M.C.
It is my understanding that the person who paid for a seat is the person who is entitled a to a carry on. For example, with my paid seat I am allowed 1 personal item and one carry-on. I can't take an extra personal item for my lap child because my lap child does not have his own seat. However, when I paid for my son's seat, we did carry another bag as his personal item which went under the seat in front of him.