Age of Incorrect Information in Uncertain Adversarial Environments via Bayesian Game Theory

Remote monitoring systems in cyber-physical infrastructures face increasing risks from adversarial interference, such as false data injection, which can distort the receiver’s perception of the system state. To measure the impact of such disruptions, the Age of Incorrect Information (AoII) has been proposed as a performance metric that captures both the freshness and correctness of remote estimates. Previous works have modeled AoII minimization using static game-theoretic frameworks under complete information, assuming that all players know each other's strategies and costs. This thesis advances the model by introducing a Bayesian game-theoretic framework that accounts for uncertainty in the adversary’s behavior. The interfering agent, referred to as Player X, may be either cooperative or malicious, and the controller maintains a probabilistic belief over this type. Players make strategic decisions under incomplete information, and their interactions are analyzed through the lens of Bayesian Nash Equilibrium. I formulate the system using a two-state Markov model, derive analytical expressions for AoII, and explore optimal strategies through numerical simulation. The results reveal how belief over player types significantly alters equilibrium behavior, influencing the controller's update frequency and the adversary's intensity. This framework captures a more realistic decision-making process in uncertain and potentially hostile environments.