THE PRISONER'S DILEMMA

The Prisoner's Dilemma is one of the great ironies of life, one that occurs with depressing frequency. Even though individuals may wish to cooperate with each other to achieve a better result, sometimes their own self-interest prevents them, and accomplishes a worse result instead. This is one of the strongest refutations around to the "invisible hand," which supposedly guides self-interested individuals to the best group benefit.

The Prisoner's Dilemma can be a little difficult to understand at first, but stick with it, because you will be rewarded with one of the great observations of life.

There are many versions of the Prisoner's Dilemma, but they all describe the same principle. Suppose two criminals, Tom and Harry, have robbed and murdered someone, been caught by the police and taken to jail. The police have excellent evidence tying them to the robbery but no evidence on who committed the murder. Therefore, the police keep the two prisoners isolated and take them to separate interrogation rooms. There, they offer them the same deal. If both do not confess, the police will at least pursue charges of robbery, which will land both of them five years in jail. If Tom does confess, however, implicating Harry in the murder, then Tom will receive only one year in jail, and Harry will receive the death sentence. The police make sure to tell him that Harry is being made the same offer. Finally, if both confess, the police will offer them both 15 years in jail.

Now, consider each prisoner's dilemma. Personally, Tom has everything to gain by confessing. If his partner confesses, Tom gets 15 years by confessing himself and the death sentence if he does not, so in this case it is better for Tom to confess. But if his partner does not confess, Tom gets one year by confessing and five if he does not, so, again, it's in his best interest to confess.

Once both prisoners confess and meet in jail to begin their 15-year sentences, both will realize they have been duped. If they had both refused to confess, they would be serving five years in jail instead of 15. Their self-interest led to an even worse result than if they had cooperated.

A diagram may help explain this irony: 
                    Tom confesses            Tom doesn't confess
                   --------------------!-------------------------
Harry confesses     Tom gets 15        !     Tom gets death
                    Harry gets 15      !     Harry gets 1
                   --------------------!-------------------------
Harry doesn't       Tom gets 1         !     Tom gets 5
confess             Harry gets death   !     Harry gets 5

If you take game theory in college, you will study dozens of these diagrams. Take some time to become completely familiar with it before proceeding, if necessary.

Each box contains the result of Tom and Harry's decisions. For example, the first box in the upper left-hand corner explains what happens when both Tom and Harry confess.

Now, notice the vertical column in which Tom confesses, and the vertical column in which Tom does not confess. Compare these two columns horizontally, and the shortest jail sentence for Tom always occur in the left column. In this case, Tom has what game theorists call a dominant strategy -- confess. It will always lead to his best personal result.

It will not, however, lead to the best joint result. In order to gain the much easier five-year sentence, each would have to risk their worst personal result: the death sentence. Each would have to trust the other not to try for a one-year prison term -- and no one trusts another person that much. In fact, suppose that the police allowed Tom and Harry the chance to meet face-to-face before striking a deal. Tom and Harry, both desiring the 5-year sentence, quickly agree not to confess. When they bring them back to their separate interrogation rooms, however, the dilemma would exist just as strongly as before! Tom would think, "I'm pretty certain Harry is not going to confess, so I can double-cross him and only get one year by confessing. I will never have to fear revenge because he will get the death sentence, so I've got nothing to lose; I'll confess. On the other hand, if I don't confess, I'm risking that Harry will not double-cross me... then I'll be risking the death sentence. The best thing to do is confess."

"Many people, firms and even nations have been gored on the horns of the prisoner's dilemma," write famed game theorists Avinash Dixit and Barry Nalebuff in their classic book, Thinking Strategically. They give the example of the nuclear arms race: in negotiations over nuclear arms reductions, the worst result for America would have been for the Soviet Union to keep its nuclear weapons but for America to disarm completely. Mutual disarmament was equally risky, because America could not be sure that the Soviets were not secretly producing these weapons in underground factories. Therefore, the safest and most self-interested option was to produce nuclear weapons no matter what the Soviets did. The prisoner's dilemma emerges here in all its terrible irony: both sides could have saved trillions of dollars and their peace of mind by undergoing mutual disarmament. But their self-interest led to an even worse result.

The same thing happens in the free market. Until a few decades ago, the tobacco industry was allowed to advertise cigarettes on TV. This was an enormously expensive cost of doing business, but competing firms had no choice; if they did not advertise, their rivals would, threatening to take over the market. It would have been in the best interest of all the tobacco companies to forge an industry-wide agreement to stop advertising. But no single firm wanted to risk it. Then along came the government, and banned TV cigarette ads for reasons of public health. Interestingly, this ban was strenuously opposed by the tobacco companies at the time. But their opposition proved to be misguided. After the ban took place, all the tobacco firms found that their profits improved. It was a classic example of individual benefit deriving not from self interest, but from group action.

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