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Game Theory's Hidden Holes

To economists, Russell Crowe is the sentimental choice for Best Actor at this year's Academy Awards. In A Beautiful Mind, Crowe plays John F. Nash Jr., the brilliant mathematician who shared the 1994 Nobel Prize in economics for his work on game theory. The groundbreaking theory describes the strategies that people should employ to maximize their payoffs in view of the strategies that others are most likely to use. It has been deployed in everything from antitrust law to auctions of wireless licenses.

Unfortunately, game theory has an Achilles' heel: People don't necessarily behave the way that game theory says they ought to. Some theorists consider that a minor difficulty. But a study by economists at the University of Virginia shows just how common it is to act in ways that seem, by game-theory standards, irrational. The study, by Jacob K. Goeree and Charles A. Holt, was based on 10 experiments with University of Virginia undergraduates who were schooled in game theory. It was published in the December issue of The American Economic Review.

In one experiment called "traveler's dilemma," two students chose numbers from a range. Each would get cash equal to the lower of the two numbers picked--for instance, $150. That means they would do best if both picked high numbers. But there was a counterincentive: The student who chose the higher number had to pay a $5 penalty. The game was played just once so the students couldn't learn cooperation. By Nash's theory, each should have tried to undercut the other just a bit to avoid the $5 penalty. In doing so, both inevitably would have chosen the lowest allowable number. In real life, though, most of the students picked the highest allowable number, to their mutual benefit. As long as the penalty for being the high-number picker was small, there was no "race to the bottom."

Another experiment tested Nash's theory that players should sometimes pursue "mixed strategies"--vary their actions to keep the other players guessing. But the experimenters found that students almost always went for the choice with the highest potential payoff. Their predictability was fatal: Their rivals correctly predicted what they would do and took counter-actions that deprived them of the big payoff.

Holt says the purpose of the paper was to "shock theorists into seeing situations where game theory doesn't work." Without insights from behavioral economics and other fields, pure game theory can be a beautiful minefield. The use of flexible pay soared during the 1990s. Companies compensated employees with bonuses and stock options. That enabled them to share the good times with workers--while preserving their ability to slash costs in bad times by rolling back the special pay. David Lewin, a business professor at the University of California at Los Angeles, estimates that 66% of U.S. workers got variable pay last year, up from 30% a decade earlier.

Nobody likes losing a bonus, but it may be the price for saving jobs. There's growing evidence that companies cut fewer workers in the recession that began last March than they would have if their pay had been less flexible. In the 1990-91 recession, the unemployment rate jumped 2.8 percentage points. This time, the jobless rate rose much less, from 4% last March to 5.6% this January. Because unemployment is a lagging indicator, economists expect the rate to rise more but not as much as in 1990-91.

While companies kept workers, they held back on variable pay. UCLA's Lewin calculates that variable pay rose 9.5% in 1999, then slowed to 6% growth in 2000, and to about 3% in 2001. Among the companies that say flexibility helped minimize layoffs are Rockwell International Corp. and Agilent Technologies Inc. While the lid on variable pay hasn't eliminated layoffs, says Steven E. Gross, a compensation consultant at William M. Mercer Inc., "it's helped reduce job cuts at the margin." How much longer can the U.S. rack up gigantic current-account deficits? The world's largest debtor is getting deeper in hock to the rest of the world by the day. Economists at Goldman, Sachs & Co. predict that the net debt of the U.S. will reach nearly $5.8 trillion by the end of 2006, which would be about 46% of that year's gross domestic product. In contrast, the net debt of the U.S. was just 13% of GDP as recently as 1997 (chart).

In a report last month, Jim O'Neill, Goldman's head of global economic research, calculated it would require a 30% increase in U.S. exports to halve the deficit in the U.S. current account--the broad measure of trade in goods and services and investment income. A 30% export increase would be a stretch, though: O'Neill calculates that to achieve it purely through more favorable exchange rates would require a 43% depreciation of the dollar against other currencies. Alternatively, he says, the current-account deficit could be halved through a 23% increase in foreign demand.

Goldman has worried about U.S. trade deficits since 1999, when it called them, in a headline, "Unsustainable!" Its alarm was premature: To date, the debt burden has been light because foreigners have financed U.S. spending by buying U.S. stocks and making direct investments in the U.S., such as building factories. But in 2001, foreigners switched to buying bonds, which place a heavier burden on the U.S. because they require interest payments. Last year, 97% of the U.S. current-account deficit was financed by net foreign purchases of bonds other than Treasuries. O'Neill concludes that "it is difficult to be anything other than cautious for the outlook for the U.S. dollar."

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