If you want to add some dimension of game play to your class, you might introduce the idea of levels. Student who complete tasks "Level Up" to a different rank. With each rank, students would earn new tools and new powers (Right). Here are some ideas worth considering:
Leader-board: It is my understanding that you can't post grades, but if the levels are built around what tasks are turned in, then it might be okay to post that. In college, my three roommates and I completed in a challenge of "Who could skip class the least often?" one semester. We kept a tally of who missed the most classes on the door. Our attendance dramatically improved that semester, just by adding a small level of competition to the matter.
Possible Rewards (Depending on School Policy):
When a student attains Level [X] she can wear a hat in class or eat something in class. (Some sort of new freedom granted to them).
When a student attains Level [Y] she can turn in an assignment late for full credit (But she gets knocked down a level so that she can't do this with every assignment).
When a student attains Level [Z] she can redo an assignment for full credit.
Just a thought