Microsoft has came out to say if you want the full experience of Halo 4 you might want to clear up a lot of space on your Hard Drives. To install the game you need 8 gigs of space. The full experience of the game you can play off the disc no problems, but if you want to be butter smooth and no lag in loading times and experience all the good stuff Halo 4 has to offer then you probably want to install. In halo 4 the mutiplayer is required for install along side for the Co-Op campaigns, and War Games. No exact details on how much exactly to be installed but it has been confirmed at least around 8 gigs of space.

-Anthony Beanes
sources: http://www.gameinformer.com/b/news/archive/2012/07/03/halo-4-requires-8gb-install-for-full-multiplayer.aspx