Consider the auction model with a continuum of possible

valuations. Bidder i's valuation, Vi

, is drawn from the uniform distribution 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 argued 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