4. Suppose there are four bidders in an auction. Each bidder's valuation i [0, 2] and is

identically distributed according to the distribution function F[] =

2

4

.

(a) Consider a first price auction. Characterize a Bayesian Nash equilibrium of this auction

in which each bidder's bid takes the form bi = si(i) = ai

. (7)

(b) Calculate the expected revenue in the first price auction. (10)

(c) Suppose the good is auctioned using the second price auction. What will be the equi-

librium bids of the three bidders? What will be the expected revenue for the seller?

2

(Note: No calculations or proofs are required for part (c). But state clearly the reasons

behind your answers.) (3)