Who is the protagonist in the play Topdog/Underdog?

Since the protagonist is the central character in a literary work, Booth fits this role because he becomes more developed as a character than the others. Unlike some protagonists, however, Booth is no hero; instead, he is morally weak, and even possesses evil traits.

For one thing, Booth manufactures his own antagonist in Lincoln since he often perceives his brother as an adversary when he is not. Certainly, he blames his dissatisfaction with his life...

Since the protagonist is the central character in a literary work, Booth fits this role because he becomes more developed as a character than the others. Unlike some protagonists, however, Booth is no hero; instead, he is morally weak, and even possesses evil traits.

For one thing, Booth manufactures his own antagonist in Lincoln since he often perceives his brother as an adversary when he is not. Certainly, he blames his dissatisfaction with his life on his brother--not unlike his namesake and that man's attitude about Abraham Lincoln. In one scene, for instance, as the brothers are having supper, Booth recalls the day his mother packed her things and abandoned them. He irrationally places blame upon his brother for his sense of abandonment since he was alone after she left. (He was truant that day whereas Lincoln had gone on to school.) 
Further, when Booth wants to become a dealer of three-card monte, he blames his brother for not helping him learn how to "hustle," despite knowing that Lincoln lost all his money this way, as well as having witnessed an acquaintance murdered over this game. Yet, when Lincoln asks Booth to help him practice his death scene in a more dramatic manner after he is "shot" by those who come to the arcade, Booth refuses.

Clearly, it is Booth's moral weakness--not unlike that of classic protagonists--which causes his downfall. He continues to blame others for his lack of success in life and does not try to obtain honest work. Instead, he tries to manipulate others. In another scene in which Link refuses to teach him how to hustle cards, Booth tells his brother,

Here I am trying to earn a living and you standing in my way. YOU STANDING IN MY WAY, LINK.

So much does Booth project his own failures onto his brother that he eventually shoots him in a tragic and ironic imitation of the historical scene of John Wilkes Booth and Abraham Lincoln.