I don’t know what you think, but for me, a social game, as opposed to an anti-social one, is one that requires a significant portion of the skills that I am pouring into the game to be of social nature, e.g. friendship, empathy, and loyalty, to name a few. From that point of view, a purely competitive game, e.g. deathmatch, would be anti-social, so we’re not simply talking multi-player games here.
Whenever there is more than one person around (to a lesser degree, this includes NPCs), there is potential for some kind of social relationship. The problem is that the thing most dangerous for any such fledging social relationship is the game itself, or rather its rules. To be exact, it is the win/loss conditions, even if there aren’t any explicit ones: Perceived ones will do just fine.
There has been a lot of talk about games and social networks lately. The Xbox 360 recently got its own share of facebook, iPhone games have been bolstering sales with facebook and twitter integration and blockbuster titles such as Uncharted 2 – Among Thieves can twitter the players game progress - if the player wants to. But what about the games that are integrated into facebook? What are they? What could they be?