Relatively early in the game, Booker Dewitt escorts Elizabeth Comstock through Battleship Bay. While crossing over the boardwalk, Elizabeth is confronted by the Lutece twins, who present her with two different broaches, one featuring a cage and one featuring a bird. After you've played through this Xbox 360 game at least once you'll find yourself scratching your head as to the meaning of selecting either the bird or cage necklace in Bioshock Infinite.
Ultimately, Elizabeth turns around and forces you, as Booker, to make the ultimate choice. She notes that the cage is somber but there's also something very special about the bird.
Parallels in the Story
Let's quickly examine some of the other places in the game that cage and bird imagery appears before wrapping up with the ultimate significance.
The first image that jumps to mind is Songbird, Elizabeth Comstock's bio-mechanical guardian and captor. Songbird is tasked with defending Columbia from internal and external threats - such as the Vox Populi - as well as with retaining Elizabeth within her mechanical tower where the Siphon restrains her powers of cross-dimensional travel.
However, though Songbird can fly, he is clearly bound by some overt bio-mechanical programming that forces him to perform these duties. Likewise, he can be given commands using Elizabeth's whistler device, which becomes crucial during the final battle aboard the Command Deck of the Hand of the Prophet Gunship.
The bird is therefore tasked with retaining one in a cage and also himself caged by his programming.
The drab scene of Booker Dewitt's detective's office in New York is a constant destination throughout the progression of the story. The littered bottles and gray appearance of the bleak two room office recommend some of the strongest cage imagery throughout the story.
I feel it's reasonable to equate Booker's existence as a private detective living out of that office, avoiding his past and some terrible and undefined debt, as being a clear reference to a cage.
Ultimate Meaning: I believe the ultimate meaning is revealed in the ending of the story - as Elizabeth leads you through the many doors of infinity and explains that you have a myriad of choices and parallel existences, that are all pointing to the same ending.
Ultimate Meaning: ***MAJOR SPOILERS**
Don't read below if you have not already completed Bioshock Infinite, or else the story will be ruined for you!
Given the big reveal that Booker is actually both Booker DeWitt and Zachary Comstock - depending upon which path or dimension or alernate reality he chose, I believe the choice between the cage and the bird is a strong reference to the two major life paths of Booker/Zachary that are presented by the story.
The cage is the symbol of Booker DeWitt, the troubled man with a violent past who is trapped within his regretful life as a detective in New York, and the bird is the symbol of the reborn prophet Zachary Comstock who accepted the baptism and launched a life and a city in the clouds.
The main point of being able to choose either Necklace at the boardwalk with Elizabeth is the same message she continues to echo throughout the final chapter - regardless of which choice you make, both roads are leading to the same place.
Bioshock Infinite for Xbox360 is a haunting work of art but its true punch manifests itself in the few days after you finish playing through this bewildering and beautiful game for the first time. What could I have done differently? Could making a different choice as far back as in Battleship Bay have dramatically altered the course of my playthrough later on?
Could I have missed certain elements of the game because I chose to walk a given path instead of another? Should I have shot Captain Slate or allowed him to live? Should I have attacked innocent citizens of the floating sky city Colombia along the way, or ensured that all non-combatants survived contact with me unharmed?
Inifinite Games has put a tremendous amount of work into this Xbox 360 game to ensure that players directly encounter the tantalizing possibilities, curiosities and mind-bending complexities of the concept of parallel universes and alternate life paths.