Medical Self-Reporting with Adversarial Data Injection Modeled via Game Theory

We present a game theoretic analysis of a personal e-health system, where a user reports self-measured data to a collection center. Our focus lies on addressing the challenge of potential mistakes in the reported data, a common issue for untrained users in e-health scenarios. The system alternates between the states of correct or erroneous data about the user being available at the collection center. Our goal function is related to age of incorrect information, a measure of the staleness of the information content. It linearly increases as time spent in the erroneous state elapses further. In this scenario, we introduce an additional malicious agent that injects erroneous measurements with the objective of exacerbating the staleness of information. This leads to an adversarial game between the user of interest and the malicious agent, the equilibrium of which we discuss. We derive closed-form expressions based on the system parameters, providing insights into the parametric ranges where the impact of the adversary is most menacing.