Consider an auction with two bidders. Valuationsxxare uniformly and independently distributed for both bidders over the interval[0,1]. Bidder 1 knows that bidder 2 always follows the bidding strategyb2(x)=x^2.

Consider an auction with two bidders. Valuations x are uniformly and independently distributed for both bidders over the interval [0, 1]. Bidder 1 knows that bidder 2 always follows the bidding strategy b2 (20 ) = 202. 1. What is the best reply of bidder 1 in a second price auction? 2. What is the best reply of bidder 1 in a first price auction? 3. What is the expected payment of a bidder 1 with valuation x in this situation in a first price auction? 4. What is the ex-ante expected payment of a bidder 1 in this situation in a first price auction? 5. What is the expected payment of a bidder 1 with valuation x in this situation in a second price auction? 6. What is the ex-ante expected payment of a bidder 1 in this situation in a second price auction