I've never seen an open source AAA game, perhaps it's impossible go get enough money to pay the developers and designers of a AAA game with an open source project.
The social benefit is that some members of the society can get fun from a AAA game if they want.
There's a few.
ID software[0] open source their games, but require the assets to actually build and run the game (which you obtain by buying the game).
Epic [1] have open sourced Unreal Tournament (note I'm not sure on the licensing, just that the code is available).
Natural Selection [2] source code was released
Star wars Jedi Knight [3] had the source released.
Note that all the AAA games that I'm aware of that have been open sourced are older games, I don't know of any in development AAA games that are open source.
ID, at least while Carmack was there, was very very good about releasing their last-gen engine tech once all licensees had published their games. A whole lot of people learned about how to do game development from those things.
Unknown Worlds only released the source code for the NS1 mod for Half-Life--and as Valve has yet to release the Gold Src source code, that's of questionable utility.
The social benefit is that some members of the society can get fun from a AAA game if they want.