The present invention relates to an interactive system, a control method for the interactive system, and a projector. Provided is the interactive system which can reduce interference of a synchronization signal even when a plurality of the interactive systems are used while being placed side by side. The interactive system (1) includes a transmitter (light-emitting pen (200)) configured to transmit an optical signal and a projector (100). The projector (100) includes a signal-intensity setting unit (22) in which intensity information of a synchronization signal is set, a signal-intensity control unit (light-emission control unit (60)) configured to control the intensity of the synchronization signal on the basis of the setting of the signal-intensity setting unit (22), a synchronization-signal transmitting unit (infrared-light emitting unit (61)) configured to transmit the synchronization signal, and an image pickup unit (51) configured to pick up an image of the optical signal transmitted from the transmitter. The transmitter includes a receiving unit (pen reception unit (230)) configured to receive the synchronization signal and an optical-signal transmitting unit (pen control unit (220) and a light-emitting diode (240)) configured to transmit the optical signal in synchronization with the synchronization signal received by the receiving unit.