Mr. Beast held a contest in this video https://www.youtube.com/watch?v=0e3GPea1Tyg&t=1295s
It goes something like where around 500 people compete in a contest to earn around $500,000.
At certain points in the video Mr. Beast offers people guaranteed money to drop out of the contest.
Sometimes I get confused about how game theory is applied in cases like this.
Is it "logical" (in game theory) for someone to drop out even if they are offered 1 dollar in the first round?
Or does it only make sense to drop out if your offered something proportionate to your chances of winning like \$1,000 (in the first round) (around \$500,000 / 500 people = \$1,000)