Ambiguous Data Injection Impacting Age of Incorrect Information: A Bayesian Game Analysis

We use Bayesian game theory to investigate the interaction between a system controller and an additional unknown agent in a cyber-physical system. The system controller performs some monitoring for real-time operation management, with the aim of minimizing the age of incorrect information (AoII). The additional agent reports some extra information, which ideally can serve to aid the controller and meet the same objective of decreasing AoII, but it is uncertain whether these actions are useful or correspond to (possibly international) false data injection in the system. The controller only has information in terms of probability of the legitimacy of this extra agent through a common prior, and also knows that, in case it is malicious, it will try to increase AoII instead. Our analysis reveals that, under rational behavior, an adversary can effectively masquerading as a sensor injecting legitimate data, as the controller can hardly distinguish the behavior of a true helper from that of an attacker. However, under variable data drift, the strategic behavior of the external agent can give away their type.