Think about it!
Of course this'd be hard to pull off, and may only be done on the Xbox 360/720 and the PS3/PS4, but it's not impossible.
EDIT: you guys seem to think that it has to be directly via the LIVE / PS network but what I was trying to say is that they could send the data from the game to a central server located at Bungie or Activision and work it that way. Software and hardware don't matter as they could send the same packets of player / enemy / etc positions to every console and have the game's engine translate it. Think outside the (x)box.
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It would happen directly through the LIVE and PlayStation networks. It's the nature of connectivity using them. They are both extended services of the platforms. When you produce a title on a console, licenses for doing so must be procured. It's a complicated process that requires developers to follow certain standards to match a level of quality and consistency across all titles. Microsoft is a bit touchy on this subject and does not allow cross platforming while Sony seems to be more open about it. This caused a similar game, Dust 514, to be exclusive to PlayStation 3.