Like Dusty said really not much more one can do for competition except lotteries, most post, most active etc. Winner can get a VIP membership for a month or how ever you want to make it and give them a little more access then regular members or a cool rank or something.
As for games, i wouldn't know as i don't have them or hold them at my site.
You would really need to sit down and think of a way to hold a competiton, make sure it runs the way you want it. You might also use other sources such as Facebook or something like that.
Just my thoughts..