What computer science can teach economics

http://web.mit.edu/newsoffice/2009/game-theory.html

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Of course, most games are more complicated than the penalty-kick game, and their Nash equilibria are more difficult to calculate. But the reason the Nash equilibrium is associated with Nash’s name — and not the names of other mathematicians who, over the preceding century, had described Nash equilibria for particular games — is that Nash was the first to prove that every game must have a Nash equilibrium. Many economists assume that, while the Nash equilibrium for a particular market may be hard to find, once found, it will accurately describe the market’s behavior.

Daskalakis’s doctoral thesis — which won the Association for Computing Machinery’s 2008 dissertation prize — casts doubts on that assumption. Daskalakis, working with Christos Papadimitriou of the University of California, Berkeley, and the University of Liverpool’s Paul Goldberg, has shown that for some games, the Nash equilibrium is so hard to calculate that all the computers in the world couldn’t find it in the lifetime of the universe. And in those cases, Daskalakis believes, human beings playing the game probably haven’t found it either.

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The argument has some empirical support. Approximations of the Nash equilibrium for two-player poker have been calculated, and professional poker players tend to adhere to it — particularly if they’ve read any of the many books or articles on game theory’s implications for poker. The Nash equilibrium for three-player poker, however, is intractably hard to calculate, and professional poker players don’t seem to have found it.