Strategic Analysis of Auctions

In many markets, transaction prices are determined in auctions. In the most common form, prospective buyers compete by submitting bids to a seller. Each bid is an offer to buy that states a quantity and a maximum price. The seller then allocates the available supply among those offering the highest prices exceeding the seller’s asking price. The actual price paid by a successful bidder depends on a pricing rule, usually selected by the seller: two common pricing rules are that each successful bidder pays the price bid; or they all pay the same price, usually the highest rejected bid or the lowest accepted bid. Auctions have been used for millennia, and remain the simplest and most familiar means of price determination for multilateral trading without intermediary ‘market makers’ such as brokers and specialists. Their trading procedures, which simply process bids and offers, are direct extensions of the usual forms of bilateral bargaining. Auctions also implement directly the demand submission procedures used in Walrasian models of markets. They therefore have prominent roles in the theory of exchange and in studies of the effects of economic institutions on the volume and terms of trade. Their allocative efficiency in many contexts ensures their continued prominence in economic theory. They are also favored in experimental designs investigating the predictive power of economic theories. Auctions are apt subjects for applications of game theory because they present explicit trading rules that largely fix the ‘rules of the game’. Moreover, they present substantive problems of strategic behavior of practical importance. They are particularly valuable as illustrations of games of incomplete information because bidders’ private information is the main factor affecting strategic behavior. The simpler forms of auctions induce normal-form games that are essentially ‘solved’ by applying directly the basic