Multiple Bids in a Multiple-Unit Common Value Auction

Michael B. Gordy
Board of Governors of the Federal Reserve System, Washington
MGordy@frb.gov

Abstract

In auctions of government treasury securities, each bidder is permitted to enter multiple price-quantity bids. Gordy (1996) finds empirical evidence from Portugal's treasury bill auctions that multiple bidding is used more intensively as the potential for winner's curse increases. That is, ceteris paribus, a bidder submits a larger number of bids and spreads these bids more widely, the greater is the expected number of competing bidders and the degree of uncertainty in the market. It is conjectured in that paper that multiple bids can be used to hedge against winner's curse, as well as to express downward sloping demand due to risk aversion. This paper provides theoretical support for these conjectures.

Direct generalization of Milgrom and Weber (1982) to the multiple-unit, multiple bid case appears to be technically intractable. Heretofore, the theoretical study of multiple bid auctions has followed Wilson (1979), in which each bidder is assumed to submit a continuous demand schedule. Although elegant, Wilson's model remains poorly understood. It has been solved only for a small number of special distributional assumptions, and appears to give rise to multiple equilibria. Furthermore, bidders in the real world typically submit only a small number of bids, so assuming continuity may be as unrealistic as assuming a single bid per bidder. In the Portuguese sample, for example, the median number of bids per bidder is three.

This paper takes a discrete approach. I model a simultaneous common value auction of two identical units to n bidders. Private signals of the good's value are assumed to be drawn from a finite set and bids are restricted to finite intervals. Each bidder submits two bids, and the two units are awarded to the two highest bids, whether from a single or two distinct bidders. This discrete framework makes a difficult problem numerically feasible, as the set of possible strategies is finite. Under discriminatory pricing, the model shows that the gap between a bidder's two bid prices increases with the degree of risk aversion of the bidder and decreases with the precision of public information on the value of the items.