cent rational with total information and unlimited mental power to figure out what everybody else will do and then calculate the best move. But sometimes (actually, almost all the time) those conditions are not satisfied. People have limited calculating power and limited information. There are situations where the game is too complex and too many people are involved to choose a foolproof decision using game theory.

And in fact, many simple situations can prove too complicated to calculate completely, even something as innocent as deciding whether to go to a bar on Friday night or stay home instead. This problem was made famous by Brian Arthur, an economist at the Santa Fe Institute, in the early 1990s. A Santa Fe bar called El Farol had become so popular that it was no longer always a pleasant place to go because of the crowds. (It was reminiscent of baseball player Yogi Berra’s famous comment about the New York City restaurant Toots Shor’s. “Toots Shor’s is so crowded,” said Yogi, “nobody goes there anymore.”)

Arthur saw in the El Farol situation a problem of decision making with limited information. You don’t know in advance how many people will go to the bar, but you assume that everybody would like to go unless too many other people are going also. Above some level of attendance, it’s no fun. This situation can be framed as a game where the winners are those in the minority— you choose to go or stay home and hope that the majority of people make the opposite choice.

In 1997, Damien Challet and Yi-Cheng Zhang developed the mathematics of the El Farol problem in detail, in the form of what they called the minority game. Since then it has been a favorite framework of many physicists for dealing with economic and social issues.11

In the basic version of the game, each would-be bar patron (in mathematical models, such customers are called “agents”) possesses a memory of how his or her last few bar-going decisions have turned out. (Players find out after every trial whether the stay-at-home or bar-going choices were the winners.) Suppose that Friday is your regular drinking night, and you can remember what hap-

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