(8th edition) (the pearson series in economics) robert pindyck, daniel rubinfeld microecon 544
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CHAPTER 13 • Game Theory and Competitive Strategy 519
formats generate nearly identical outcomes. (The outcomes should differ in theory only by a dollar or two.) To illustrate, suppose that there are three bidders
whose valuations are $50, $40, and $30, respectively, and furthermore the auctioneer and the bidders have complete information about these valuations. In
an English auction, if your valuation was $50 you would offer a winning bid of
$40.01 in order to win the bidding from the individual whose reservation price
was $40.00. You would make the identical bid in a sealed-bid auction.
Even in a world of incomplete information, we would expect similar
results. Indeed, you know that as a seller, you should be indifferent between
an oral English auction and a second-price sealed-bid auction, because bidders in each case have private values. Suppose that you plan to sell an item
using a sealed-bid auction. Which should you choose, a first-price or a secondprice auction? You might think that the first-price auction is better because the
payment is given by the highest rather than the second-highest bid. Bidders,
however, are aware of this reasoning and will alter their bidding strategies
accordingly: They will bid less in anticipation of paying the winning bid if
they are successful.
The second-price sealed-bid auction generates revenue equal to the secondhighest reservation price. However, the revenue implications of a first-price
sealed-bid auction for the seller are more complicated because the optimal strategy of bidders is more complex. The best strategy is to choose a bid that you
believe will be equal to or slightly above the reservation price of the individual
with the second-highest reservation price.21 Why? Because the winner must pay
his or her bid, and it is never worth paying more than the second-highest reservation price. Thus, we see that the first-price and second-price sealed-bid auctions generate the same expected revenue.
Common-Value Auctions
Suppose that you and four other people participate in an oral auction to purchase a large jar of pennies, which will go to the winning bidder at a price equal
to the highest bid. Each bidder can examine the jar but cannot open it and count
the pennies. Once you have estimated the number of pennies in the jar, what is
your optimal bidding strategy? This is a classic common-value auction, because
the jar of pennies has the same value for all bidders. The problem for you and
other bidders is the fact that the value is unknown.
You might be tempted to do what many novices would do in this situation—
bid up to your own estimate of the number of pennies in the jar, and no higher.
This, however, is not the best way to bid. Remember that neither you nor the
other bidders knows the number of pennies for certain. All of you have independently made estimates of the number, and those estimates are subject to
error—some will be too high and some too low. Who, then, will be the winning
bidder? If each bidder bids up to his or her estimate, the winning bidder is likely to
be the person with the largest positive error—i.e., the person with the largest overestimate of the number of pennies.
THE WINNER’S CURSE To appreciate this possibility, suppose that there are
actually 620 pennies in the jar. Let’s say the bidders’ estimates are 540, 590,
615, 650, and 690. Finally, suppose that you are the bidder whose estimate is
21
To be more exact, the best strategy is to choose a bid that you believe will be equal to or slightly
above the second-highest expected reservation price conditional on your value being the highest.
