A Denial of Service Game for Age of Incorrect Information in Cyber-Physical Systems

We analyze denial of service attacks for cyber-physical systems aimed at increasing age of incorrect information, a metric combining the description of staleness and incorrectness of the data exchanged. We utilize game theory to study the strategic interaction between two players; the former is a legitimate transmitter that wants to deliver status updates about the cyber-physical system to a control unit, whereas the latter is an adversary that, when active, prevents this communication from happening so as to cause the information at the control unit to become wrong and obsolete over time. These players act in an adversarial setup with contrasting objectives, but also being constrained by a costs term for their activity. To this end, we develop an original model based on Markov chains to quantify the average age of incorrect information as the result of both players' actions. Our analysis explores the equilibria of the resulting interaction and, especially, quantifies the regions of the parameters for which the attacker is most harmful or, conversely, where a proper strategic reaction by the transmitter can keep the attack at bay. This enables a quantification of information security in cyber-physical systems that go beyond the simple need to oppose the attacker, rather identifying quantitative evaluations and precise countermeasures.