Auctions in defense acquisition: theory and experimental evidence - Research

Acquisition Review Quarterly, Summer, 2002 by Bruce G. Linster, David R. Mullin

The theory of auctions has been developed and refined recently through the development of game theory and experimental economic methods. As the DoD shifts toward the use of auctions for purchasing goods and services, an understanding of these auctions becomes ever more important. This article examined some of the theory and experimental evidence with respect to auctions.

We first described the predicted bidding strategies in sealed-offer and reverse auctions. Although the expected results are the same for risk-neutral participants in both auctions, we pointed out that lower offer prices would obtain in the sealed offer auctions with risk-averse suppliers. The experimental evidence suggests, however, that the two auctions will not yield the same offer prices, and suppliers in a sealed-offer auction will tend to offer lower prices more than predicted. This result is fully consistent with risk-averse behavior.

We also explored the importance of the number of bidders in an auction. Here the evidence from experimental auctions reflects the sort of behavior we predict from the theory. As the number of participants increases, the winning offer price decreases. When uncertainty over the number of participants is present, behavior consistent with risk-averse participants is once again apparent.

Although buying goods and services through auctions is relatively new to DoD, auctions have been studied in other contexts since game theory was introduced as an economic tool, and the use of laboratory experiments has become popular. Achieving efficiency or low price goals will be more likely in DoD auctions if we look to the economic literature for some insight.

APPENDIX A

Suppose the government is buying a good through an auction in which potential suppliers submit a sealed offer for a price at which they will provide the good. We will assume initially that there are only two risk-neutral suppliers with different costs, which we assume to be independently and identically distributed according to a uniform distribution with support [0,1]. Strategies in this auction will be offer price functions that yield an offer price as a function of the supplier's actual cost.

It is not difficult to show that an equilibrium offer price function, or relationship between the supplier's cost and his offer price, in the auction described above is p(c) = 1 c/2, where c is the cost to the supplier and p(c) is the price paid by the government. To see this, consider a supplier's expected profit maximization problem. We will contemplate only affine (straight line) offer price functions; that is, we are thinking about offer price functions of the form p(c)= [alpha] [beta]c with [alpha], [beta] [greater than or equal to]0. Notice that this function is strictly increasing in cost. If suppliers employ this offer price function and costs are uniformly distributed on [0,1], then the probability the supplier has a cost higher than c is just 1 - c. Also, the increasing offer price function ensures that the seller with the lower cost will make the lower offer and win the auction. Therefore, the probability a seller with a cost c has the lower cost is 1 - c = 1 - p - [alpha]/[beta]. The profit a supplier gets if he wins the auction is 1/n 1. Hence, each supplier solves the following program and maximizes his expected profit: [max.sub.p] (1 - /p - [alpha]/[beta])(p - c).