Robust Nash Equilibria of Age of Incorrect Information Games in Cyber-Physical Systems

This paper studies the impact of uncertainty in the attacker's cost on equilibrium behavior in adversarial systems competing over the age of incorrect information (AoII). We consider a game-theoretic framework in which a defender and an attacker select their activity levels so as to respectively minimize and maximize AoII, while incurring linear costs. Unlike standard formulations, the attacker's cost is assumed to be uncertain and known only within a bounded interval, reflecting incomplete information about the adversary's capabilities. To address this uncertainty, we adopt a robust game-theoretic approach and characterize the resulting Robust Nash Equilibrium (RNE), where players optimize their strategies against worst-case parameter realizations. We derive structural properties of the equilibrium and provide insights into how uncertainty affects both players' strategies and system performance. Numerical results show that the robust formulation leads to more conservative strategies and highlights the sensitivity of the equilibrium to the attacker's cost. The proposed framework provides a tractable and practically relevant tool for the design of security mechanisms under incomplete information.