4. (6 points) Consider the auction model with a continuum of possible valuations. Bidder i's valuation, Vi, is drawn from the uniform distri- bution on [0,1], for i = 1,2,...,n. In other words, the cdf of Vi, can be defined as F (v) = v for v [0, 1] (and, of course, F (v) = 0 for v < 0 and F (v) = 1 for v > 1). Each bidder's valuation is independent of any other bidder's valuation. Consider the first-price auction. As I have ar- gued in class, the strategy profile in which Bi(v) = B(v) (n1)/nv for all v [0,1] and i = 1,2,...,n is a Nash equilibrium. For this problem, focus on the case n = 3. (a) Consider Bidder 1. Given Bidders 2 and 3 bid B(v) = 2v/3 for all v [0,1], show that when V1 = 3/4, the best response for bidder 1 to bid 3 2 3 1 B 4 =34=2. Hint: Express his payoff as a function of his bid, b, and show that b = 1/2 maximizes his expected payoff. (b) Suppose the seller uses a posted price p. What is her expected revenue? Which price