The episode draws it name from a term used in chess, which refers to the final stage of a game, at which point most of the pieces are removed from the board. In the endgame, strategy changes, as the pawns (the smallest pieces on the chess board) who protected the king from checkmate, become less important as the king exercises his increasing power.
Late in the episode, Carter discovers the judge she contacted is in league with HR. In response, she looks at him and says, "I'll spare you the Shakespeare quote." The quote she refers to is very likely "Et tu, Brute?" (And you, Brutus?) from Julius Caesar. In the play, Brutus, Caesar's great friend, betrays Caesar to his enemies, then participates in his murder in the Roman Senate. "Et tu, Brute" has become a common response to betrayal.
Shortly thereafter, Simmons responds with "To be or not to be, bitch." That quote, from Hamlet, begins one of Shakespeare's greatest soliloquies, about the decision Hamlet must make: to live and face the trouble he knows is coming, or to die and face the unknown, which may be even worse.
Just before she calls on Finch, Carter reminds Quinn and the others that it's a "brave new world." Her quote alludes to the 1931 novel "Brave New World" by Aldous Huxley. In the novel, set in 2540, Earth is governed under One World State, society is divided into a series of castes, social mores have changed dramatically, and reproduction is done artificially. Huxley intended the novel as a counter-point to the utopian novels of authors such as H.G. Wells, examining the negative possibilities of the world to come. Like the two quotes before it, the novel's title also is drawn from Shakespeare, where in The Tempest a young woman raised on an isolated island meets new people for the first time and proclaims, "How beauteous mankind is! O brave new world, That has such people in't." The novel also heavily quotes Shakespeare throughout the story.
This episode is the first of a three-episode arc, entitled "Endgame". The arc continues through "The Crossing" and "The Devil's Share". The advertising campaign was designed to lead viewers to believe that Detective Fusco would be killed during one of the episodes.