http://bioshock.wikia.com/wiki/BioShock_Infinite
BioShock Infinite has players assume the role of Booker DeWitt as they are given one simple but mysterious ultimatum: “Give us the girl and wipe away the debt.” Booker, who initially seems like just a mercenary or disgraced employee, is thrust (back) into the world of Columbia — a floating, Dixie-esque dystopia in the sky invented by a dual-bodied physicist named Lutece and run by a “prophet” named Zachary Hale Comstock — in order to find a girl named Elizabeth, Comstock’s daughter. However, BioShock Infinite has its name for a reason: the game plays around with multiverse theory, and, by the game’s end, DeWitt discovers that he is both himself and Comstock (the game’s villain) simultaneously, as the world runs on a looping system in which DeWitt becomes Comstock over and over again through the deliverance of Elizabeth (also his daughter, logically). With this realization, players soon find themselves to be equally responsible for the creation of and participation in the system of Columbia.