The magazine Science 84 planned to announce a contest in which anyone could submit a request for… 1 answer below »

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 equilibrium would predict. Suppose 100,000 people might participate in the contest, and assume that payoffs are measured in money.

a. Assume that every possible participant submits a request for either $20 or $100. Find a Nash equilibrium.

b. 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 three elements: do not buy the magazine, buy the magazine and submit a request for $20, and buy the magazine and submit a request for $100. Suppose zero value is attached to the magazine. Find a Nash equilibrium.

c. Consider again the situation described in part (b), but now suppose the magazine costs $19.95. Find a Nash equilibrium.