The game I had the most fun with as a kid with my friends was for one guy to fly his plane about 10 feet away from you and to try to "tag" it with your plane. Maybe it could be fun if you each have to use a slower flying target plane, and use your predator plane when it's your turn to tag. I didn't have the Sharky back then but I think it would really rock at this game.

If you're playing this game be especially careful about streets, sidewalks, etc. Watch where you're going if chasing the planes.

And, be careful not to hit the other guy with your plane. It's usually best to orient your game so the predator plane isn't aimed wery nearly toward the target thrower. If someone is flying a Sharky or Dart you may want to use protective eyewear.

Then there are distance and duration contests. I don't have much information on those right now but it's something of interest.

There's probably a multitude of paper airplane games.

There are a couple of old favorite games using pencil and paper which perhaps I'll describe later, though they're not paper airplanes. One of them is 4-dimensional tic tac toe (an abstraction in our 3-d space).