dec04_Article 5 12/14/04 2:27 PM Page 1102 Journal of Economic Literature Vol. XVII (December 2004) pp. 1102–1115 The Unity of Auction Theory: Milgrom’s Masterclass1 2 ERIC MASKIN 1. Introduction One explanation for this success is good timing. Many researchers started working y any standard measure, auction theory seriously on auctions in the late 1970s and has been an enormous success. Even B early 1980s,6 just when the right game-the- after 25 years of intensive work, the literature oretic methods for studying this subject— continues to grow at a prodigious, even accel- games of incomplete information (John erating rate;3 it has spawned much empirical Harsanyi 1967–68) and perfect equilibrium and experimental research;4 its tentacles (Reinhard Selten 1975)—were becoming have spread into other disciplines; 5 and auc- widely known. Of course, numerous other tion theorists have been influential in the fields, e.g., industrial organization (I.O.), design of mechanisms for the privatization of benefited from the same symbiosis of tech- public assets (such as spectrum bands) and nique and application; collectively, they for the allocation of electricity and other resulted in the game theory revolution. But goods (they have also often served as con- the study of auctions has had more staying sultants to the bidders in those mechanisms). power than many other applications of game theory. Whereas enthusiasm for theo- 1 Paul Milgrom, Putting Auction Theory to Work. retical industrial organization has cooled Cambridge, Churchill Lectures in Economics: Cambridge somewhat since the heady days of twenty University Press, 2004. NY, Melbourne, Pp. xxi, 368. ISBN years ago, research on auctions, as I have 0-521-55184-6. 2 Institute for Advanced Study and Princeton noted, continues apace. There are, I University. I thank the NSF (SES-0318103) for research believe, several reasons why auction theory support. has fared comparatively well. 3 To give just one indication: at the August 2004 joint meeting of the Econometric Society and European First, theorists of I.O. and other applied Economic Association, there were seven separate sessions fields labor under the constraint that they do on auction theory, a figure well beyond that for any other not know the games that the players they sort of theory. 4 Again, to cite only one, conference-related datum, the organizers of the 2005 Econometric Society World 6 Auction theory actually began well before then. Congress, who attempt to invite special talks on the most Indeed, the seminal contribution was William Vickrey lively and interesting developments in recent economics, (1961). But until game theory came into its own fifteen are planning a set of talks on empirical auctions work. years later, Vickrey’s work—as well as that of other early 5 So, for example, there is now a sizeable computer-sci- pioneers such as James Griesmer, Richard Levitan, and ence literature on auction theory, often focusing on com- Martin Shubik (1967), Armando Ortega Reichert (1968), putational issues. and Robert Wilson (1969)—remained largely ignored. 1102 dec04_Article 5 12/14/04 2:27 PM Page 1103 Maskin: The Unity of Auction Theory 1103 study (e.g., firms or consumers) are actually most auction theory, numbers are small playing; models are at best approximations (indeed, one implication of the papers of of reality. By contrast, auction theorists typi- footnote 8 is that, as numbers grow, most cally know the rules that their players follow reasonable sorts of auctions converge in per- precisely. If, for example, a high-bid auction formance; only in the small-numbers case do is the object of study, the theorist knows that the differences between auction forms come (i) the bidders submit nonnegative real num- into their own). bers as sealed bids; (ii) the winner is the bid- Finally, auction theory is a genuinely der submitting the highest bid; and (iii) the beautiful edifice:9 many of its major proposi- winner pays his bid (of course, there may tions deliver remarkably powerful conclu- still be uncertainty about how the buyers sions from apparently modest hypotheses. behave under these rules). This precision Despite all these attractions, auctions helps put the auction theorist’s findings on a might have disappeared from the economic relatively strong footing; it also simplifies the theory scene had they not received an job of the experimentalist or empiricist. important rejuvenating boost from the Second, auction theory appeals to econo- worldwide impulse toward privatization that mists’ “social engineering” instincts. Many began in the early 1990s. This trend was people go into economics at least in part brought on by the fall of communism in the because they want to improve the world. The East—and the consequent need to sell off mechanism-design 7 aspect of auction theo- state assets—and the disenchantment with ry—tinkering with the rules of the game in public ownership in the West. But state order to achieve a better outcome—helps bureaucracy’s loss proved to be auction the- gratify that urge. No doubt, one reason ory’s gain, as auction mechanisms, to great Vickrey’s work is so celebrated is that his public acclaim, were increasingly invoked to famous creation, the Vickrey auction, provides implement the transfer of resources. More an attractive solution to an important social recently, online auction enterprises such as problem: designing an efficient allocation eBay have provided further impetus for the mechanism. theory. Third, the basic transaction of an auc- tion—the transfer of a good from seller to 2. Milgrom’s Unified View buyer in exchange for a monetary pay- Paul Milgrom has played a starring role in ment—is fundamental to all of economics, auction theory’s success story. Not only has and so auction theory has been nourished by he been a seminal contributor to the theo- its connection with other theoretical areas. retical literature (e.g., Milgrom 1981; and For example, it has sometimes been used as Milgrom and Robert Weber 1982), but a foundation for understanding the workings 8 together with Robert Wilson, he had a major of competitive markets. Of course, there hand in designing the simultaneous ascend- are important differences: competitive theo- ing auction format used by the Federal ry usually supposes that there are large Communication Commission to sell off numbers of buyers and sellers, whereas in much of the radio spectrum in the United States. Thus, his book Putting Auction 7 Of course, auction theory is only a small part of a vast mechanism design/implementation theory literature. For Theory to Work has been eagerly awaited recent surveys of the literature from a general perspective see Thomas Palfrey (2002); Roberto Serrano (2004); and 9 Economists, being a hard-boiled lot, sometimes deny Eric Maskin and Tomas Sjöström (2002). that esthetics have anything to do with what they are up to. 8 See for example Milgrom (1981), Wolfgang But this sentiment belies the fact that the most important Pesendorfer and Jeroen Swinkels (1997); Mark economic ideas, e.g., the first welfare theorem of compet- Satterthwaite and Steven Williams (1989); and Wilson itive theory or the principle of comparative advantage, are (1977). things of real beauty. dec04_Article 5 12/14/04 2:27 PM Page 1104 1104 Journal of Economic Literature, Vol. XLII (December 2004) since his 1995 Churchill lectures, on which it But, as they sometimes depend as much on is based. judgment (albeit very well-informed judg- The wait has clearly been worth it. The ment) as logic, they occasionally contrast jar- book covers a great deal of theoretical mate- ringly with the authority and precision of the rial and does so with extraordinary economy theory. For example, in Milgrom’s opinion, (without sacrificing rigor). This economy the Vickrey auction (more precisely, its derives from Milgrom’s conception of auc- multigood generalization due to Theodore tion theory as a subspecies of demand theo- Groves 1973, and Edward Clarke 1971) is ry, in which a few key tools—the envelope “unsuitable for most applications”—a con- theorem in particular—do most of the work. clusion that is far from being a theorem and Indeed, once these tools are in place, he that I will come back to in section 7. establishes most theorems with just a few But putting such quibbles aside, I should lines of proof. As the title suggests, he also emphasize that Milgrom is completely per- discusses the extent to which the results bear suasive on the general point that auction the- on the design of real auctions. ory matters in practice. In chapter one, he Admittedly, the monograph is not the only shows that the 1990 New Zealand spectrum current volume of reflections by a leading auction’s failure to raise the revenue antici- auction expert on theory and practice.10 Nor, pated can be traced to its seriously flawed despite its unfailing clarity, is it the most design: separate simultaneous sealed-bid likely candidate for a graduate text on the auctions for each license. Specifically, he subject.11 Rather, its signal contribution is to points out why this auction form cannot lay out Milgrom’s unified view of the theory. properly accommodate substitutability or This vision is notably distinct from that of complementarity across licenses. And he other major auction scholars. For example, responds to those who argue that how gov- he must be nearly alone in deliberately ernment assets are sold off is irrelevant for avoiding the revelation principle as an auc- efficiency (because, in their view, the “mar- tion-theoretic technique. But we quickly ket” will correct any misallocation after- learn to enjoy seeing things his way. In this wards) with the theoretical riposte that, sense, the book is more a “master class” (to under incomplete information, there exists quote Al Roth’s blurb on the back cover) no nonconfiscatory mechanism (market- than a text.