A key point is the significant element of interdependenceamong bidding
strategies. As we saw earlier, one firm’s optimal bid depends on the number of
competitors and how those competitors are expected to bid. For instance,
higher bids from competitors may call for higher bids from the firm itself.
Recall that in Chapters 9 and 10 we introduced the concept of equilibrium
strategies in the context of oligopoly competitive interdependence.
Equilibrium analysis is equally applicable to sealed competitive bidding. Firms’
strategies constitute an equilibrium if each firm is profit maximizing against
the behavior of the others—that is, if there is no opportunity for any firm to
make a profitable unilateral deviation from its current bidding strategy.
The simplest example of equilibrium bidding occurs when buyers com-
pete for a good with a known,common value. For example, suppose all bid-
ders have the same reservation price for the office building, say, $348
thousand (and all recognize this as the common value). The unique equilibrium
has each bidder submitting a sealed bid exactly equal to this common value,so this
value becomes the final price. The seller obtains full value for the item. Any
set of bids with the high bid below $348 thousand is not in equilibrium
because any one of the losing bidders can increase its profit by slightly topping
the current high bid.^9 Profit-increasing deviations are exhausted when bids
match the item’s full value.
With this simple observation in hand, let’s examine equilibrium bidding
in the case of differing private values. Again, there are n bidders, with bidder
i holding value viand placing sealed bid bi. Buyer values are drawn inde-
pendently from a commondistribution; that is, each buyer’s value comes from
the common, cumulative probability distribution F(v). To illustrate, consider
the office building example and assume for the moment that there are only
twobidders. Suppose each buyer’s value is uniformly distributedbetween $300
thousand to $360 thousand. (This means that all values in this range are pos-
sible and equally likely.) Furthermore, bidder values are independentof one
another. Knowing its own value, but not knowing its opponent’s, how should
each buyer determine its optimal bid? The answer is provided by the equilib-
rium bidding strategywhere values and bids are measured in thousands of dollars. Using this strategy,
a buyer with value $300 thousand bids $300 thousand; with value $340 thousand
it bids $320 thousand; and with value $360 thousand (the maximum value) it
submits a maximum bid of $330 thousand. In short, the buyer bids a price mid-
way between its true value and the lowest possible value (here, $300 thousand).bi(.5)(300).5vi,682 Chapter 16 Auctions and Competitive Bidding(^9) In the real world, prices below full value would be temporary at best. In repeated auctions, losing
bidders would certainly raise their bids, seeking to claim any positive profit. These upward bid
adjustments cease when there is no longer any bid profit available, that is, when all buyers are bid-
ding full value.
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