Alpha males would consider buying a woman a drink as supplication and would never attempt it. Beta males do buy women drinks and it lowers their value to the female. Omega Males would not buy a woman anything that is applicable to raise their emotional level for the short run at the expense of lowering their value. Rather, the Omega Male would cleverly tip the bartender prior to speaking with the beautiful woman so there would be no shock when while the Omega Male is next to the female and the bartender asks him what he would like to drink, then takes the order, and says to the Omega Male "aren't you going to buy the beautiful lady a drink? The Omega Male would look at the bartender, then smile at the beautiful woman while saying something like "No quite contrary, I would never trade drinks for a Beautiful ladies time, it is cheap and would have me appear be seeking sexual favors. I need no favors from anyone but that guy over there looks like he would would gladly buy her a drink" as the Omega Male casually points to a competitive Alpha male. As planned, the bartender then walks over to the Alpha male, and while appearing discrete, asks if he needs another drink, finally the bartender returns immediately with the Lady's drink on queue. Meanwhile the Omega Male has already raised the Lady's emotional energy, with strength and honor, while listening to her favorite vacation place.

I am a MAN!

no need for any other labels.

Alpha, Beta, Gamma, Delta, Omega - its all superfluous.

There's always a social heirarchy though, even if you remove the labels it still exists.

And what makes you think that I play the social game?

There may be a social hierarchy, if you play within the social construct.

If you do not, it does not apply.
It is merely something to be amused by as you watch others play within it.