A smart room of the future is expected to facilitate intelligent interaction with its occupants while respecting their privacy. Although standard video cameras can be used to learn where the occupants are and what they do, they raise privacy concerns. While this can be mitigated by severely reducing camera resolution, it will also impact the utility of the camera network. This work investigates and quantifies the tradeoff between camera resolution and action recognition accuracy. Rather than building a physical testbed to carry out this study, we use a graphics engine to simulate a room with 5 cameras, and to animate avatars using skeletal movements of real users captured by a Kinect v2 camera. We study resolutions from 100×100 pixels down to 1×1 using a state-of-the-art action recognition method at higher resolutions and we propose a new approach at ultra-low resolutions. In extensive simulations, we conclude that on a dataset of 12 individuals performing 4 actions our algorithm applied to single-pixel data performs very close to the state-of-the-art method applied to 100×100 data, suggesting that reliable action recognition can be achieved without compromising occupant's identity.