People CAN be selfish and manipulative. And the only way to zap that is to call a spade a spade. Call out the behavior, not in a nasty, accusational way, but in a clear, factual way and explain that that kind of thing will never result in anything but drama and hurt.
Good relationship skills (and relationships) call for compassion and consideration. Competition as you noted is the antithesis of this. But you have to own that philosophy - not just mouth it. Takes practice.