When I first got my hands on Minecraft 17 hours evaporated before I realized I was in the grasp of the most addictive substance that could possibly be conceived with me as a personal target in mind. I've done 30 hrs of straight work-at-my-job-then-come-home-and-work-in-the-studio just because I was trying to get something done and I wouldn't stop until I was finished. I spent one spring break of straight 15 hr days in the studio with nine hrs to sleep/eat. So.... competition.... for money?.... I'd say I could probably do a week without sleep. Call it five days before the brain seriously starts to blow fuses. I'd still be up, but if I was playing anything more difficult than Minecraft on "peaceful" I probably would be failing in epic fashion.
Though, a non-stop how-long-can-you-game scenario with all the players are in one competitive game where the inevitable four-way crazy-man stalemate (everyone else has dropped out by a reasonable 72 hours in, each of these guys is still going at like, six days or whatever) would be ended by who has the highest score would be a pretty novel twist. Or like the ending conditions are that once there're fewer than 25% of the people left, and no one has dropped out for, say 24 hrs (or 12 or whatever to keep the audience interested, because 24 hrs of watching near catatonic gamers crumbling spectacularly in competence will probably get pretty boring,) then whoever remains and has the highest score wins. It would be an endurance run to begin with, but players would have to pace themselves, and pull out actual skill at the end, a "sprint for the finish" so to speak.