Business Week - March 18, 2002
Economic Trends Edited by Peter Coy
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.