The big cage fight in this play is between Drummond and Brady, it seems. But really, the battle is between two intellectual giants—even if Brady wants to call himself an underdog and identify with David rather than Goliath.
Brady welcomes the arrival of his ex-friend, now-rival, Drummond, saying that "if the enemy sends its Goliath into battle, it magnifies our cause" (I, I, 628-29). However, the description of Brady falling in the final act of the play shows that he is actually Goliath, brought down by a little stone:
(There seems to be some violent, volcanic upheaval within him. His lower lip quivers, his eyes stare. Very slowly, he seems to be leaning toward the audience. Then, like a figure in a waxworks, toppling from its pedestal, he falls stiffly, face forward.) (III, 429-33)
The harder they fall, right?
The fact that this Battle Royale is compared to David and Goliath's fight gives the viewer a little hint as to what's to come. Anyone who's read their Bible stories knows that the little guy ends up winning. And while Brady tries to make himself out to be David to Drummond's Goliath, his eating abilities and physical presence let us know that he's a lot more of a giant than an underdog.