I sometimes watch Food Network competitions; these are invitation-only, winner-take-all deals. The winner gets $10,000, and no one else gets anything except publicity.
And yet, the competitors are generous with each other.
The first time I saw this was, I don't know, a year ago maybe, when a team made a cake that was too heavy for them to move to the judging table. Just as they were about to resign, the other three teams all moved (rather like a flock of birds -- no sense of any consultation, just everyone did the same thing at the same time) to their kitchen to help with the job.
Today they went one step further. During the competition, one of the pastry chefs passed out. Literally stepped away from her cake, reached for her water bottle, and dropped. For a few minutes, it was controlled chaos: the challenge staff called 911 and started general first aid. The other competitors stopped what they were doing, probably more out of a sense of shock than a sense of fairness, but still. The judges stopped the clock. Everyone waited until the EMTs arrived and took her away on a stretcher (the announcement was made that she was okay, but they wanted to keep her under observation for a while).
The judges asked the assistant what she wanted to do. She looked simultaneously terrified and resolute, and said that she'd do her best to finish the cake on her own. The two guys in the kitchen next to her looked at each other, nodded, and stepped up. "We'll help. We're ahead of our schedule, and we'll help."
Granted, neither of those teams won, but they were both highly praised by Kerry Vincent (who gives every impression of being a major hard-ass as a judge) for their sportsmanship.