In a series of experiments, researchers investigated the extent to which people perceive others versus how much they themselves think they are perceived.
People often observe those aroud them but fail to realize that others are doing the same, and that they, therefore, are also being observed.
See the full study here :
Boothby, E. J., Clark, M. S., & Bargh, J. A. (2017). The invisibility cloak illusion: People (incorrectly) believe they observe others more than others observe them. Journal of Personality and Social Psychology, 112(4), 589–606. https://doi.org/10.1037/pspi0000082