The other matter of course is that the bully is likely to be acting out / repeating behaviours due to matters of concern in their own home life. The bullying child will have a bullying parent, step-parent or sibling etc.
Not necessarily. I think bullying is an innate behaviour, and it is gratifying because it gives the bully power. We have all met bullies in the corporate world, and they gain and retain power. Because unfortunately in a lot of workplaces bullying works. I have seen it work, in the short term at least.
I was bullied a fair bit at school, I was very small and an academic type, so an obvious target, and I'm rather ashamed to admit I did a bit of bullying in my turn. If there is some other kid getting the shit kicked out of him, then it's not you.
As I got older, around 16, the bullying took a more subtle psychological turn, as I understand it currently does on Facebook etc. I dealt with it by following the ringleader home one night, waiting until he was on his own and then giving him a shove and saying "Right, you and me. Let's go. You haven't got your mates to back you up, so let's go. Right now". It was a gamble, he was bigger, stronger and fitter than I and he would have won very convincingly, but I reckoned correctly that he firstly wasn't a fighter and secondly didn't want the collateral damage. I knew at 16 we were both big enough to do proper damage and I was determined that win or lose we were both going to go home bleeding. I also reckoned that as the popular kid and the son of the local doctor he wasn't going to want to face his parents and his mates at school with a black eye, a fat lip and bruises. Win or lose, he was going to lose. I didn't have anything to lose. He backed down and left me alone thereafter. His little gang had a few goes but he never joined in, because he knew damn well that he was going to be walking down Schoolhouse Lane again that evening, and it was only too easy for me to follow him for that quarter-mile stroll and pick up where we'd left off.
I'm not sure how this translates into a modern world. Corporate bullying is a very real thing and it is glamorised by the TV shows like Apprentice, Gordon Ramsey in kitchens and so on. I know very well they wouldn't walk into a meat factory and throw their weight about like that, if they didn't have an accident by falling in the cold store they would have an unfortunate meeting one night in the car park. However not everyone is prepared to tackle the bullies like that, and the bullies become very adept at not bullying the slaughterman with convictions for assault and ABH because they know very well how it will end.