A Bayesian Game-Theoretic Framework for False Data Injection in Cyber-Physical Systems

We use Bayesian game theory to model the strategic interplay of a transmitter in a cyber-physical system (CPS) that is under false data injection (FDI) by a malicious agent, whose characteristics are partially known. The transmitter aims to minimize age of incorrect information (AoII), whereas the malicious agent seeks to maximize it. The uncertain representation of the transmission costs of the malicious agent complicates the equilibrium. Existing studies on false data injection in CPS largely assume complete knowledge of the adversary or concentrate on detection mechanisms. However, the problem of how incomplete information affects information timeliness—measured by the AoII—remains unresolved. We show how the attack can be effectively contained by reacting to the expected value of injection costs. The novelty of our approach lies in combining the AoII metric with Bayesian game-theoretic modeling under incomplete information to derive optimal defense strategies against FDI attacks. More in general, we provide insights into strategic countermeasures to mitigate the impact of malicious interventions and enhancing the overall resilience of CPSs.