Controlling Age of Incorrect Information Violation Under Data Drift and Strategic Attacks

We study a control system where sensor measurements are transmitted to a remote station. Information may become outdated due to system drift or compromised by malicious false data injection. To quantify the impact of staleness and inaccuracy in the information at the receiver's side, we use Age of Incorrect Information (AoII). In particular, we consider the Excess AoII above a certain threshold as our key objective to minimize, which we argue to be a sensible goal for many real-time control systems. We adopt a game-theoretic framework to model the strategic interaction between a transmitter, which aims to minimize both Excess AoII and transmission costs, and a malicious agent, which seeks to maximize the same Excess AoII metric while minimizing its own costs. Our analysis reveals the existence of a Nash equilibrium for this game, and we investigate how the system parameters influence the adversary's decision to attack, identifying the conditions under which an attack becomes advantageous or not.