Mimicking Duolingo's fun and interactive system, and maybe add "invite/challange a friend" feature such as:
  1. Streak competition
Where, progress is competing in daily quest to get a streaks, (separate from the general daily streaks).
  1. Pages being read
Where, we just read as much as possible in a date range of the challange
  1. Memorization being reviewed
The financial and economy.
Make the "challange a friend" cost a <X amount> via in-app currency make it cheap to enter, and the winner gets to keep half of the X% of the loser. Or something to penalize the lower and in-game reward to the winner.
Premium users gets free access to these challenges and its opponents gets cheaper entrance cost.