(a) Suppose that the private values of two buyers in a sealed-bid first-price auction are independent and uniformly distributed over the set {0, 1, 2}. In other words, each buyer has three possible private values. The bids in the auction must be nonnegative integers. Find all the equilibria.
(b) Find all the equilibria, under the same assumptions, when the auction is a sealed-bid second-price auction.
(c) Compare the seller's expected revenue under both auction methods. What have you discovered?