I feel as if a lot of people from my school take the grappling class as a competition, as you say. It is split up into about 45 minutes of instruction, and another 45 minutes of free rolling (optional). What bothers me is that some people just go through the motions of instruction and when it comes to open mat, they just go nuts trying to submit people, disregarding whatever it was their instructor just taught them. When I am rolling with a partner, I do my best to help him along and I expect the same from him. For example, we begin and I immediately get a slick takedown and take side control. If I keep that position and just hold him down OR just put him in an americana, he'll learn nothing except "don't roll with that dude". Instead, I'll do my best to maintain my posistion, but if he has too much trouble, I'll either ease up or say "bridge and slide your knee past me, take half guard; good job!". I feel that open mat is a great time to work on your skills, maybe show off a little, but, a) be smart, don't hurt anybody, and b) make sure everyone is learning something useful, taking something away from class. You're not there to tap everybody; you're there to work as a team and build each other up.