The same is true of spectrum licenses. Economists specializing in game theory argued that the allocation of public a.s.sets, from the right to drill oil to the right to use radio spectrum, ought to be determined by methods similar to those that determine a game of poker. In order to sift out competing companies' cheap talk and empty promises, the government had to impose high stakes and, to use an old phrase, force each negotiator to "put his money where his mouth is."

Games within games: How to sell a $300,000 house for $3,000

The US government employed game theorists to help sell spectrum rights throughout the second half of the 1990s. This was not an easy task: a company bidding for a Los Angeles license and a San Diego license might want both of them, or neither, because it is cheaper to run adjacent networks. But how to bid sensibly on Los Angeles before knowing who will get San Di-ego? This is a complex problem represented by a complex piece of game theory. The theorists duly designed a complex set of parallel auctions.

The first sales were highly successful (and very lucrative for the government), but after a few auctions things went wrong. The theorists had got the complex things right but made some simple mistakes, like publishing the bids without rounding them to the nearest few thousand dollars. Firms took advantage by making bids which contained area codes. This allowed them to signal which licenses they'd prefer, and so carve up the US telecom market without having to bid aggressively against each other. This scheme didn't even require an (illegal) agreement, because the auction allowed such clear signals. It looked like cheating, but n.o.body could prove it. Three years after the first auctions, an auction in April 1997 raised less than 1 percent of the ex-pected revenue because, claimed many commentators, firms had learned to cheat by avoiding compet.i.tion with each other.

This is the equivalent of selling your $300,000 house for less than $3,000. It seems hard to understand how this might hap-pen, but it's simple. If there are only a small number of potential buyers for your house, they could agree among themselves not to bid against each other. The one who buys the house cheaply needs to find some way to compensate the others. The most ob-vious form of compensation would be to agree not to bid against them in future auctions. In the same way, telecom firms seemed to work out a way of agreeing not to bid against each other for spectrum licenses in different regions. It was a humiliation for game theory, only slightly better than having given away the li-censes for nothing.

An alternative way of seeing the problems of the American auctions is that the game theorists failed to see that what they had a.n.a.lyzed was only part of a wider game. The government was like the poker player blissfully unaware of hidden cameras in the room; oblivious to the fact that the other players, by a series of nods and winks, are taking turns winning his money. The game he thinks he's playing isn't the real game at all.

Game theory for dummies Whether applied to colluding at auctions or cheating at cards, it must be clear by now that game theory is as much art as it is mathematics. All games need some simplifying a.s.sumptions be-fore they can be modeled; if the theorists use the wrong a.s.sump-tions (for example, that bidders won't use area codes to coordinate a carve-up) then they will produce perfect solutions to the wrong problems.

One of the most difficult challenges of all is rooted in the very origins of game theory: it was developed by men of nearly super-human intellect like Nash and Von Neumann. That is both its great strength and its great weakness, because for game theory to be successful, it has to provide insight into what mere mortals do. Game theory expresses the way people would act as the solu-tion to a mathematical equation. It presumes hyperrational play-ers who are able instantly to solve very tough problems, and this description starts to look unrealistic if game theory is to be a practical tool for explaining how real people actually behave. Nash and Von Neumann really could solve such problems instantly. The rest of us cannot.

For instance, game theory tells us that chess is not worth play-ing because in theory its outcome is predetermined: one player can force a result. However, we do not know whether it is black or white that can force the result, we do not know whether the forced result is a win or a draw, and we certainly do not know how the game would be played. We only know that in theory, the forced result is possible. In practice even the strongest players (computer or human) do not know this optimal strategy, and in practice the outcome of a game of chess is far from being prede-termined. So what use is a theory that tells us that chess would be trivial, if only we were all smart enough to know how to play it?

Not all of us think like a genius. Most of us would try to bluff at poker with a halfway good hand; Von Neumann showed that the correct play is to bluff with the worst possible hand. Chris "Jesus" Ferguson, a disciple of Von Neumann, proved it when he won the World Series of Poker in 2000. But poker with your buddies in the garage is not the World Series; what can game theory say about players who get drunk and bluff badly?

This is not a knockdown objection to game theory. It is possible to model mistakes, forgetfulness, misinformation, and any other kind of failure on the part of the players to live up to the impossibly high standards of John Von Neumann. The trouble is that the more mistakes that need to be taken into account, the more complicated and the less useful game theory becomes. It is always useful for the game theorist to draw on experience as well as pure theory, because if the game becomes too complex for the players to understand, then the theory becomes nearly useless for practical purposes since it tells us nothing about what they will actually do.

Enter the auctioneers In late 1996, I saw one of the country's leading auction theorists ill.u.s.trating this point-in pa.s.sing-in a seminar on applying game theory to auctions. As part of his talk, Paul Klemperer confis-cated the wallets of two members of the audience, counted the money they contained, and then offered to sell that (unknown) sum of money back to whichever of the victims would bid high-est. The two members of the audience, put on the spot, were quite unable to work out what the optimal strategy was for bid-ding in the auction.

The difficulty-which is a challenge for bidders in many auctions, including spectrum auctions-is that the two victims just didn't know the value of what they were bidding for. They knew part of the value, of course, because they knew how much money had been in their own wallet. But each knew nothing about the contents of the other's wallet. In a spectrum auction, the problem is similar: each bidder has his own forecasts and technology plans, but each knows that other bidders will probably have dif-ferent insights. The optimal strategy would take advantage of any information revealed by other players' bids-but this is not easy. (In the wallet game, one solution is for each player to keep bidding until he reaches twice the sum in his own wallet. The player with the fatter wallet would win but pay less than the combined contents of the wallets. Bidding more aggressively risks paying too much.) The failure of the two dumbfounded "volunteers" to work out how to bid in the auction was more remarkable because they were Ken Binmore and Tilman Borgers, themselves experts in the game theory of auctions. Klemperer, Binmore, and Borgers were about to become members of the team of academics who designed the mechanism for distributing the licenses in the UK for "third generation" (3G) cell-phone services.

They had two serious difficulties to wrestle with. First, to avoid being outmaneuvered by cheating bidders as the US authorities had been. Second, even if they couldn't find the optimal strategy for each others' auctions on the spot, how could they expect a collection of businessmen to behave as game theory predicts? And if those businessmen behaved unpredictably, who was to say what might happen?

John Maynard Keynes, the most influential economist of the twentieth century, longed for a day when economists were no longer archtheorists but instead, "rather like dentists," consulted to fix everyday problems and give straightforward advice. Eco-nomics is not there yet, and any economist who wishes to be even half as helpful as a dentist must temper economic theories with heavy doses of the hard lessons of real life: players cheat; bidders make mistakes; appearances matter. Auctions, like games of poker and chess, do not always unfold in the way the game theorist would predict.

The New Zealand government, which auctioned radio spectrum as early as 1990 with advice from some economists who seemed to have a slender grasp on reality, learned such lessons the hard way. The auctions were held without making sure that there was any interest from bidders, without minimum prices, and using a theoretical curiosity called a "Vickrey auction," which led to considerable embarra.s.sment. (The auction was named after its inventor, n.o.bel laureate William Vickrey, who made major early advances in applying game theory to auctions.) The Vickrey auction is a second-price sealed-bid auction. The "sealed bid" means that each bidder writes down a single bid and seals it in an envelope. When the envelopes are opened, the high-est bidder wins. "Second-price" is the curious rule that the win-ner pays not his bid but that of the second-highest bidder. The elegant reasoning behind this auction is that no bidder ever has an incentive to shave his bid in an effort to make more profit; making a lower bid affects his chance of winning but not the price. To a theorist, this doesn't seem odd at all: after all, in a traditional auction at Sotheby's or Christies, the price is also set by the second-highest bidder, because bidding stops when the second-highest bidder drops out. To the press and many others, this Vickrey auction looked nothing short of crazy. The problem with the Vickrey auction is not substantive but stylistic: in a tra-ditional auction n.o.body ever finds out the maximum price the highest bidder would have been willing to pay, but in a Vickrey auction that fact is made public. Justifiably, New Zealanders wanted to know why a bidder who had offered NZ$100,000 (about $72,000) for a license only had to pay NZ$6 ($4+) or why one who had offered NZ$7 ($5+) million was only coughing up NZ$5,000 (around $3,600). These figures were embarra.s.sing. The theorists knew that on average, Vickrey auctions make just as much money as other auctions because, by not demanding payment of the highest bid, they encourage all bidders to offer more. But what the theorists knew did not matter to the press and to the public: the harsh reality is that Vickrey auctions were seen as a failure of the New Zealand government.

Game theory can help predict some problems, such as cheating in the US auction. Others, such as the public reaction in New Zealand, simply don't show up in the theoretical a.n.a.lysis. Economists who aspire to dentistry have to think carefully and learn from mistakes: new ones will continue to be discovered the hard way.

Why use an auction?

When the UK government started to consider using an auction to sell spectrum rights, they were taking a bold step. After initial success, the US auctions had fallen apart because the game theory used to construct them had been far too narrowly conceived. The New Zealand government had made itself a laughing stock. And they weren't the only ones: Australia had also run auctions for TV licenses and left loopholes in the bidding rules, which had been so badly exploited that the minister responsible lost his job. Why did Britain even consider using an auction, given the risks?

Like the US government, the UK government wanted to sell the licenses to the companies that could use them best and to raise money while doing so. Of course, there was an additional unstated aim: to avoid embarra.s.sment for bureaucrats and politicians alike. For the taxpayers of New Zealand and the United States, an auc-tion that raised some money was better than simply giving the licenses away, but for a politician, giving away public a.s.sets is a great way to make friends and allies. Auction theorists therefore had to make a strong case for auctions.

That case relies on game theory, which clearly demonstrates the power of simple auctions. One of the trickiest problems is making sure that the licenses end up in the right hands. With a limited number of licenses it would be a criminal waste if one of them went to timharford.com, an Internet-bubble company with no relevant experience and no capability to use the valuable as-set. The licenses should go, instead, to companies that will use them to deliver the best quality services at the lowest cost. Com-pet.i.tion between license holders will then set prices.

So what is the best way to identify the most capable companies? One possibility is simply to ask them, but companies will boast and bl.u.s.ter. Some will point to their experience, others to the latest technology. But would any really tell the truth? Talk is cheap.

Another idea that might seem more promising is to appoint experts to decide which companies are most deserving. But in the fast-moving world of cell telephony, most experts would have some financial interest in one company or another-who is ex-pert yet totally detached from the industry? Even if a truly im-partial expert could be found, he would still have little success in penetrating trade secrets and judging the true potential of rival technologies.

Game theory shows how a simple auction can cut through all the complexity and solve the problem elegantly. For simplicity, imagine a straightforward auction of a single license, which is like a traditional auction where bidders yell out higher and higher offers, with one difference: anyone who stays in the room is pre-sumed to be willing to pay the current high bid. Anyone who drops out must leave the room and not reenter. This slightly different auction is easier for game theory to a.n.a.lyze, but also closely reflects many of the actual auctions used to sell licenses.

Each bidder must now make a straightforward judgment about what the license is worth. The better their innovative ideas and the cheaper their technology, the more money they will make if they win a license. Of course, none of the companies can per-fectly forecast what profits they would make with a license, but each is in a better position than any external expert to make the judgment.

When the auction starts and the price begins to rise, bidders will start to drop out once the asking price for the license exceeds their own estimate of its value to them. Companies without con-fidence in their business plans and technologies will be the first to go. If the price rises a long way without anyone leaving the room, each bidder learns that the others are confident about the prospects for the market as a whole. (This provides the distinc-tion between this auction and a traditional auction at Sotheby's- while a Sotheby's auction is in progress you never know who is still a potential bidder and who is just watching.) If some bidders leave surprisingly early, the rest should take note and revise their own a.s.sumptions. The auction neatly summarizes the collective wisdom of all the bidders.

Meanwhile, n.o.body is in a position to lie. Talk is cheap, but bidding is expensive. No company will drop out while the price is still lower than their prediction of the license's value, and no company will keep bidding once the price rises too high. In a sense, the auction is like Von Neumann's game of poker: be-cause money is at stake, the bids have to be taken very seriously. In another sense, it is not like poker at all, because the auction makes it absolutely impossible to bluff.

The auction forces each bidder to tell the truth about his own estimate of the license's value. At the same time, the auction broad-casts the collective view to all the bidders, so that they can update their own opinions accordingly. What's more, it collects cash while it does so.

Game theory also shows that this simple auction is generally a better cash-generating machine than the alternative ways of ne-gotiating a sale. This is not obvious. One alternative would be for the seller to run an auction but to set a reserve price (open or secret) below which he will not sell. Another would be to negoti-ate in secret with several buyers in parallel and lie about how the negotiations were going. Or the seller could make a one-shot, "take-it-or-leave-it" offer to each seller in turn. Or something else. Given the perplexing array of possibilities, how can a seller choose the most lucrative way of making a sale?

Game theory slices through to the core of the problem. In the mid-1990s, Klemperer and Jeremy Bulow (who became another member of the auction design team) published a paper showing if the simplicity of the auction attracted just one extra serious bidder, that straightforward auction would raise more money than any other kind of negotiating set-up.

In addition to the central claim that auctions really do raise more cash, the paper finally focused the attention of auction theo-rists on what should have been obvious: if you want a successful auction, you need plenty of serious bidders.

The UK auction in action The UK auction design team certainly went all-out to make sure those serious bidders turned up. By March 2000, the UK auction was ready to go with thirteen registered bidders who had paid 50-million deposits and were hooked up to the Internet to sub-mit their bids remotely. The team had been advertising the auc-tion for more than a year in advance and had made sure they were the first European nation to hold an auction for third gen-eration phone licenses. The result promised to be a highly com-pet.i.tive auction.

The team had been focusing obsessively on the details. They'd tested the auction design using computer simulations and test-runs with London students playing the role of telecom execu-tives. They crawled over the fine print of the auction, trying to eliminate loopholes. They even gave themselves options to post-pone the auction if something suspicious appeared to be going on. But despite all this preparation, n.o.body really knew if the auction would work, or whether it would be yet another bungle by the economists.

The auction was set to run in short rounds-lasting half an hour or so-during which the bidders had to submit new bids or withdraw. Those who chose not to enter a valid bid had to drop out of the auction; each bidder was allowed to "pa.s.s" three times before finally withdrawing. There would be a couple of rounds every day, maybe more once the bidders became comfortable with the bidding process. Each of the rounds would be posted promptly on the Internet; this auction was to take place in full view of the world.

The initial expectations were that the auction might raise a lot of money: two or three billion pounds, enough to knock a penny off the UK income tax for the year. While the team was obviously nervous, they were thrilled to have nine new companies join the four established players in the bidding, and they expected the auction to be a success.

They attributed the interest from new companies in part to the fact that five licenses were available. Originally, the engi-neers had believed that the airwaves could accommodate four licenses, operating on adjacent wavelengths of radio spectrum and each covering the entire country. But with four established companies, an auction for four licenses would have had obvious winners and the new entrants would not have bothered turning up simply to get beaten. The economists on the project were therefore very relieved when the engineers worked out that there was enough radio spectrum available for one extra license. This license, called "license A," was reserved for new companies who were not currently operating in the UK cell-phone market.

The idea of the auction was that compet.i.tion for license A would drive up the prices of the other four licenses. Any firm not cur-rently in the lead for a license had to keep bidding or withdraw; but as long as firms kept making legal bids, they could switch bids from one license to another. The firms would obviously choose to bid on whichever license appeared to offer the best value at the time. This meant that the hot compet.i.tion for li-cense A kept the auctions for the other licenses simmering nicely-every time the price of A rose above the rest, the other licenses looked like bargains. Entrants would peel away and chal-lenge the established companies for the licenses they had staked out for themselves. When the established firms raised the price, the underdogs flipped back to bidding on license A.

Although the simultaneous auction of five licenses is complex to explain, it is quite simple for a bidder to understand the best strategy. Because bidders never know when the auction is going to end, they need to make sure they are always comfortable in their current position. The best strategy is to look at all the li-censes and submit a new high bid on whichever license looks like the best value. If none looks like a good value at that time, then the right move is to withdraw. The simplicity of the auction may help to explain why so many companies decided to bid, and un-like World Series Poker or the wallet game, it is close to being idiot-proof.

Imagine selling your house in a prolonged auction that goes on for weeks and weeks. You've heard the stories about other auc-tions, and you're afraid that instead of getting the $300,000 you expect, you'll end up like your unfortunate neighbor, divorced and penniless. The first week is agony. But the price slowly starts to rise, and your blood pressure starts to fall. Eventually the bid-ding gets to $250,000-you realize that, whatever happens, you're not going to do too badly. A few days later the bidding reaches $300,000 and you're smiling. From here on everything is a bo-nus; maybe you'll get $310,000, or $320,000, or even $350,000. Who knows? Then the price keeps going up. It hits $320,000. It reaches $350,000. $400,000. $500,000. What's happening? You can scarcely believe it.

This unexpected turn of events is similar to what happened in the UK spectrum auction, except the stakes were ten thousand times higher: not 300,000 but 3 billion. For a week, the bidding went smoothly; the rules about continuous bidding kept the total revenue rising steadily. After about twenty-five rounds of bidding, bidders were committed to around 400 million for each license. After fifty rounds of bidding the total stood at 3 billion: what the government had been hoping to raise. (In comparison, the depos-its, even though they had been raised to 100 million, were start-ing to look a little trivial.) But something extraordinary was happening. Bidders were staying in the auction. All thirteen com-panies continued submitting bids regularly and the prices of the licenses kept rising without any sign of slowing down.

As the auction rolled on, the press started to take interest. Photographs of the design team began appearing in the newspapers. Journalists struggled to explain exactly what the team had done, but everybody started to realize that something remarkable was happening.

The bidding moved through round sixty (total revenue: 4 billion). Round seventy (5 billion). Round eighty (7 billion). The end of March came and went. The price was still rising.

The auction designers were keeping quiet about what they thought of all this, but behind closed doors they were both ex-cited and nervous. The auction was becoming a victim of its own success: it was lasting too long. There were jitters on the US stock market-what if a stock-market crash spread to the UK, destroyed the confidence of the bidders, and brought the whole auction to a sudden stop? The deposit of a 100 million suddenly looked pretty small. Maybe the bidders would just walk away. Perhaps the bidding should be speeded up? It turned out that there was no need to worry.

On the morning of April 3, almost a month after the first bid had been cast, with more than 10 billion (200 or almost $400 per person in the UK) raised, something finally happened. After round ninety-four had finished, it was announced that one of the bidders, Crescent, had dropped out. The auction then started to change quickly. That afternoon, in round ninety-five, a sec-ond bidder, the 3G-UK consortium, dropped out. The next morning, in round ninety-seven, a third bidder, Spectrum, also quit. Some other bidders were stalling for time by playing their "waivers" to stay in without raising a bid. In round ninety-eight Epsilon withdrew. The next day, at lunchtime on April 5, One-Tel quit.

After ninety-three rounds of bidding without any withdrawals, the auction had lost five bidders in eight rounds over the course of three days. Now only eight bidders remained. Why was the bidding stuttering so suddenly? Perhaps it was pride: n.o.body wanted to be the first to drop out, but once Crescent quit, others who had been waiting for the chance also quit soon after.

Game theorists have an alternative explanation: bidders were learning from each others' bids about what the 3G licenses were likely to be worth. This was one of the advantages of the auction's transparent design. A commonly used alternative would simply have been to run a "sealed bid" auction where everyone handed in an envelope containing a single bid. But such an auction would have left every bidder guessing in the dark, probably leading to much more conservative bidding and a much less profitable out-come for the government. With an open auction, even when the bidding rose higher than anyone had expected, each bidder could see that its twelve compet.i.tors were making equally large offers and shared confidence that the licenses would prove hugely valu-able. Each company had its own business plan, its own technology partners, its own sales projections. All of these were speculative, but the transparent auction gathered signals of these plans together and put the information at the disposal of all the bidders. (The auction also put the information at the disposal of the government and collected revenue on that basis at the same time-all very neat.) Crescent's withdrawal sent a signal to the other bidders that the company felt the licenses were not worth a higher bid. Tak-ing into account Crescent's doubts, other bidders who were also having second thoughts were tipped into withdrawing. Crescent set off a spiral: each new withdrawal reinforced the news that the bidding was getting too high.

Of course, the companies who dropped out were just sticking with the herd, but remember that herds run together for good reasons. The transparent auction was designed to spread infor-mation around, so it was hardly surprising that bidders looked at the same facts and came to the same conclusions.

The auction had seen a sudden run of withdrawals but it was far from over. By the middle of April the total revenue of the auction topped 29 billion. The government's profit was almost enough to halve the basic rate of income tax for a year. What actually happened was that the British chancellor, Gordon Brown, launched a generous round of spending in the run-up to the elec-tion without a large increase in taxes or borrowing. The British public was given an enormous free lunch, courtesy of the telecom boom and the painstaking determination of the auction design-ers to take advantage of it.

The last three withdrawals happened gradually over the course of April. Just after breakfast on April 27, NTL Mobile announced that it would be withdrawing, and suddenly all the excitement was over. A company called TIW was the new name in cell tele-phony, having paid 4,384,700,000 for license A. Vodafone had won its b.l.o.o.d.y struggle with British Telecom and was the proud holder of license B, at a price of almost 6 billion. British Tele-com settled for a smaller license. The auction raised 22.5 bil-lion and in the process had become the biggest auction in modern history.

If you had been selling your $300,000 house at an auction, which exceeded expectations like this one, you would eventu-ally have closed the deal at $2.25 million-and you'd have had to pinch yourself the next morning to check that you weren't dreaming.

Remember: strength from scarcity Critics of the auctions a.s.sumed that because the telecoms had paid so much for the licenses, they would in turn charge con-sumers very high prices for 3G services. But did the auctions ruin 3G? Consider the following sentence: If 3G licenses are very expensive, then firms will charge cus tomers more.

It seems persuasive, but think like an economist for a mo-ment: if 3G licenses are very cheap, will firms charge customers less? What if the government gave the licenses away for noth-ing, would firms charge customers nothing? And if the govern-ment paid telecom companies to take the licenses off its hands, would firms give each customer a cash bonus along with her free wireless service?

We learned way back in chapters 1 and 2 that firms will charge the maximum they possibly can, under any circ.u.mstance. We also know that their ability to do this is limited by their scarcity power.

For the UK, the crucial determinant is that there are five licenses. Five licenses are few enough to give each company enough scarcity power to be able to charge quite high prices. If only two licenses were available, then the scarcity power would be greater and the prices would be higher. If twenty licenses were available, the scarcity power would be less and the prices would be lower. It is the scarcity power, and not the price of the licenses, which determines the price for customers.

In the UK there was scarcity built into the amount of radio spectrum available: five licenses were the most the technicians could offer. It does not make any difference to the customer how much the licenses cost, but it does matter to the taxpayers, who would like the government to get a lot of money for this valuable public resource, and the telecoms' shareholders, who would like their companies to dish out as little as possible.

The hangover In the previous chapter we heard all about the stock market crash, which (in retrospect) began to unfold during the series of Euro-pean 3G auctions. Telecoms were among the worst sufferers, and their distress has been widely reported. In Europe alone, telecom companies lost $700 billion in stock market value in the two and a half years following the first 3G auction.

Many people have blamed the auctions for the woes of the telecoms, and argued that the UK design team, far from being clever by raising so much money, stupidly crippled the industry by charging such outrageous sums. Less widely reported is that the most seriously afflicted firms did not win 3G licenses-they are US firms who did not partic.i.p.ate in the European auctions, or troubled cable companies such as NTL and Telewest, who withdrew from the 3G auctions without spending anything. The 3G license winners, such as Vodafone, remain successful firms, sadder and wiser after the telecom bubble, perhaps, but still perfectly viable.

Telecom executives may curse the British auctions since 3G remains commercially unproven and threatened by compet.i.tors like Wi-Fi, but the public should celebrate them. All the companies involved were convinced that the 3G licenses offered tre-mendous scarcity value, and these auctions successfully secured a fair price for that apparent value. John von Neumann's succes-sors used game theory to achieve one of the most spectacular, if controversial, policy triumphs that economics had ever seen. The men who knew the "value of nothing" had shown that econo-mists, like dentists, could finally earn their keep.

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EIGHT

Why Poor Countries Are Poor

They call Douala "the Armpit of Africa." The description is perfect. Lodged neatly beneath the bulging shoulder of West Africa, the malaria-infested city of Douala is humid, unattractive, and it stinks. But if you live in Cameroon, Douala is where the action is. Cameroon is a very poor country indeed; the average Cameroonian is eight times poorer than the average citizen of the world and almost fifty times poorer than the typical American. In late 2001 I went to Douala to find out why.

I'm not sure who first applied the "armpit" label but I wouldn't be surprised if it was Cameroon's Ministry of Tourism. We all know that in most countries the Ministry of Defense is in charge of attacking other countries and that the Ministry of Employment presides over the unemployment lines. Cameroon's Ministry of Tourism is in that n.o.ble tradition. Its job is to discourage tourists from getting into the country.

One colleague had warned me that the Cameroonian emba.s.sy in London would be so obstructive that I'd have to go to Paris to get my tourist visa. In the end I had less trouble because I had a man on the inside: a friend in Cameroon paid the equivalent of a half-day's wages to get me an official stamp of invitation. Armed with this official stamp, I paid another five days' Cam-eroonian wages to get my visa, in a process that required only three trips to the emba.s.sy and some mild groveling. Funnily enough, my companions and I did not meet many tourists in our three weeks in Cameroon.

But I don't want to give too much credit to the Ministry of Tourism. Discouraging tourists is a real team effort. According to Transparency International, Cameroon is one of the most corrupt countries in the world. In 1999, it was the most corrupt country surveyed. When I visited in 2001 it was the fifth most corrupt, an improvement much celebrated by the government. A moment's reflection should tell you that earning the t.i.tle of "Most Corrupt Country in the World" takes some effort. Because Trans-parency International ranks countries based on international per-ceptions of corruption, a winning strategy is to concentrate on s.c.r.e.w.i.n.g bribes out of foreign businessmen-for instance, at the airport. But the Cameroon authorities have spread themselves too thin, because Cameroon is ma.s.sively corrupt at every level and does not just target foreigners. Perhaps it's this lack of focus that has caused them to slip from the top spot.

That's not to say that Douala international airport is a well-oiled machine. Far from it: it's a humid, chaotic shambles where you have to fight your way through packed crowds despite the fact that the place deals with only three or four flights a day. Thankfully, on a torrid evening, we were guided out by my friend Andrew and his driver, Sam, who would have whisked us imme-diately to the cooler hillside town of Buea, if Douala were at all conducive to being whisked anywhere. It isn't. Douala, a city of two million people, has no real roads.

A typical Douala street is fifty yards wide, from shack to shack. This is not because the s.p.a.ce is required for tree-lined boule-vards. It's packed with street vendors, slouched beside a tray of peanuts or an impromptu plantain barbeque; and with little clus-ters of people, standing around a motorbike, or drinking beer or palm wine, or cooking on a small fire. Piles of rubble and vast holes mark unfinished construction or demolition work. Along the middle is a strip of potholes, which twenty years ago had been a road. Down that strip drive four streams of traffic, mostly taxis. The streams on the outside are usually made up of stationary- or nearly stationary-cabs picking up fares, while the taxis on the inside weave in and out of the potholes and other cars with all the unpredictability of b.a.l.l.s in a lottery machine. There are no hard and fast rules. Sometimes a taxi on the shoulder, over-loaded with pa.s.sengers, will lurch off and overtake the stuttering traffic on the inside; often the road is more potholed than the shoulder. The noise is incredible, because not only does every man, woman, and child in Douala seem to carry a boom box with the volume stuck on full, but the car horn has become a form of universal communication. I worked out some of the most com-mon phrases: BEEEP-"You don't see me, but I have spare seats in my cab."

BEEEP-"I see you, but I do not have spare seats in my cab."

BEEEP-"I cannot take your fare because I'm going in a different direction."

BEEEP-"I can take your fare . . . get in."

BEEEP-"In a moment I will swerve around a pothole, and knock you over. Move!"

Douala used to have buses, but the buses can no longer cope with the decaying roads. So the taxis are all that is left. The cabs are beaten-up old Toyotas, carrying four in the back and three in the front, sprayed New York yellow, each with a unique slogan: for instance, "G.o.d is great," "In G.o.d We Trust," "Powered by G.o.d," or "Toss Man."

n.o.body who sees a Douala street scene can conclude that Cameroon is poor because of a lack of entrepreneurial spirit. But poor it is, and it's getting poorer. Is there anything to be done to reverse the decline and help Cameroon grow richer instead? That's no small question. As n.o.bel laureate Robert Lucas put it: The consequences for human welfare involved in questions like these are simply staggering: Once one starts to think about them, it is hard to think about anything else.

The missing jigsaw piece Economists used to think that economic wealth came from a com-bination of man-made resources (roads, factories, machines, tele-phone systems), human resources (hard work and education) and technological resources (technical know-how, or simply hi-tech machinery). Obviously, then, poor countries grew into rich coun-tries by investing money in physical resources and by improving human and technological resources with education and technol-ogy transfer programs.

What's wrong with this picture? Nothing, as far as it goes. Education, factories, infrastructure, and technical know-how are indeed in abundance in rich countries and severely lacking in poor ones. But the picture is incomplete: a puzzle with the most important piece missing.

The first clue that something is amiss with the traditional story is its implication that poor countries should have been catching up with rich ones for the past century or so, and the farther be-hind they are, the faster the catch-up should be. The poorer coun-tries should catch up quickly because in a country, which has very little in the way of infrastructure or education, new invest-ments have the biggest rewards. Rich countries don't gain much from further investment: this is called "diminishing returns." For instance, a few roads in a poor country can open up whole new areas for trade; in a rich country, a few more roads just relieve a little congestion. The first few telephones in a poor country are of huge importance; in a rich country, phones are used by schoolkids to send text messages in cla.s.s. A little more education in a poor country can make all the difference; in a rich country, people with degrees often can't find jobs. And of course, it should be much easier for a poor country to copy technology than for a rich country to invent it: the citizens of Douala can enjoy taxis without waiting for a Cameroonian Gottlieb Daimler to rein-vent the internal combustion engine.

When you look at places like Taiwan, South Korea, or China, which have been doubling their incomes every decade or quicker, the theory of catch-up seems reasonable. But many poor coun-tries are not growing faster than rich ones; in fact, they are grow-ing more slowly or, like Cameroon, getting poorer. In order to patch up the traditional story, economists combined their "di-minishing returns" model with one that also takes into account "increasing returns." The new theory says that sometimes the more you have, the faster you grow: phones are useful if other people have phones; roads are useful if everyone has a car; tech-nology is easier to invent if you've done a lot of inventing before.

That story would explain why rich countries stay rich and poor countries fall farther behind, but it doesn't explain how countries like China, Taiwan, and South Korea-not to mention Botswana, Chile, India, Mauritius, and Singapore-are catching up. These dynamic countries, not j.a.pan, the United States, or Switzerland have become the fastest-growing economies on the planet. Fifty years ago, they were mired in poverty-lacking man-made, hu-man, technical, and sometimes natural resources-and have grown much richer since then. Along the way they have improved education, technology, and infrastructure.

And why not? Since technology is so widely available and in-creasingly inexpensive, that is really what economists should ex-pect of every developing country. In a world of diminishing returns, the poorest countries gain the most from new technol-ogy, infrastructure, and education. South Korea, for example, acquired technology by encouraging foreign companies to invest or by paying licensing fees. It wasn't free: in addition to the fees, the investing companies sent profits back home. But the gains to Korean workers and investors, in the form of economic growth, were fifty times greater than the fees and profits that left the country.

As for education and infrastructure, since the returns seem to be so high, there should be no shortage of investors willing to fund infrastructure projects or lend money to students or indeed to governments who provide free education. Banks, domestic and foreign, should be lining up to lend people the money to get through school or to build a new road or a new power plant. In turn, poor people, or poor countries, should be very happy to take out such loans, confident that investment returns are so high that the repayments will not be difficult. Even if, for some rea-son, that didn't happen, the World Bank, established after World War II with the express aim of providing loans to countries for reconstruction and development, lends billions of dollars a year to developing countries. Investment money is clearly not the issue-either the investments are not being made, or they are not delivering the returns the traditional models predict.

Even the "increasing returns" model suggests that it should be possible for poor countries to grow richer as long as they can make a number of complementary investments all at once, such as factories, roads, electricity, and ports, to allow goods to be manufactured and exported. This "big push" theory of invest-ment was advanced by the economist Paul Rosenstein-Rodan, who spent some time at the World Bank in its early years. Whether through a big push or otherwise, many poor countries have managed to grow quickly over the past few decades, so why have so many others been left behind?

A theory of government banditry As our car slowly b.u.mped and lurched through the crowds, I tried to make sense of it all by asking Sam, the driver, about the country.

"Sam, how long was it since the roads were last fixed?"

"The roads, they have not been fixed for nineteen years."

(President Paul Biya came to power in November 1982 and had been in office for nineteen years by the time I visited Cameroon. Four years later, in 2005, he is still in power. He recently described his opponents as "political amateurs"-they are certainly out of practice.) "Don't people complain about the roads?" "They complain, but nothing is done. The government tells us there is no money. But there is plenty of money coming from the World Bank and from France and Britain and America-but they put it in their pockets. They do not spend it on the roads."

"Are there elections in Cameroon?"