Just to get off this argument....
In a civil circumstance (ie. corporates), one of the ways I found to deal with alphas is to be extraordinary polite to them, nod at their achievements, but treat them like the rest of the pack.
Think of alphas as huge steamrollers. Russian Empire. The Russians lost 10,000 men in Afghanistan and got beaten by a bunch of poorly-armed amateurs....think of yourself as the Afghans.
Taking on alphas directly, especially in civil circumstances, will get you killed/fired/arrested. Instead, undermine them like a gurellia. The alpha hangs around other alphas....hang around with the betas and win their support to oust the Alpha (maybe you'd like to be CEO?). When the alpha gets into tough times, spread rumours that he might not be suited to the position.
You can't go face-to-face with an alpha, but you can undermine him by doing little things he never notices. Eventually he'll be stepping on a minefield while you sit back and wait for the next meeting.
In an uncivil circumstance....well if you want to be successful why are you hanging out with losers?
(P.S. Remember the weakness of alpha males - they have to constantly fight to keep their power. Admit it or not, alpha males DO have to fight for their status on a daily basis. They don't give a sh*t, but secretly they do. Exploit that)
And Jake, remember that Asian guys should never let loose their temper. "Let your enemy exhaust himself on arguments, then kill him." (its not sun tzu, I just made it up)