Competition and kids is sometimes a tricky one. 'Challenge day', replaces sports day and everyone's a winner at birthday parties (to non parents, you would be surprised at the politics of pass the parcel!).
Two player games can be incredibly collaborative, e.g. toca boca shopper, or competitive e.g. Tiny wings on split screen. In the classroom competition can be great e.g. question races, prises for best sketch/ presentation/ rap, etc. Touch screens have the capacity to be two player but is it bringing anything to the party??
When dealing with the more complex knowledge of exam based subject how to avoid making a child feel inferior but still ramp up the engagement? Building on the knowledge of others? writing questions for each other? One to think about.