This dataset comprises electroencephalographic recordings from 38 healthy subjects engaged in a multi-user P300-based brain-computer interface experiment called Brain Invaders. Participants played in pairs across three conditions (Solo1, Solo2, and Collaboration) using a visual oddball paradigm with 36 symbols to elicit P300 responses. The study investigates inter-brain synchrony during collaborative BCI gaming, with 32-channel EEG recordings sampled at 512 Hz using wet electrodes in a standard 10-10 montage.