Problem 2 - A Simple Auction A sellerwishesto auction a single indivisible object among H potential buyers eachofwhorn has values drawn independently from some absolutely continuous distribution F on [I]. 1] with the associated density f. let u, be buyer E's valuation. The auction mechanism used is a sealed-bid second price auction. Ties are broken by assigning the object randomly to one ofthe highest bidders. Suppose the seller's valuation is also drawn from F independently and that he also sub mits a bid. [fthe seller's bid is the highest. he simply keeps the object and his payoff is equal to his valuation. [f not. the highest bidder pays the second highest bid. and the seller's pay- off is the payment received from the winner. We thus have a sealed second-price auction with [H + 1} bidders. la) Conrm that it is still a weakly dominant strategy for buyers to subrrlit their own val uations. regardless ofthe seller's valuation and bid. Eb) let 1'] be the highest valuation among n buyers and Y2 be the second highest. Show that Pro; b. You will nd it useful to dene the distribution function of the second highest valuation conditional on Y; :> b. which is given by G[x] = Prib