Pricing the priceless

Imagine that you are lucky enough to inherit a Picasso painting. Suppose, now, that you are in dire straits, and need to sell the painting. How should you go about it? If you knew the potential buyers and their valuations (or the maximum price they are willing to pay for the painting), the answer is simple.

You call the person with the highest valuation and sell it to this person at a price equal to his valuation. The trouble is that you, the seller, have only incomplete information about the buyers' valuations.

And no buyer would be ready to reveal his or her actual willingness to pay for the painting. So, to arrive at the best price, you have to organise an auction.

Ever since William Vickery's pioneering work in the early 1960s, auction theory has come of age. It is one of economics' success stories. Lessons from auction theory have led to important insights elsewhere in economics. It is also of great practical importance because many of the world's most important markets are auction markets.

In this context, An Introduction to Auction Theory is welcome. The objective of the book is to start, whenever possible, from basic principles and equip students with the techniques that are necessary to master the theory of auctions.

The first chapter provides a brief introduction. Chapter 2 discusses the basic auction forms: the first-price /second-price sealed-bid auction, the ascending (English) and descending (Dutch) auction. Auctions are modeled as incomplete information games, and this chapter discusses such games.

In chapter 3, the authors introduce the symmetric independent private-value model of auctions. This is the benchmark model in auction theory, and all its results are derived systematically. Beginners in auction theory would learn that in a second price auction (that is, where the highest bidder wins but pays a price equal to the second highest bid), it is optimal for a bidder to bid her true value. This chapter also discusses one of auction theory's most celebrated theorems "" The Revenue Equivalence Theorem. This theorem tells us that subject to some reasonable-sounding conditions, the seller can expect equal profits on average from all the standard types of auctions.

Chapter 4 provides the basic results on common-value auctions. It may be noted that in the basic private-value model, each bidder knows how much she values the object for sale, but her value is private information to herself. In the pure common-value model, by contrast, the actual value is the same for everyone, but the bidders have different private information about what the value actually is. For example, the value of an oil lease depends on how much oil is under ground, and bidders may have access to different geological signals about that amount. In this case, the bidder would change the estimate of the value if she learnt another bidder's signal, in contrast to the private-value case in which her value would be unaffected. A key feature of bidding in auctions with common-value components is the "winner's curse": each bidder must recognise that she wins the object only when she has the highest signal. Failure to take into account the bad news about other's signals that comes with any victory can lead to the winner paying more, on average, than the prize is worth, and this is said to happen often in practice.

Chapter 5 discusses the case of affiliated values. Very roughly, bidders' signals are "affiliated" if a high value of one bidder's signal makes high values of other bidders' signals more likely. Chapter 6 discusses mechanism design theory in the context of auctions. The literature on optimal auctions (how to design an auction which maximises seller's revenue) is also explored here. Chapter 7 introduces multi-unit auctions. This is currently a hot area for research. The book concludes with four appendices that review the fundamentals of probability theory and basic mathematical tools.

On the whole, the book has been carefully written, and there is remarkable clarity in the presentation. What it lacks is a review of the applications of auction theory in real life, like the US FCC spectrum auctions or the UK 3G mobile licence auctions. But this is a minor criticism. For the first-time visitor to the field of auction theory, this is a superb guidebook that I am glad to recommend. But the high price is a big deterrent for students or teachers in emerging economies.

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AN INTRODUCTION TO AUCTION THEORY

Flavio M. Menezes and Paulo K. Monteiro
Oxford University Press
Pages: 178 Price: $53.28