He is asserting himself, have you asked the school about their input on what is happening here, I would say no punishments till you have all the facts why he is doing this..when bullying is involved the children do not tell as it will involve parents going to school ,taking it up with Parents of other children and making it worse...You know what how about you show him how to stand up for him self, in every city and area we have defence Classes Karate , judo, he may not need these moves, but its very enpowering to know you can defend your self if you have to , build his self esteeem .
I think he needs more chores added to the list at home. The more reports of hitting, the more chores at home. Washing the kitchen floor usually works in our household.