Can I run the game Civilization on mid-2011 MacBook Air?
I have the same generation MBA.  You don't specify 11 or 13 inch, and that makes a potential considerable CPU difference, but on my 11" 1.6Ghz 4Gb RAM Air I have played Civilization V just fine.  Slows down a little as the game progresses, but looks good and plays perfectly acceptably to me.