We first heard about BioShock Infinite: The Siege of Columbia just a few weeks ago, and this week, Plaid Hat Games has released a PDF of the game's rulebook for your perusal. Board game geeks may want to read it from cover to cover; there is some interesting stuff in there.
One of my favorite game mechanics is cards that can be used for multiple functions. It's an idea that has been employed by Gears of War: the Board Game and Battlestar Galactica: the Board Game (also known as "the best board game ever"), and it's seen in The Siege of Columbia with cards that can be used for their combat power, voting influence, or monetary value.
Other notable game mechanics include variable short term objectives, a voting mechanic to try to influence Columbia, and multiple story paths for Elizabeth and Booker, who act as neutral characters in the battle between the Founders and the Vox Populi. If Booker and Elizabeth escape Columbia before one faction can declare a victory, then the rulebook even describes the winner as having achieved "a flawed and hollow victory." Too cool.
Expect a review of The Siege of Columbia when it releases later this year.