In Topdog/Underdog, it could easily be argued that of the two brothers, Booth and Lincoln, either is the true protagonist. However, when we consider what makes a protagonist a protagonist—progression, psychological depth, and so on—it can be more soundly argued that Lincoln is the true protagonist of the play. Lincoln is certainly the more relatable of the two, particularly since he seems to try harder to "clean-up" and make a better life for himself.
Booth (played on the stage originally by Don Cheadle and later by the MC/actor Mos Def), serves as a sort of antagonist for Lincoln. Booth challenges Lincoln literally and figuratively; he serves as a sort of foil for Lincoln, and he will eventually cause Lincoln's downfall.
Lincoln, meanwhile, struggles existentially with his own purpose. His gig as dressing up as Abraham Lincoln pays very little—far less than what the white actors make. He wants more from life while struggling with the desire to return to the streets to hustle cards. This is what makes Lincoln the true protagonist: he has a foreseeable goal and the desire—and ability—to change. He aims to find meaning and purpose in his life while avoiding the dangerous behavior that led to his friend being shot. His relatability as well as his psychological depth make him the main protagonist of the play.
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.