The guy has a recognition issue. In my opinion, he thinks you are better than him somewhere and envy you for that ---- or you really look like the school nerd that gets his ass kicked by everyone (it's okay if you are, I almost was one).
Anyway, in my opinion he is not an alpha male at all. Just a psychologically disturb sad person that seek for something. This thing is the thing you need to control him.
-- Here is my plan for you, start from Zero to the end, stop as soon as he stops --
0 - retrospect yourself
See what you have better than him, what he got better than you. Do a
SWOT analysis of the guy and of yourself as well. You need to know yourself before analysing others. Understand yourself and others in order to control things. That would help for all three different plans. Always know your enemy.
0.5 - Help him to give him what he doesn't have
I know you hate the guy, but put your feelings aside. Help him to get what he desires the most, he will eat in your hand when he will get by himself but thanks to you.
-- That should fix your issue. If not, do what a logical person would do --
1 - ignore him
Stop smiling bro!!!!! You are encouraging him by doing this. It's like "I think it is funny when you are clowning me, please carry on". So stop that, don't give him any credit when he is doing this. Treat him like the fly in the office that you never seen.
-- if after couple weeks it doesn't stop, then do this --
2 - do a 1-on-1 talk
Tell him what you feel, try to make him feel that little kid at school that takes all the shit on him from others, make him feel that it is not right and that he should stop. It has to come from him, so ask him question to make it go having that final conclusion which should be: "I think you are right, it is inappropriate to talk to you like this". But do not make him feel that by stopping he will make you a favour. You go to him to make him a favour as he could lose his job for acting like this. He should feel lucky that you have a sense of professionalism and you act smarter than him by taking the lead on this issue.
-- if he carries on... --
2 - Talk to HR
Let the HR knows, at this point you are being professional, there is an issue in your work, you want to fix it because this impact your efficiency and represent a pollution. So go green! But, calmly, let him know you go to HR as at this point he is aware of the problem as you shared it with him in previous plan. He will respect you from letting him know before and will actually try to say "come on... I'm sorry okay? don't do that". Do not listen to him and carry on. Make him begging you to not go. Unless he begs you like a pussy, just go to HR and ask her to make him stop whatever it takes for the sake of the productivity. Make sure they will go threat him because this is the only "how" he will stop, else then rollback and tell them to not do anything about it. And (only) if he asks you, tell him that you thought about twice and you wanted to give him a second chance.
-- if he carries on after HR talked to him and threaten him and you can't stand to ignore him anymore --
3 - confront him in front of a group he cares about
Best is to ignore again.... but... If you really can't ignore him because other people are witnessing your clowning moment, then give him lots of importance. Not from you, but from people. Confront him to his own game and destroy him. Maybe this is too advance actually, but if you're good at "poker face" then wear the chinese one (the worst one, the one you can't tell what you think) and go deeper in his thoughts and clownings. Ask him "what else?", "tell us more?", "interesting... why do you say that?", "oh really?". You have to be seeking for more information and making few foot steps toward him in order to subconstiously "challenge him" in front of the group. As an Alpha, he will have to answer your questions and give you more info, and at some point (I believe very soon) he will run out of content and start to justify himself, lose his confidence in front of the group, start to get nervous, he will probably get angry at you, but don't get affected to it. Just look at him right in the eyes, don't break eyes contact or remove your poker face. Don't say anything except reacting to his clownings. You have to get the confidence that you left behind on day 1 with him in order to stand right in the middle of the group with everyone looking at you. He will start giving you something, and something else, and something else, just empty that piece of shit of all of his shit, let it flow... when he runs out, he will feel stupid, will have nothing to say. So let him loose his shit, whatever the output of this, whatever if he gets mad, angry, shouts, punches you or whatever... he will at some point loose his shit in front of the group if you stand and act like you expect something from him. He will try to reverse the situation to his advantage, at that point he will need control to go back to his confort zone. He will be asking you questions (don't pay attention to them, don't reply! ignore!). It is crucial that you do not lose your shit! Be a man, and stand! Prove the group that you are a better person than him by just being smarter. That awkward moment can last from 20 seconds to 5min. Be ready for it if you go for it.
PS: if you opt for that last step confrontation, do that in front of more than 5 people, else it won't worth it. Best remains ignorance again.
Hope that helps