In a joint Simon task, a pair of co-acting individuals divide labors of performing a choice-reaction task in such a way that each actor responds to one type of stimuli and ignores the other type that is assigned to the co-actor. It has been suggested that the actors share the mental representation of the joint task and perform the co-actor’s trials as if they were their own. However, it remains unclear exactly which aspects of co-actor’s task-set the actors share in the joint Simon task. The present study addressed this issue by manipulating the proportions of compatible and incompatible trials for one actor (inducer actor) and observing its influences on the performance of the other actor (diagnostic actor) for whom there were always an equal proportion of compatible and incompatible trials. The design of the present study disentangled the effect of trial proportion from the confounding effect of compatibility on the preceding trial. The results showed that the trial proportions for the inducer actor had strong influences on the inducer actor’s own performance, but it had little influence on the diagnostic actor’s performance. Thus, the diagnostic actor did not represent aspects of the inducer actor’s task-set beyond stimuli and responses of the inducer actor. We propose a new account of the effect of preceding compatibility on the joint Simon effect.