Exercise 2.5 Suppose you want to hire a contractor to perform some task, like remodeling a house. Each contractor has a cost for perform ing the task, which a priori is known only to the contractor. Give an analog of a secondprice auction in which contractors report their costs and the auction chooses a contractor and a payment. Truthful reporting should be a dominant strategy in your auction and, assum ing truthful bids, your auction should select the contractor with the smallest cost. The payment to the winner should be at least her reported cost, and losers should be paid nothing. [Auctions of this type are called procurement or reverse auctions]