Auction Theory with Private Values

Abstract

For many centuries, auctions have been a common form of selling procedure. Although auction methods vary across country and product, the two most frequently observed are the open, ascending bid (or English) auction and the sealed-bid auction. Recent theoretical research has led to a theory of equilibrium bidding in these two auctions and a wide range of alternatives as well. As a result it has been possible to compare the revenue extracted by the seller under different auction methods and even to characterize the revenue-maximizing auction. The Revenue Equivalence Theorem (see for example, William Vickrey, 1961, Roger Myerson, 1981, and Riley and William Samuelson, 1981) asserts that when each bidder's reservation price for a unit of an indivisible good is an independent draw from the same distribution, and bidders are risk neutral, the sealed-bid auction generates the same expected revenue as the open auction. Much recent research has involved weakening each of the main hypotheses-risk neutrality, identically distributed values, and independence of values-in turn. We shall illustrate some of the principal conclusions of this work by considering the properties of open and sealed-bid auctions in a model of two bidders whose reservation prices can assume only two values, and by comparing these auctions to the optimal or revenuemaximizing auction. I. Revenue Equivalence