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Friday, February 08, 2008

Is Prisoner's Dilemma still teachable?

For over three decades I’ve been teaching the Prisoner’s Dilemma. This is a classic problem — perhaps the classic problem — of game theory, the misleadingly named field that lies at the intersection of mathematics and economics (with a dash of psychology and philosophy throw into the mix). Dating back to 1950, the problem can be stated as follows according to the Stanford Encyclopedia of Philosophy:
Tanya and Cinque have been arrested for robbing the Hibernia Savings Bank and placed in separate isolation cells. Both care much more about their personal freedom than about the welfare of their accomplice. A clever prosecutor makes the following offer to each. “You may choose to confess or remain silent. If you confess and your accomplice remains silent I will drop all charges against you and use your testimony to ensure that your accomplice does serious time. Likewise, if your accomplice confesses while you remain silent, they will go free while you do the time. If you both confess I get two convictions, but I’ll see to it that you both get early parole. If you both remain silent, I’ll have to settle for token sentences on firearms possession charges. If you wish to confess, you must leave a note with the jailer before my return tomorrow morning.”

The “dilemma” faced by the prisoners here is that, whatever the other does, each is better off confessing than remaining silent. But the outcome obtained when both confess is worse for each than the outcome they would have obtained had both remained silent. A common view is that the puzzle illustrates a conflict between individual and group rationality.
You can see why it is indeed a dilemma. If each prisoner acts rationally (as the economists would put it), each must confess (or defect, in the language of game theory). But both would be better off if both remain silent (or cooperate with each other, in the language of game theory)!

This used to be easy to teach. First the class discusses the problem and does the mathematics in order to understand the four options, usually presented in a 2-by-2 table (the row prisoner can cooperate or defect, the column prisoner can cooperate or defect). This is known as a simultaneous game, since neither party knows the other’s decision before making their own decision. I’ve taught this problem to a truly wide variety of classes, ranging from fifth-graders to high-school students to adults, from inner-city kids to wealthy suburbanites, and in past years the outcome was almost always the same: approximately two-thirds would choose to defect, thereby ensuring a non-optimal outcome. After further discussion of the mathematics, a few defectors would choose to cooperate, but a few cooperators would choose to defect, on the (rational) grounds that they couldn’t afford to trust the other guy. After all, no matter what the other guy does, you are indisputably better off if you defect.

But the situation has changed in recent years. Because of the infection of the “don’t snitch” ethic in our society, the vote is now overwhelming in favor of cooperating, especially among inner-city kids. No matter how much you tell them to treat it as a math problem, no matter how much you add conditions like “your accomplice has no powerful friends and can’t go after you,” people are unwilling to defect. The problem becomes unteachable. In the students’ eyes it’s no longer a dilemma.

There seem to be two solutions to this difficulty if one still believes that the Prisoner’s Dilemma provides important fodder for discussing ethical and political decisions. One solution is to modify the payoffs so that they are positive rather than negative, thereby removing the story from the realm of crime to some other less charged realm. Another possibility is to change the context so that defecting doesn’t consist of “snitching.” I’m working on it. I’ll figure out a plan before I need to teach the problem again this summer at the Crimson Summer Academy, where it forms the Big Question for half of the eleventh-grade portion of the Quantitative Reasoning course.

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