The Advantages of Auctions 673sell its division at the highest possible price. The division is worth $40 mil-
lion under the company’s own management. The investment banker is hope-
ful that it can find as many as four to six potential buyers for the division.
The banker believes the range of buyer values to be between $40 million
and $64 million with all values in the range equally likely. In addition, the
banker believes that buyers’ values are independent of one another. Thus,
if one buyer is willing to pay $44 million, the next buyer’s independent value
might be $55 million (or any other equally likely value in the $40–$64 mil-
lion range).
What price could the firm expect to obtain in negotiations with a single
buyer? There is certainly room for a mutually beneficial agreement. For
instance, if the buyer’s actual value were $52 million, a negotiated price of
$46 million (halfway between the parties’ values) would generate a profit of $6
million for each side. If the bargainers were equally matched, one would expect
the final price to be close to this split-the-difference prediction. Moreover, since
$52 million is the single buyer’s expected value for the transaction, one-on-one
bargaining by equally matched parties should result in a price of $46 million
on average.
The firm can obtain a much higher sale price on average by putting the
division up for competitive bid and enlisting as many potential buyers as pos-
sible. Suppose the firm solicits sealed price bids from the buyers. In placing its
bid, each buyer will assess the (independent) monetary value it places on the
division and will submit a sealed bid below this value, aiming to win the division
at a profit. As we show later in the chapter, with seven buyers, the price paid by
the highest bidder will be $58 million on average.
The firm obtains a much better price for its division by soliciting bids
from multiple competitors than from a single one-on-one negotiation. The
sources of the advantage are twofold. First, as the number of potential buy-
ers increases, it is more likely that one will hold a high value (in the upper
part of the $40–$64 million range) and make a high bid. Second, the
increase in the number of competitors forces each bidder (including the
high-value buyer) to place a bid near to its true value. This implies lower
profit for the bidder and a better price for the seller. In an auction, the bid-
der must compete against other would-be buyers, instead of against the seller
alone, as in a one-on-one negotiation. In sum, competitive bidding serves
to marshal the competition among a number of buyers to deliver the best
price to the seller.CHECK
STATION 1In attempting to sell an item, firm S has approached buyer A, whose last best price offer
is $24. It now plans to approach firm B but is uncertain of the price it might get. Its best
assessment is that B’s final price offer lies in the range $20 to $28, with all (continuous)
values in between equally likely. Show that firm S can improve its payoff (to $25 on aver-
age) by selling to the firm offering the better price.c16AuctionsandCompetitiveBidding.qxd 9/26/11 1:09 PM Page 673