The magazine Science 84 planned to announce 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. Although the magazine wound up not running the contest, because Lloyds of London was unwilling to insure against losses, we can still analyze what Nash equilibrium would predict. Suppose 100,000 people participate in the contest, and assume that payoffs are measured in money.

I) Now suppose that a request form comes only with the purchase of Science 84 and that the magazine costs $21.95. Then each person’s strategy set has 3 elements: do not buy the magazine, buy the magazine and submit a request of $20, and buy the magazine and submit a request of $100. Suppose zero value is attached to the magazine. Find a Nash equilibrium.

The answer is that the Nash Equilibrium is when no one buys the magazine. I understand that when no one buys the magazine, the pay off is 0. When someone wants to buy the magazine, the pay off will then become -1.95 (20-21.95) if less than 20% of the population bid $100. But won't the payoff also be 78.05 (100-21.95) if that person bids $100 when 20% of the overall population bids less than $100? The payoff is positive, and people would want to deviate.