When two individuals engage in their tasks with a common stimulus display, the partner’s presence, response, task, and/or focus of attention often affects one’s own task performance. The present study investigates how the partner’s task affects one’s own task performance when one of two adjacently sitting participants engages in location-relevant task and the other in location-irrelevant task, with a common stimulus display and separate response sets. The target appeared at left or right. One participant pressed a left or right button according to the color of the target when it was green or red. The other participant pressed a left or right button of another response set according to the location of the target when it was white. Although the spatial compatibility effects were observed within each task, no cross-task (i.e., cross-participant) interference was observed. Results are discussed in terms of what is co-represented in joint task settings.