I tend to describe Dartmouth students (from my own personal experience there) as very competitive, but internally competitive – that is to say they compete with themselves, not amongst themselves. It’s a highly motivated bunch but they are driven to succeed without comparing themselves to everyone else and, most importantly, without trying to beat the person next to them. I consistently had other students help me on homework and explain concepts after class during their own free time to help me do better, and me to them as well. There was never an air of “I’m number 1, you’re number 2 so I can’t help you because class rank is all that matters”
That’s one reason why I loved it. Everyone was always willing to help out and collaborate, not compete.