This year’s Nobel Prize in Economics has been awarded to Paul Milgrom and Robert Wilson for improvements to auction theory and inventions of new auction formats. In this post, Parikshit Ghosh discusses the evolution of auction theory and the significant contributions of the Laureates.
How should you sell the Hussain painting hanging on your wall if you must? One option is to put it up for sale in a gallery with a non-negotiable price tag. Another is to find an interested collector and start haggling. Both these approaches have their disadvantages.
If the collector has a fair idea how low you can go but you are in the dark about the most he is willing to pay, he can negotiate the price down to rock bottom (the Coase conjecture). Posting a firm price avoids this race to the bottom. However, it is a ‘Sophie’s choice’ between the risks of overpricing (in which case you may not find a buyer) and underpricing (in which case you will leave money on the table). A fixed price is a one-size-fits-all solution.
A more profitable selling strategy is to put the painting up for auction. Auctions are advantageous because they are adaptive. Competition among buyers ensures they reveal their private information through the bidding process, submitting higher bids if they value the object more. The final price incorporates this information and becomes flexible. Highly coveted objects sell dear. Less desired items go for a discount, but they go.
In 1996, William Vickrey won a Nobel Prize for laying the foundations of modern auction theory, and in 2007, Roger Myerson earned his shiny medal for adding significantly to Vickrey’s insights. There are many kinds of auctions found in practice. Descending-bid Dutch auctions have been common in wholesale flower markets in Holland, while ascending-bid English auctions are the preferred mode of selling for auction houses like Christie’s and Sotheby’s. Government tenders are often issued based on sealed bids and under various rules, such as the first-price and second-price auctions.
Which of these auction formats should a smart seller choose? Vickrey showed that it does not matter – in many problems, these different auctions should raise the same revenue for the seller on average (the revenue equivalence theorem). Myerson went a step further, and using a powerful theoretical argument called the revelation principle, proved that it is impossible to beat these common auctions. Not only are they efficient (that is, the object goes to the buyer who values it most), they also fetch the highest revenue that is theoretically possible, provided a suitable reserve price is set. No other selling strategy, however clever or complex, can raise more money.
Indian policymakers learnt belatedly, after the 2G controversy, that auctions can reduce corruption, allocate scarce resources efficiently, and maximise revenues – all at the same time. The lesson may be extended to solve some of our other woes; for example, the perennial trouble with land acquisition.
Paintings versus penny jars
The US government has, for many years, been auctioning off drilling rights in earmarked tracts in the Gulf of Mexico to private oil companies. In a 1971 paper (Capen et al. 1971), three industry engineers found that on average, winners of these auctions systematically overpay – they would have earned a higher rate of return if they simply put their money in the bank!
The reason for this persistent penury is the winner’s curse. If a thousand people are asked to bid on a jar of coins based on their eye estimate, the winning bidder will be the one with the highest estimate. A thousand guesses are likely to be close to the true value on average (a phenomenon underlying the notion of the wisdom of crowds), but the highest guess will most likely be an overestimate.
A painting is an example of private values – the worth of a Hussain to a private collector depends on his/her own artistic taste, not that of a rival collector. The jar of coins, on the other hand, is worth the same to everyone – it is just that different bidders’ guesses are wrong in different ways. If I learn of your estimate, it should influence mine. This is an example of common values. Many real-life auctions have both private and common-value components. For example, in oil-lease auctions, the value of the oil reserves under the ground is the same for everyone (but hard to assess accurately), yet the cost of drilling may vary, depending on the technological know-how of the bidder.
This year’s Nobel laureates, Robert Wilson and Paul Milgrom, expanded the scope of auction theory by analysing common as well as private values, and combinations thereof. As Wilson (1969) showed, canny bidders should eventually wisen up to the winner’s curse and start shading their bids to escape it. That shifts the problem to the seller, who will experience a drop in revenues as this caution kicks in.
In a seminal paper written with Robert Weber (1982), Milgrom proved the linkage principle. Any information bidders receive about the value of the object before submitting their bids makes their assessment more confident, weakens the winner’s curse and reduces bid shading. This works to the seller’s advantage. One implication is that sellers should commit to be transparent about the object under the hammer – allow inspections and expert assessments, for example.
In sealed bid or Dutch auctions, bidders never get an opportunity to learn about the value estimates of their rivals. In the English auction, by contrast, as bidders drop out at various points, it tells those who remain how much the quitters thought it is worth. This information spillover, thanks to the linkage principle, makes the English auction fetch higher revenues on average.
All auctions are created equal, said Vickrey and Myerson. Under the shadow of the winner’s curse, some auctions are more equal than others, added Wilson and Milgrom. Take note, sellers!
The anatomy of markets
In introductory economics textbooks, one learns of a fictional market maker who moves around prices till demand matches supply. In the real world, outside of some stock exchanges, such a deliberate, centralised procedure for ‘price discovery’ is hard to find. The creators of that parable hoped that the simple story well approximates whatever complex process (involving bargaining, bidding, and trial and error) leads up to market equilibrium.
A major intellectual contribution of Milgrom, Wilson, and others is to open up the black box of classical price theory developed by Walras and Marshall, look closely at the nuts, bolts and gears, and give us a better idea of when the machine may run smoothly and when it might become jammed. The details of the price formation process may affect the outcome.
In 1994, as the telecom revolution was taking off, the Federal Communications Commission (FCC) in the US was poised to give out licenses for the use of spectrum bands to telephone companies. Given the stakes involved, the FCC decided to move away from non-price allocation methods like beauty contests and lotteries, and turn to auctions instead.
The problem was that the FCC was not selling a single item but a whole range of frequencies. The value to a company of holding the license to a particular frequency would depend on what other frequencies they owned, that is, the whole could be worth more (or less) than the sum of parts. To design an auction that did justice to this complicated scenario, top auction theorists were called in. Milgrom and Wilson’s design – the Simultaneous Multi-Round Auction Format (SMRA), which is in the spirit of the English auction – won the day (Bichler 2017). It has raised an impressive US$121 billion in revenues to date and has been widely adopted in many countries, including India.
Philosophers have interpreted the world, said Karl Marx; the point, however, is to change it. Since Adam Smith, economists have passively studied markets – the country fairs, stock exchanges, yard sales, and classified ads the world is teeming with. They have sung their eulogies and damned their inequities. Modern technology and a complex world is opening up new markets whose architecture cannot just borrow from custom. How should Google price its ads? How should online dating websites charge men and women? How to price pollution permits? How should hospitals be matched with medical interns or kidney donors with recipients? This is the arena of market design, a New World in which Milgrom and Wilson are among the Pilgrim Fathers.
The cynic, said Oscar Wilde, knows the price of everything and the value of nothing. Milgrom and Wilson have spent their lives trying to devise ways in which price can be made to align with value. Their achievements are worthy of celebration but also to be taken with caution.
First, auction theory assumes bidders behave in a rational and sophisticated manner. For novel and complicated auctions, this assumption may be questionable, at least until players figure out the tricks of the trade through experience (oil companies falling prey to the winner’s curse early on is one example of bounded rationality in action).
Second, auctions are nothing but rules that govern transactions. If institutions are weak, the credibility of these rules cannot be taken for granted. Although India switched firmly to auction-based allocation of spectrum after the 2G scam, a crisis looms over the telecom industry today. Rules have been changed or disputed after the fact too many times – in 1999, when license fees were replaced by revenue sharing, in 2012, when the Supreme Court cancelled outstanding licenses, in the same year when the government slapped retrospective taxation on Vodafone, and more recently in court battles over the definition of revenues to be shared with the government. The result is tepid bidding by spooked and financially hobbled operators in recent spectrum auctions, resulting in loss of revenues and a market that is dangerously close to devolving into a duopoly. Auctions are not a panacea for all problems – they are as effective as the ecosystem in which they operate.
Third, the recommendations of an auction model are only as good as its assumptions. For example, if bidders must incur large fixed costs to qualify, the auction design must allow them to recover their investments by taking off some of the competitive edge. Traditionally, national governments and international organisations like UNICEF procured vaccines through winner-take-all auctions where the lowest bidder was awarded the entire contract.
This led to the exit of a lot of manufacturers who lost out in the bidding war and could not justify the cost of maintaining idle capacity. In the long run, it reduced the number of suppliers, drove up the price of vaccines and created shortages. Many European countries have now switched to a system of split awards, whereby even manufacturers who do not bid the lowest price may be given a fraction of the order as consolation prize (Wilsden et al. 2020).
The moral limits of markets
Imagine you are a musician about to perform in a theatre that has a hundred seats. How do you want to allocate the tickets? If you want to maximise gate receipts, letting interested people bid for them is a good idea. But what if you want to attract the hundred people who will understand and appreciate the performance better than all others? A high price may well admit the wealthy charlatan and keep out the poor aficionado.
The philosopher Michael Sandel has lamented the cultural trend towards letting markets mediate all social exchange. One of his objections is some kind of domain specific inequality aversion. We may not care if luxury yachts are allocated through the price system, but if health care resources also go to the highest bidder, plastic surgery for the rich will get precedence over bypass surgery for the poor.
“To each according to his need, from each according to his ability,” pronounced Marx. The problem is, need and ability are often private information, making it difficult to put this wonderful dictum into practice. Auctions take us halfway, but only halfway, towards achieving it (the study of auctions with financially constrained bidders (Che and Gale 1998) could take us further along). High bids can be as much an expression of wealth as need. It may be socially desirable, on some occasions, to call a truce in the bidding war and resort to other means.
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- Aryan, A (2020), ‘Retrospective taxation: the Vodafone case, and the Hague court ruling’, The Indian Express, 27 September.
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