William S. Vickrey

Entry for William Vickrey, prepared for the Dictionary of Scientific BiographyVickrey's Contributions, Vickrey Auction, Public Economics, Asymmetric Information

Does a Seller Really Want Another Bidder?

Several papers compare auctioning heterogeneous assets sequentially with sequentially selling the right to choose among assets not yet taken. Typically motivated by auctions of condos for owner occupation, these papers have assumed that each winning bidder exits, so each successive auction has less competition. In many heterogeneous-asset-sale situations, a winning bidder may still be interested in acquiring further assets. We build a simple model of persistent competition, in which the distribution of equilibrium revenue from separate sales is shown to be a mean-preserving spread of the distribution of revenue from selling rights to choose. Persistent competition reveals that a high bidder does not always select his most preferred asset, and that one asset being slightly more likely to be a favored asset discontinuously affects equilibrium bidding.auction theory; rights-to-choose auctions; revenue comparisons; persistent competition; private information

Rational Participation Revolutionizes Auction Theory

Potential bidders respond to a seller's choice of auction mechanism for a common-value or affiliated-values asset by endogenous decisions whether to incur a participation cost (and observe a private signal), or forego competing. Privately informed participants decide whether to incur a bid-preparation cost and pay an entry fee, or cease competing. Auction rules and information flows are quite general; participation decisions may be simultaneous or sequential. The resulting revenue identity for any auction mechanism implies that optimal auctions are allocatively efficient; a nontrivial reserve price is revenue-inferior for any common-value auction. Optimal auctions are otherwise contentless: any auction that sells without reserve becomes optimal by adjusting any one of the continuous, spanning parameters, e.g., the entry fee. Seller.s surplus-extracting tools are now substitutes, not complements. Many econometric studies of auction markets are seen to be flawed in their identification of the number of bidders.Optimal Auctions, Endegenous Bidder Participation, Affiliated-Values, Common-Value Auctions, Surplus-Extracting Devices

Endogenous Competition Alters the Structure of Optimal Auctions

Potential bidders respond to a sellerfs choice of auction mechanism for a common-value or affiliated-values asset by endogenous decisions whether to incur an information-acquisition cost (and observe a private estimate), or forgo competing. Privately informed participants decide whether to incur a bid-preparation cost and pay an entry fee, or cease competing. Auction rules and information flows are quite general; participation decisions may be simultaneous or sequential. The resulting revenue identity for any auction mechanism implies that optimal auctions are allocatively efficient; a nontrivial reserve price is revenue-inferior. Optimal auctions are otherwise contentless: any auction that sells without reserve becomes optimal by adjusting any one of the continuous, spanning parameters, e.g., the entry fee. Sellerfs surplus-extracting tools are now substitutes, not complements. Many econometric studies of auction markets are seen to be flawed in their identification of the number of bidders.

William S. Vickrey

Entry for William Vickrey, prepared for the Dictionary of Scientific Biography

Does a Seller Really Want Another Bidder?

Jeremy I. Bulow and Paul D. Klemperer (AER, 1996) argue that the usual concerns of auction design miss the big picture, and show that a simple English auction without a reserve price and N + 1 bidders attains expected revenue in excess of any auction with N bidders. The issue of how this additional bidder might be attracted is not treated in their model. In fact, that an auction can convince another bidder it is worth his while to compete carries a critical message about expected revenue. In those many markets where potential bidders decide whether to compete in an auction based on the expected probability of bidding, Bulow and Klemperer's conclusion is shown here to be overturned. I explore the symmetric equilibrium of a model where potential bidders first decide whether to participate in an auction, and then participants select bidding strategies. Expected revenue is increased by some degree of bidder discouragement, in that it is never optimal to have all N potential bidders participate with probability one, even for very small N

Information Aggregation in Auctions with an Unknown Number of Bidders

Information aggregation, a key concern for uniform-price, common-value auctions with many bidders, has been characterized in models where bidders know exactly how many rivals they face. A model allowing for uncertainty over the number of bidders is essential for capturing a critical condition for information to aggregate: as the numbers of winning and losing bidders grow large, information aggregates if and only if uncertainty about the fraction of winning bidders vanishes. It is possible for the seller to impart this information by precommitting to a specified fraction of winning bidders, via a proportional selling policy. Intuitively, this makes the proportion of winners known, and thus provides all the information that bidders need to make winners curse corrections.information aggregation, common-value auctions, uncertain level of competition