ECON 448 Problem Set 1

Recall that in class we showed that truthful bidding is weakly dominant inthe Japanese Button English Auction (see chapter 1.5 in Steiglitz book) but thatwhen jump bidding is allowed that is no longer true.Now consider an ascending-price English auction with …xed increment $1 startingat $10. At each price level, you can either sit on your hands or bid the next pricelevel (which is old price +$1). More precisely, we assume that at each price levelthe auctioneer asks for the next highest price at which point each bidder eithermakes a bid or not and that action happens simulaneously amongst all players andthe actions of all players are visible to all players.If no bidder makes the next highest bid, the good is sold to the person who madethe last bid. We allow for more than one bidder to make the last bid. If that isthe case, we determine the winner from those bidders through randomization witheach bidder having equal probability to win. In any case, the winner pays his lastbid. If no bid is made at $10, the auction stops with nobody winning the good.Summarizing, each player (bidder) is asked to take action at each announcementof the auctioneer. The possible actions are to make a bid or not.Let’s assume the private value assumption holds and that each private value isa …nite integer $10 or bigger. The higher the surplus of a player (which we de…nedas (private value-price paid) if the auction is won, and 0 otherwise), the better fora player.De…ne truthful bidding of a bidder as making a bid if and only if the currentprice level is strictly smaller than his private value.a) Assume there are two bidders. Write down the part of the extensive form ofthe game that corresponds to price levels $10 and $11.b) Is truthful bidding a weakly dominant strategy? As in the jump biddingexample in class, we allow for crazy bidders. 1