Essays on auctions and efficiency

Auctions are among the oldest economic institutions in place—they have been used since antiquity to sell a wide variety of goods, and their basic form has remained unchanged. In this dissertation, I explore the efficiency of common auctions when values are interdependent—the value to a particular bidder may depend on information available only to others—and asymmetric. In this setting, it is well known that sealed-bid auctions do not achieve efficient allocations in general since they do not allow the information held by different bidders to be shared. Open auctions, however, do allow such sharing of information and form the subject of this thesis.; In the first essay, I present a model of the English auction. Typically, in an English auction, say of the kind used to sell art, the auctioneer sets a relatively low initial price. This price is then increased until only one bidder is willing to buy the object, and the exact manner in which this is done varies. In my model a bidder who drops out at some price can “reenter” at a higher price. This feature is realistic, but previous analyses ruled out the possibility of reentry for analytical convenience. The main result is that the English auction with reentry has an efficient equilibrium under weak conditions, a feature not shared by the standard model without reentry. The required conditions are the pairwise single-crossing property—known to be necessary for efficiency—and a new signal intensity condition. These conditions are much weaker than the conditions under which the standard English auction is efficient. Thus the modification is not only a more realistic model of the real-world auction but has superior theoretical properties.; The second essay, written jointly with my colleague, Oleksii Birulin, examines the question of when the standard English auction without reentry has an efficient equilibrium. Maskin (1992) shows that the pairwise single-crossing condition is necessary and sufficient when there are only two bidders. It is known; however, that this condition is not sufficient once there are three or more bidders. We identify a condition that is both necessary and sufficient for efficiency with a general number of bidders. This new condition, called generalized single crossing, is a multilateral version of pairwise single-crossing,; In the third essay, I examine some extensions to situations in which multiple identical objects are to be sold. I present an efficient multi-unit auction that consists of a number of sequential English auctions with reentry and show that this allocates efficiently under quite general circumstances. In each of the individual auctions all bidders compete simultaneously in the open ascending price format. The distinctive feature of the mechanism is that winners are determined first, and then additional auctions are conducted to determine prices. Total number of auctions depends only on the number of goods to be allocated and not on the number of bidders.