For the record, Alcibiades is the example that Cleckley, the psychiatrist who introduced psychopathy in the DSM, uses as the quintessential psychopath, in his Magnum Opus The Mask of Sanity.
Maybe this is a way to put it: "Alpha" and "Beta" refer to female perceptions. So, they are contextual.
Being authentically masculine and self-aware, is innate. You might come off either as Alpha or Beta to observing females, depending on the context. (Although it tends to land you on the Alpha side).
Sigma... Is my favorite disagreement with Typo. Imo, there is a "sigma" disposition. When you could, but don't bother to.