The MP aspect is Civ5 is EXTREMELY poorly designed. In all likelihood there are a lot of games running in the background, and no we can't see them because the MP design is complete crap, but no one can see or join a game in progress so they effectively don't exist unless you were in the lobby at the time the game launched. This is especially bad when you're in a game and the game crashes (which happens ALL THE TIME) so that you can't rejoin the game unless everyone leaves and you relaunch from a save. Hell, you can't even see the ping of other players so you don't know who has good or bad ping and thus the game becomes even more likely to lag or crash.
There is just so much which is standard and accepted practice in MP games which Civ5 doesn't live up too that Civ5's MP becomes a complete joke. It's very clear they rushed this game just to get it out before Xmas and said "Well, good enough!" thinking they'd just charge up more for expansion packs to fix the stuff they didn't bother to do correctly. There are so many problems that I honestly believe Civ5 is right down there with Civ3 as the worst Civ game of the series (and, yes, I've been playing since Civ1). It just seems that the odd numbered games (3, 5) come up with new ideas that get poorly implemented or which are broken and then the even numbered games (2, 4) fix those ideas and improve upon them resulting in really great games. Sadly, Civ5 is destined to be a test case rather then a really good game.