The perception of gaze from an animated agenton a 2D display has been shown to suffer fromthe Mona Lisa effect, which means that exclusive mutual gaze cannot be established if there is more than one observer. In this study, we investigate this effect when it comes to turntaking control in a multi-party human-computerdialog setting, where a 2D display is compared to a 3D projection. The results show that the 2D setting results in longer response times andlower turn-taking accuracy.