It seems there won't be any kind of competitive or cooerative multiplayer included when BioShock Infinite hits stores on February 26, 2013. Irrational Games' Ken Levine confirmed as much on Twitter in response to fan queries.
The original BioShock was a single player-only affair as well, though BioShock 2 added an adversarial online mode that was good-not-great; it never really took off. It should also be mentioned here that BioShock 2 wasn't an Irrational Games production; Infinite brings the series back to the loving hands of Irrational and Levine. So "no multiplayer" isn't exactly anything new for the developer.