Plate iii in print

The Auction

Myerson; how the design of the rules, not the competition alone, decides the outcome — the same bidders yielding different ends under different rules.

Set the same bidders to compete for the same prize, and change only the rules by which they bid, and the outcome changes with them — what the seller earns, who wins, whether the prize goes to the one who values it most. The rules are not the stage; they are the play.

— the argument of this plate, after Roger Myerson, 1981

If the rulebook's claim is that markets are designed, the auction is its sharpest proof. An auction is a market stripped to its essentials — one good, several buyers, a set of rules for turning their competition into a price and an allocation — and because it is so simple, the effect of the rules is visible and even measurable. Change nothing but the rules of the auction, holding the bidders and the prize fixed, and the outcome changes: a different price, sometimes a different winner. The auction is where one can watch the design do its work, and where economists first learned, with precision, how much the rules decide.

There are several ways to run an auction, and they are not equivalent in their workings. In the open ascending auction, the price rises as bidders compete openly until one remains — the format of the art house and the cattle yard. In the open descending auction, the price falls from a high start until someone accepts — the Dutch auction of the flower market. In the sealed-bid auction, each bidder submits one secret bid, and the highest wins and pays his bid — the format of public tenders. And in the second-price sealed-bid auction, the highest bidder wins but pays only the second-highest bid — a format that, strikingly, rewards each bidder for bidding exactly his true value, since what he pays does not depend on his own bid. Four formats, four different games, each setting the bidders a different strategic problem: in some, a bidder should shade his bid below his value to avoid overpaying; in one, he should bid his value exactly; in others, he must guess what the others will do.1

1. The standard auction formats: open ascending (price rises until one bidder remains), open descending or "Dutch" (price falls until someone accepts), first-price sealed-bid (highest secret bid wins and pays it), and second-price sealed-bid (highest wins but pays the second-highest bid — which rewards bidding one's true value, since the payment is independent of one's own bid). Each sets bidders a different strategic problem — shade below value, bid value exactly, or guess others' bids.

One might expect these different formats to earn the seller different amounts, and sometimes they do; but a celebrated result shows that, under certain conditions, they do not. The revenue equivalence theorem holds that when bidders are similar and value the good independently, when they are neutral toward risk, and when the good goes to the highest bidder, all the standard auctions yield the same expected revenue — for the bidders adjust their strategies to the format, shading more where they pay their own bid and less where they do not, in just the way that leaves the seller equally well off on average. This is a deep and surprising equivalence. But its importance lies as much in its conditions as in its claim, for when the conditions fail — when bidders are different, or share information, or fear risk, or when their values are correlated — the equivalence breaks, and the formats diverge: now one auction earns more than another, one is more vulnerable to collusion, one more prone to the winner's curse. And then the choice of format is no longer neutral; it is a lever on the outcome, and the designer must choose.2

2. The revenue equivalence theorem (Myerson, 1981): under conditions — similar bidders, independent private values, risk-neutrality, the good to the highest bidder — all standard auctions yield the same expected revenue, since bidders adjust their strategies to the format. But when the conditions fail (different bidders, shared or correlated information, risk-aversion), the equivalence breaks and formats diverge in revenue, vulnerability to collusion, and exposure to the winner's curse. Then the format is a lever, and the designer must choose.
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Roger Myerson asked the designer's question in its purest form: among all possible auction rules — not just the standard four, but any conceivable set of rules — which earns the seller the most? His answer, the theory of optimal auctions, showed that the best auction is not always the one that gives the good to the highest bidder. To maximize his revenue, a seller should sometimes set a reserve price below which he will not sell, even at the cost of occasionally keeping the good when a buyer would have paid something for it; and when bidders differ in known ways, he should sometimes handicap the strong and favor the weak, to make the strong bid harder. The optimal auction, in short, deliberately departs from simple efficiency to extract more revenue — a designed distortion, chosen by the seller, that the rules make possible. Myerson's analysis did more than solve the seller's problem; it showed that the space of possible market rules is vast, that the familiar formats are a tiny corner of it, and that within that space the designer can pursue whatever end he chooses — revenue, efficiency, fairness — by the rules he sets.3

3. Myerson's optimal auction theory (1981): among all possible auction rules, which maximizes the seller's revenue? The optimal auction need not give the good to the highest bidder — the seller should set a reserve price (forgoing some sales) and, when bidders differ, handicap the strong to make them bid harder. The optimal auction deliberately departs from efficiency to extract revenue — a designed distortion. The space of possible rules is vast; the designer can pursue revenue, efficiency, or fairness by the rules he sets.

The power of auction design is no mere theory; it has been put to work in some of the largest markets ever created by deliberate design. When governments came to sell the rights to the radio spectrum — the airwaves on which mobile telephones and broadcasts run — they faced a problem of staggering complexity: many licenses, covering different regions and frequencies, wanted in combinations, since a carrier needs adjacent regions to build a network, by bidders whose values depended on what else they could win. A simple auction would have failed; the design had to be invented. Economists built new formats — the simultaneous ascending auction and its successors — in which all the licenses are sold at once, with the bidding open and iterative, so that bidders can assemble the combinations they need and the prices can find their levels together. These auctions, raising hundreds of billions and allocating the spectrum far better than the lotteries and hearings they replaced, are monuments to the proposition that the design is the market: the same spectrum, the same carriers, under the old rules wasted and under the new ones well allocated, the difference made entirely by the rules.4

4. Auction design built real markets: the radio-spectrum auctions. Selling many licenses (different regions, frequencies) wanted in combinations by interdependent bidders defeated simple auctions; economists invented the simultaneous ascending auction (all licenses sold at once, bidding open and iterative, so bidders assemble combinations and prices find levels together). These raised hundreds of billions and allocated far better than prior lotteries and hearings — monuments to "the design is the market": the same spectrum and bidders, wasted under old rules, well allocated under new ones.

The auction proves, with a rigor the rest of economics rarely allows, the author's claim that the design matters as much as the competition it governs. The same bidders, competing for the same prize, reach different outcomes under different rules; the seller can choose, by the format, what he earns and even who wins; and the largest designed markets in the world were made to work by the choice of their rules. The competition is real, but it runs inside a frame, and the frame is chosen. Yet the auction, for all its power, is still a market with prices — money clears it, and the rules decide how. The next plate turns to the harder and stranger case, where the design must do its work without any price at all: the matching markets, where money is forbidden or useless, and the allocation of doctors to hospitals, students to schools, organs to patients, must be accomplished by rules alone. There the design is not half the story but the whole of it. The next plate is the match.5

5. The auction proves the author's claim — the design matters as much as the competition: the same bidders reach different outcomes under different rules; the format decides revenue and the winner; great designed markets work by their rules. But the auction still has prices. The next plate (The Match) turns to markets without prices — doctors to hospitals, students to schools, organs to patients — where money cannot clear and the design must do everything. There design is not half the story but the whole.

The auction is the clearest demonstration that a market's rules decide its outcome. Whether the price rises or falls, whether bids are open or sealed, whether the winner pays his own bid or the next — these choices set the bidders different problems and yield the seller different results, and where the simple conditions of revenue equivalence fail, the format becomes a lever the designer must pull. Myerson showed that the space of possible rules is vast, that the optimal auction departs from efficiency by design, and that the designer can aim the rules at whatever end he chooses. And the spectrum auctions showed it all in practice, conjuring hundreds of billions and a well-ordered market out of the right rules where the wrong ones had wasted both. The design is the market. But the auction still clears with money; the next plate asks what design must do when there is no money to clear with at all. The next plate is the match.