The magazine Science 84 announced a contest in which anyone could submit

a request for either $20 or $100. If fewer than 20% of the submissions requested $100, then everybody would receive what they requested. If 20% or more asked for $100, then everybody would get nothing. Suppose 100,000 people participate in the contest and assume that payoffs are measured in money. Assume that every possible participant submits a request for either $20 or $100. Find the Nash equilibrium(s). Careful!