A great idea!
As suggested by Libbyowly, I personally think this would be a great idea and should be ensued by the DuoLingo team to present in the next or future updates: if you have friends on duolingo who you like to challenge then you will love this! all you have to do is go to their profile and click a button that says 'invite to challenge' and then you can pick what the challenge is, for example you could pick, first person to reach 1,000 points this week wins! and when you win you get a prize of points! (say 20-40), Thank You -Duolinguo