In their simplest example, two players, whom we will call Jacob and Charles, independently and simultaneously choose an amount from 180 units to 300 units. Both players are paid the lower of the two amounts, and some amount R (greater than 1) is transferred from the player who chooses the larger amount to the player who chooses the smaller one. If they both pick the same number, they both are paid that amount, but no transfer is made. So if Jacob chooses 200 and Charles chooses 220, the payoff to Jacob is 200+R and the payoff to Charles is 200-R.
If Jacob thinks Charles will say 200, then Jacob will want to announce 199. But if Charles thinks Jacob will announce 199, then Charles should say 198. And so on. The only consistent pair of beliefs is when each thinks the other will say 180.
When Goeree and Holt performed this experiment with R(EQ)180, nearly 80 percent of the subjects picked 180, which is the Nash prediction. When they set R(EQ)5, and reran the experiment (with different subjects), however, the outcomes were completely reversed, with nearly 80 percent choosing 300.
Findings of this sort have stimulated the development of "behavioral game theory," which tries to formulate a theory of how to understand games involving real people, rather than those mythical "fully rational" people.
Consider, for example, the "guess half the average" game described earlier. Oscar, a simpleminded player, might think that any number between zero and 100 is equally likely, so he would guess 50. Emmy, who is more sophisticated, might figure that if lots of people were like Oscar and say 50, then she should say 25. Tony, who is yet more sophisticated, figures that if lots of people think like Emmy, then he should say 12 or 13.
An economist named Rosmarie Nagel ran a game like this a few years ago and found that the choices do tend to cluster around 50, 25 and 12.
In fact, the winning choice turned out to be close to 13, a number chosen by about 30 percent of the players. In this game the best strategy wasn't the Nash equilibrium, but it wasn't so far away from it either.
Back to picking up girls. In the movie, the fictional John Nash described a strategy for his male drinking buddies but didn't look at the game from the woman's perspective, a mistake no game theorist would ever make. A female economist I know once told me that when men tried to pick her up, the first question she asked was: "Are you a turkey?" She usually got one of three answers: "Yes," "No," and "Gobble-gobble." She said the last group was the most interesting by far. Go figure.
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