Q4 A Second-Price Auction with Encouragement An auctioneer is selling a car by a sealedbid auction. There are two [N = 2] bidders. The valuations that the two bidders place on the car are private information and these valuations are independently drawn from the uniform distribution on the interval [2000, 3000] dollars. To encourage bidders to place bids, the auctioneer oers to give the losing bidder a free scooter. It is connnon knowledge that both bidders assign a value of $1000 to the scooter. The auction works as follows. Both bidders submit bids. The high bidder wins the car and pays the low bidder's bid for the car, but does not receive the scooter. The low bidder does not win the car and does not pay anything, but receives the scooter for free. (a) How should bidders bid in this auction? Determine bidding function for each bidder. Hint: In a secondprice auction, bidders bid their value of winning. Think about the true value of winning in an auction in which the loser also gets some value