In addition to the article of mine cited above (thanks!) which covers leaderboards in an online course, I would direct you toward this broader bit of theory I put together - specifically, I think you're talking about the "human interaction" game element, which can be used either cooperatively or competitively (I suspect both work, but under different circumstances and with different caveats).  It's probably a false dichotomy to say that some learners are competitively motivated and some are cooperatively motivated - it is probably dependent on the particular task and context.  Both competition and cooperation are quite human. :)

Article Developing a Theory of Gamified Learning

Not sure if it helps but recently came across this survey

http://www.sciencedirect.com/science/article/pii/S1071581914001256

Thank you all - it seems though that still "little empirical work has sought to validate gamification as a meaningful concept and provide evidence of its effectiveness as a tool for motivating and engaging users in non-entertainment contexts." (stated in the survey Goncalo mentioned: "Gamification in theory and action: A survey" by Seaborn and Fels, 2014). Especially in education/online learning contexts. I`ll keep looking!

You might also read Hamari's review of empirical gamification efforts up to 2014 as a good starting point. 

Conference Paper Does Gamification Work? — A Literature Review of Empirical S...

It looks like the first person that responded and left a bunch of citations deleted their response - one of them was the one I've attached here, which is definitely empirical.  But yes, it is quite sparse.  The Hamari paper gives a good summary of available empirical work as of 2013 or so.

Article An Empirical Test of the Theory of Gamified Learning

Maybe you can find information at:

http://tll.mit.edu/sites/default/files/library/LINC%20'13.pdf

http://www.irrodl.org/index.php/irrodl/article/view/1954/3111

http://www.computer.org/web/csdl/index/-/csdl/mags/ex/2013/03/mex2013030070.html

This might be useful: http://www.sciencedirect.com/science/article/pii/S0747563216306203

I agree with Jesse Fox

Hello my dear Gaby K. Slezák ,

Conference Paper An empirical study of gamification impact on e-Learning environment