This paper discusses a novel framework designed to increase human-robot interaction through robotic imitation of the user's gestures. The set up consists of a humanoid robotic agent that socializes with and play games with the user. For the experimental group, the robot also imitates one of the user's novel gestures during a play session. We hypothesize that the robot's use of imitation will increase the user's openness towards engaging with the robot. Preliminary results from a pilot study of 12 subjects are promising in that post-imitation, experimental subjects displayed a more positive emotional state, had higher instances of mood contagion towards the robot, and interpreted the robot to have a higher level of autonomy than their control group counterparts. These results point to an increased user interest in engagement fueled by personalized imitation during interaction.