518 PART • Market Structure and Competitive Strategy • common-value auction Auction in which the item has the same value to all bidders, but bidders not know that value precisely and their estimates of it vary In common-value auctions, the item to be auctioned has approximately the same value to all bidders Bidders, however, not know precisely what that value is—they can only estimate it, and bidders’ estimates will vary For example, in an auction of an offshore oil reserve, the value of the reserve is the price of oil minus the extraction cost, times the amount of oil in the reserve As a result, the value should be about the same for all bidders However, bidders will not know the amount of oil or the extraction cost—they can only estimate these numbers Because their estimates will differ, they might bid very different amounts to get the reserve In reality, auctions can have both private-value and common-value elements In the oil reserve auction, for example, there may be some private-value elements because different oil reserves may entail different extraction costs However, to simplify matters we will separate the two We begin our discussion with private-value auctions and then move on to common-value auctions Private-Value Auctions In private-value auctions, bidders have different reservation prices for the offered item We might suppose, for example, that in an auction for a signed Barry Bonds baseball, individuals’ reservation prices range from $1 (someone who doesn’t like baseball but is bidding just for fun) to $600 (a San Francisco Giants fan) Of course, if you are bidding for the baseball, you don’t know how many people will bid against you or what their bids will be Whatever the auction format, each bidder must choose his or her bidding strategy For an open English auction, this strategy is a choice of a price at which to stop bidding For a Dutch auction, the strategy is the price at which the individual expects to make his or her only bid For a sealed-bid auction, the strategy is the choice of bid to place in a sealed envelope What are the payoffs in this bidding game? The payoff for winning is the difference between the winner’s reservation price and the price paid; the payoff for losing is zero Given these payoffs, let’s examine bidding strategies and outcomes for different auction formats We will begin by showing that English oral auctions and second-price sealed-bid auctions generate nearly identical outcomes Let’s begin with the second-price sealed-bid auction In this auction, bidding truthfully is a dominant strategy—there is no advantage to bidding below your reservation price Why? Because the price you pay is based on the valuation of the second highest bidder, not on your own valuation Suppose that your reservation price is $100 If you bid below your reservation price—say, $80—you risk losing to the secondhighest bidder, who bids $85, when winning (at, say, $87) would have given you a positive payoff If you bid above your reservation price—say $105—you risk winning but receiving a negative payoff Similarly, in an English auction the dominant strategy is to continue bidding until the second person is unwilling to make a bid Then the winning bid will be approximately equal to the reservation price of the second person In any case, you should stop bidding when the bidding reaches your reservation price Why? Because if you stop bidding at a point below your reservation price, you risk losing a positive payoff; if you continue beyond your reservation price, you will be guaranteed a negative payoff How high will the bidding go? It will continue until the winning bid is approximately equal to the reservation price of the second-highest bidder Likewise, in the sealed-bid auction the winning bid will equal the reservation price of the second-highest bidder Thus, both auction