Auction Theory

Standard formats and Vickrey's insight

Auctions are an ancient way to sell goods whose price is hard to set in advance. Theory usually distinguishes four standard formats: the ascending English auction; the descending Dutch auction, in which the first bidder to accept a falling price wins; the first-price sealed-bid auction, in which the highest bidder pays their own bid; and the second-price sealed-bid auction, in which the highest bidder pays the second-highest bid. William Vickrey (1961) showed that in the second-price auction bidding one's true value is a dominant strategy: because the price paid does not depend on one's own bid, shading or inflating it can never help. The format now bears his name, and Vickrey received the Nobel Prize in 1996.

Revenue equivalence and optimal auctions

Vickrey also found that with risk-neutral bidders and independently distributed values, the four formats yield the same expected revenue. Roger Myerson (1981) and Riley and Samuelson (1981) generalized this into the revenue equivalence theorem: any mechanism that gives the object to the highest-value bidder and leaves the lowest type the same expected payoff earns the seller the same expected revenue. Myerson then characterized the revenue-maximizing optimal auction, showing that a well-chosen reserve price raises revenue; this work became central to mechanism design and contributed to his 2007 Nobel Prize. Equivalence breaks down with risk aversion, correlated values or asymmetric bidders, and those departures are where practical auction design begins.

Common values, the winner's curse and applications

When an object such as an oil lease is worth the same to everyone but each bidder holds only a noisy estimate, the auction has common values. Capen, Clapp and Campbell (1971) reported that winners of offshore oil lease auctions systematically lost money: the most optimistic estimator tends to win, so bidders who ignore this overpay, the winner's curse (Thaler, 1988; Kagel and Levin, 2002). Milgrom and Weber (1982) introduced the linkage principle, showing that with affiliated values open ascending auctions reveal information and raise revenue. This research shaped the US Federal Communications Commission's 1994 simultaneous multiple-round spectrum auctions, and the UK's 2000 3G auction raised about £22.5 billion (Binmore and Klemperer, 2002). Search ads today are sold through generalized second-price auctions (Edelman et al., 2007), and the field remains closely tied to work on adverse selection and asymmetric information.

FAQ

Why should you bid your true value in a Vickrey auction?

Because the price you pay is set by the second-highest bid, not your own, misreporting your value can never gain you anything and can only cost you.

What is the winner's curse?

In auctions for items of uncertain value, the bidder with the most optimistic estimate tends to win and therefore often pays more than the item is really worth.

Sources reviewed: 2026-10-26

References

1. Vickrey, W. (1961). Counterspeculation, auctions, and competitive sealed tenders. Journal of Finance, 16(1), 8–37.
2. Myerson, R. B. (1981). Optimal auction design. Mathematics of Operations Research, 6(1), 58–73.
3. Riley, J. G., & Samuelson, W. F. (1981). Optimal auctions. American Economic Review, 71(3), 381–392.
4. Milgrom, P. R., & Weber, R. J. (1982). A theory of auctions and competitive bidding. Econometrica, 50(5), 1089–1122.
5. Capen, E. C., Clapp, R. V., & Campbell, W. M. (1971). Competitive bidding in high-risk situations. Journal of Petroleum Technology, 23(6), 641–653.
6. Thaler, R. H. (1988). Anomalies: The winner's curse. Journal of Economic Perspectives, 2(1), 191–202.
7. Klemperer, P. (1999). Auction theory: A guide to the literature. Journal of Economic Surveys, 13(3), 227–286.
8. Krishna, V. (2010). Auction Theory (2nd ed.). San Diego: Academic Press.
9. Milgrom, P. (2004). Putting Auction Theory to Work. Cambridge: Cambridge University Press.
10. Ausubel, L. M., & Milgrom, P. (2006). The lovely but lonely Vickrey auction. In P. Cramton, Y. Shoham, & R. Steinberg (Eds.), Combinatorial Auctions (pp. 17–40). Cambridge, MA: MIT Press.
11. Edelman, B., Ostrovsky, M., & Schwarz, M. (2007). Internet advertising and the generalized second-price auction. American Economic Review, 97(1), 242–259.
12. Binmore, K., & Klemperer, P. (2002). The biggest auction ever: The sale of the British 3G telecom licences. Economic Journal, 112(478), C74–C96.
13. Kagel, J. H., & Levin, D. (2002). Common Value Auctions and the Winner's Curse. Princeton: Princeton University Press.