Using robots to reward and stimulate children doing tasks together can be helpful in improving their social skills. Robots implemented 3 types of behavior scenarios - imitate, enhance and counteract - in a collaborative game of teaching robots perform movements shown by hand gestures. The paper presents a novel account of ASD symptoms based on the interplay of empathic concern and empathic accuracy in different personalities with and without cognitive deficits. Performance of autistic children was compared with two age groups of typically developing children - under and above the age of 7. The study confirmed the limited resource hypothesis - cognitive and motivational - bringing about the observed phenomena in situations of limited attention resources and performance under distraction. The robotic framework for educating children has shown potential for developing of various complex cognitive and social skills and has substantial developmental impact.