  Recent years have witnessed a significant increase in cyber crimes and system
failures caused by misinformation. Many of these instances can be classified as
gaslighting, which involves manipulating the perceptions of others through the
use of information. In this paper, we propose a dynamic game-theoretic
framework built on a partially observed stochastic control system to study
gaslighting. The decision-maker (DM) in the game only accesses partial
observations, and she determines the controls by constructing information
states that capture her perceptions of the system. The gaslighter in the game
influences the system indirectly by designing the observations to manipulate
the DM's perceptions and decisions. We analyze the impact of the gaslighter's
efforts using robustness analysis of the information states and optimal value
to deviations in the observations. A stealthiness constraint is introduced to
restrict the power of the gaslighter and to help him stay undetected. We
consider approximate feedback Stackelberg equilibrium as the solution concept
and estimate the cost of gaslighting.
