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empirical evidence suggests that this uniform price procedure (analogous to

a second-price auction) has slightly lowered the government’s overall bor-

rowing costs.^18

Competitive Procurement

Thus far, we have presented an analysis of bidding strategy in the case of auc-

tions for the sale of goods or services. Exactly analogous results apply in the case

of competitive procurements—that is, when a number of firms submit bids to

supply a good or service and the lowest bid is selected to fulfill the contract.

Here each supplier seeks to maximize its expected bidding profit given by

where c denotes the firm’s cost. Other things being equal, a higher bid implies

a greater profit from the contract but a lower probability of being the winning

(i.e., lowest) bid. Taking this trade-off into account, the firm’s optimal bid

involves marking upits bid price above cost. Increasing the number of com-

petitors causes the firm to set a lower markup in its optimal bid.^19 In addition,

winner’s curse considerations will lead bidders to increase their bids when there

is a common, unknown element to the firms’ costs.

However, there is an important difference in the contractual terms used in

sale auctions and in a large number of procurements. Auctions almost always

involve a sale at a fixedprice. By contrast, many competitive procurements rely

on contingent contracts as an efficient response to the presence of risk and

uncertainty. At the time of contract signing, the ultimate quality, cost, and time

of delivery of the good or service all may be subject to considerable risk. Thus,

it is common for the procurement contract to permit risk sharing between the

buyer and winning contractor.

Incentive contracts are used widely in high-risk procurement environments

(defense programs, research and development, and so on). Under such a con-

tract, the supplier’s profit is given by

Tb(cTc),

E()(bc)Pr(b wins),

(^18) For an overview of the experimental evidence on bidding behavior, see W. Samuelson, “Auctions in
Theory and Practice,” Chapter 10 in K. Chatterjee and W. Samuelson (Eds.), Game Theory and Business
Applications(Boston: Kluwer Academic Publishers, 2001); and J. H. Kagel and D. Levin, Common Value
Auctions and the Winner’s Curse, Chapter 1 (Princeton, NJ: Princeton University Press, 2002).
(^19) In equilibrium, a risk-neutral firm sets its bid at the expected value of the next lowest competing
cost, conditional on this cost being greater than the firm’s own cost. For instance, if each firm’s cost
is distributed uniformly between L and U, firm 1’s equilibrium bid is bi[(n 1)/n]ciU/n.
Note that biis a weighted average of ciand U and that biapproaches cias the total number of bid-
ders increases.
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