysis to determine the conditions for the costs paid by the players and the consequences of their actions on the resulting system performance.