Ken Levine has revealed that Bioshock Infinite will not feature a multiplayer component. Previously, Levine had talked of experimenting with online models for the game, though he was speaking in 2010 at the time. Further speculation about multiplayer was fueled in May when Irrational posted a position for a network programmer on their jobs page. However, as you can read below, this has been roundly refuted by Ken Levine.
Responding to questions on Twitter, Levine was asked:
People were quick to spot that Levine's answer was ambiguous, and could have been saying "nope" he can't clear up whether Bioshock Infinite would feature multiplayer. It is after all common for studios to not discuss whole swathes of a game prior to release.
Though a later tweet cleared up any ambiguity:
As I said up top, back in May Eurogamer reported that Irrational games were hiring a network programmer, saying "if BioShock Infinite was to ship without multiplayer the successful applicant would likely have a very boring time of it." Which does beg the question, what did that applicant get hired for? Maybe they experimented briefly with multiplayer, or there's another project at Irrational that's multiplayer focused and in the early stages of development.
Bioshock Infinite is currently on track for release in February.