Egotism and 'One-Upmanship'

Honestly, I have quite a large problem with extremely egotistical people; or even slightly over egotistical people. Each of the above (and anyone who may be caught in between) always practice mockery and humiliation of others that they see as 'uncool' or less cool then them.
I'm willing to accept that everyone is egotistical to some vague level; but the normal, more kindly people are only very slightly egotistical, and in most cases its not easily visible.

I, like many others, have been a victim of mockery and humiliation in the past. Somewhere along the line I learned to either just laugh along, shoot it back at them, or completely ignore it, which eventually caused those people who once mocked and humiliated me to gain a respect for me, no matter how slight.
I'd have to admit that people like this have caused me short-term depression in the past, or have contributed to an already existing problem. I find it quite easy to laugh them off if they're simply acting like an idiot in an attempt to make me seem feeble, and I find it quite easy to ignore them or shoot it right back at them if they attempt to lip me off for some reason or another (with a majority of the time leaving it unreasoned), but when they physically annoy me (ex: poke me constantly, steal a hat/ pull off a hood) I tend to get upset and angry at them, especially if this harassment is accompanied by the other forms of annoyance, mockery, and humiliation.
If the harassment seems unreasoned, it's usually because they've made themselves look like an idiot by doing something stupid, so they have to pawn that stupidity off on someone else, so they practice 'one-upmanship' on the closest unaffiliated person, in which they belittle the victim for no visible reason, and cause the victim to become upset to at least some extent.

I really don't know what anyone can do to quell these sort of people, or to even put them in their place (aside from, you know, just outright punching them in the face) because we all know attempting to rationally talk to them about it only leads to more annoyance, mockery, and humiliation (providing they've got at least a couple of their friends around to continue supporting them in this venture).

These people are usually people looking to scape goat their problems or someone or something else, people trying to look cool, or people simply forced to do so as so they're not assaulted in the same way.

I just hope some of these people don't begin to wonder why I may outright break there nose, because most (if not all) have it coming.
That's not to say this happens to myself often, but when it does, it can really put an unnecessary dent in the rest of the day.