Chapter 8 Strategic analysis of auctions This chapter describes several forms of auctions presents the formulations used in the main models reviews some of the general results and empirical findings and indicates a few applications. 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. 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 equilibrium concepts of noncooperative game theory such as the Nash equilibrium without recourse to criteria for selecting among multiple equilibria. The common knowledge assumption on which game theory relies is often tenable or innocuous applied to an auction.