Ultimately the parents since what punishment the school can dish out, at least in Australia, is so limited as to actually be laughable. Punishment doesn't have to be physical. Take away a child's allowance for a week or two and hear them howl.
A full investigation might reveal a pattern of bullying. Perhaps the child has been bullied in the past by this other child or this other child's gang or it is ongoing bullying. A bullied child will eventually snap and attack the bully even if they don't stand a chance in a fight. If this is the case then the attacked child also has to answer for past deeds.