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Prisoner's Dilemma

By Joseph Lawler on 10.26.09 @ 4:18PM

The economist Scott Sumner calls this scene from the British show Golden Balls "he best 3:53 clip in game show history":

Sumner got the link from the famed Stanford economist John Taylor (he of the "Taylor Rule"), and notes, "As Taylor says, this is a great example to use when teaching the Prisoner's Dilemma."

There's just one problem: this is not the Prisoner's Dilemma at all. The Golden Balls' "split or steal" differs from the classic Prisoner's Dilemma in a key way, and the difference brings about a different dominant strategy.

In the classic Prisoner's Dilemma, the dominant strategy is always to betray the other prisoner, or steal, in the Golden Balls example. But the entire point of the Prisoner's dilemma is that the two participants are separated and cannot communicate -- that's why they are prisoners.

If you can communicate, as these two contestants clearly can, the game changes entirely. Because the dominant strategy (which the girl in the clip employs) is to steal, you have to assume that the person up against you is going to steal. So instead of trying to convince them to split with you, why not simply announce that you are going to steal, no matter what? You can even make a contract to give them back a certain amount of the winnings, buying off their cooperation. If you convince them that you are going to split no matter what, they are going to have to resign to accepting whatever you hand out to them, because otherwise they'll get nothing. In doing so you will in fact turn the situation into another well-known game: the ultimatum game.