Competitive exchange process in which each trader from one market side submits a bid, the most favorable one of which is selected by the complementary market side for the transaction. Most commonly, the bidders form the potential buyers of a commodity, and the bid-taker is a monopolistic seller. Also common is the converse constellation, where a monopsonic buyer elicits price offers from competing sellers ( procurement auction). In a narrow sense, auctions form a variety of familiar and less familiar selling and buying mechanisms for goods reaching from objects of art and collectibles to natural resources like minerals and agricultural products, to treasury bonds, construction and supply contracts, oil drilling rights and broadcasting licenses. Also take-over battles for firms or conglomerates are an explicit auction.

In a broader sense, auctions provide an explicit description of price formation processes that arise from strategic interaction in markets. More general auction mechanisms with competition on both market sides, so-called double auctions, form exchange institutions that map competing price bids (buying demands) and price asks (selling offers) into an allocation of the goods among the traders. Given the vector of bids and asks (and some matching rule), the terms of trade for various quantities of one or several goods are endogenously determined. A prototypical example for double auctions are institutionalized markets of financial assets and financial derivatives.

Auctions are models of 'thin markets', making precise the sense in which markets 'find prices' that can 'reveal' an underlying economic value. This is shown distinctively by the fact they are the unique exchange mechanism adopted whenever competitive market prices do not exist but the object sold is of particular uniqueness and size, such as in privatizations of government enterprises, in the the sale of complex procurement contracts, or seldom goods of arts; or when the resource in question does not have a price other than the terms of trade which are revealed through strategic interaction of traders, such as financial assets like stock, options, corporate or government bonds.

In a sense, strategic equilibria of competitive bidding games have many efficiency properties that generalize those of competitive market equilibrium. As it is the highest (buying) asks and the lowest (selling) offers that are selected for the transaction, the resulting allocation of commodites and quantities is efficient ex post. Under appropriate conditions, equilibrium outcomes from double auctions are even efficient in an interim sense (see efficiency). Under reasonable informational assumptions, the equilibrium bids of common value auctions (see below) converge to the competitive equilibrium price as the number of bidders grows large (see also competitive market equilibrium).

Auctions are modelled as bidding games of incomplete information. The bidders' (players') strategies are bid functions converting their private information about the objects in sale, and previous bids observed, into a money amount that is bid. Such bidding games provide unified descriptions of many competitive processes from diverse contexts. Together with the most common auction formats, we mention some examples below.

First price (sealed bid) auction: Simultaneous bidding game where the bidder that has submitted the highest bid is awarded the object and pays his own bid (which is the 'first highest' bid). The multi-object form of the first price auction is called discriminatory auction . The equilibrium bid functions of first price auctions balance the trade- off that a higher winning probability is 'bought' by a higher expected payment. As a result, the bidders' private information is revealed in the bids in shaded form only. Oligopolistic competition of price setting firms under incomplete information (Betrand competition) is an instance of a first price procurement auction.

Second price (sealed bid) auction: Simultaneous bidding game where the bidder that has submitted the highest bid is awarded the object, and he pays the highest competing bid only (which is the 'second highest' bid). In second price auctions with statictically independent private valuations, each bidder has a dominant strategy to bid exactly his valuation. The second price auction also is called Vickrey auction ; its multi-object form is the uniform price auction.

English (open bid) auction: Sequential bidding game where the standing bid wins the item unless another, higher bid is submitted. Bidders can submit bids as often as they want to, and they observe (hear) all previous bids. Often, a new bid has to increase the standing bid by some minimal amount (advance). The English auction is known to have been in use since antique times; from this auction format the word derives: the latin word augere means to increase. With stastitically independent private valuations, an English auction is equivalent in terms of payoffs to a second price sealed bid auction.

Dutch auction: Sequential biding game where the standing price is gradually lowered, typically by means of an exogenous counting device (a clock, or a pointer), until it is stopped by a bidder. The first bidder to halt the clock wins the item and pays the price where he stopped the wheel. Dutch auctions are strategically equivalent to first price sealed bid auctions. The name derives from the fact that many agricultural products worldwide, but in particular Dutch flowers, are sold in this way.

All-pay auction: Simultaneous bidding game where the bidder that has submitted the highest bid is awarded the object, and all bidders pay their own bids. A subvariant is the second price all pay auction, also war of attrition, where each bidder pays his own bid but the winner only pays the second highest bid. For example, campaign spending and political lobbying processes are second-price all pay auctions; liekwise, timing decisions on the private provision of public goods have the structure of second price all pay auctions.

Common value auction: Instead of having statstically independent information, the bidders' typically obtain private signals about an unknown common value of the resource in sale which are correlated with the underlying (unknown) common value, and correlated with one another. For example, prior to auctions of oil drilling licenses, the bidding companies obtain extensive seismic information on the likely quantity of oil hidden in the earth (or sea). In order to prepare profitable bids, the bidders then have to estimate the likely information obtained by rivalling bidders. In particular, the equilibrium bids must incoporate the fact that given a bidder wins the auction, all rivalling bids will have been lower, and thus the (unknown) common value on average will assessed to be lower than it would have been estimated without having won the auction. In this sense, winning the auction is 'bad news' that must be anticipated and incorporated into the bids, in order to avoid falling prey to a so-called winner's curse.

Reserve price: Minimal amount that has to be bid in order that the the bid-taker concedes his property rights for the object to the highest bidder. If the highest bid fails to reach at least the reserve price, the auctioneer keeps the object (abstains from a sale). Although reserve prices reduce the probability of a sale, they can improve the seller's expected returns because they force bidders with higher valuations to bid more than they otherwise would. Appropriately designed reserve prices thus are devices to extract more of the bidders' information rents (see the entry on rents).

See also: revenue equivalence

Entry by: Jan Vleugels

December 1, 1997
Direct questions and comments to: Glossary master