Asymmetric Auctions

The revenue-equivalence theorem' for auctions predicts that expected seller revenue is independent of the bidding rules, as long as equilibrium has the properties that the buyer with the highest reservation price wins and any buyer with the lowest possible reservation price has zero expected surplus. Thus, in particular, the two most common auction institutions-the open "English" auction and the sealed high-bid auction are equivalent despite their rather different strategic properties. This strong prediction of equivalence seems at odds, however, with the empirical observation that rarely is any given kind of commodity sold through more than one sort of auction. Thus, for example, art is nearly always auctioned off according to the English rules, whereas job contracts are normally awarded through sealed bids. Admittedly, in the public sector, there have been a few attempts to use both methods (lumber contracts in the Pacific Northwest) or to switch from one to the other (Treasury Bills). But changes have typically met great resistance. This is also in conflict with theory, since a corollary of the revenue equivalence theorem is that the expected surplus for any buyer is the same in the two auctions. These discrepancies suggest that the hypotheses of the revenue-equivalence theorem may be too strong. The principal assumptions are (i) risk neutrality, (ii) independence of different buyers' private signals about the item's value, (iii) lack of collusion among buyers, and (iv) symmetry of buyers' beliefs. Over the last fifteen years, a number of papers have explored the implications of relaxing these assumptions. Typically a clear-cut prediction has emerged in each of these papers in favour of either the high-bid or open auction. Thus under increasingly general assumptions, Holt (1980), Riley and Samuelson (1981), and Maskin and Riley (1984) show that, when buyers are risk averse, the high-bid auction should be favoured by a seller even if he also exhibits risk aversion.2 In turn, the assumption of independence of private signals of the item's value is relaxed by Milgrom and Weber (1982). If reservation prices are "affiliated" (technically, pair-wise positively correlated), they show that the English auction generates higher expected revenue than