To help us determine the answer, let's come up with a payoff matrix for each prisoner. The value in each cell is the time spent in prison, so the prisoners will try to end up in the matrix cell with the lowest number. The first number of each pair refers to the prison time of prisoner 1, and the second number to prisoner 2.

Prisoner 2


Not Confess

Prisoner 1  


5, 5

0, 20

Not Confess

20, 0

1, 1

Let's assume the role of prisoner 1. We're looking to minimize our prison time. Since we have no way of knowing whether our partner in crime has confessed, let's first assume that he has not. If Prisoner 1 doesn't confess either, both will go to prison for 1 year. Not bad. But, if Prisoner 1 confesses, he will go free, while his partner rots away in jail. We'll assume that there is no "honor among thieves" and each prisoner only cares about minimizing his jail time. From the above discussion, it is obvious that if Prisoner 2 does not confess, Prisoner 1 is definitely better off confessing.

Now let's look at the other possibility. Say prisoner 2 confesses. If Prisoner 1 does not confess, he will go to jail for 20 years. But if he does confess, he will get only 5 years in prison. It is clearly better to confess in this case as well.

So is that it? Is the problem solved? Is each prisoner better off confessing? Well, it may seem so from the above discussion, but if we look at the payoff matrix, it is clear that the best payoff for both prisoners is when neither confesses! But game theory advocates that both confess.

This "game" can be generalized to any situation when two players are in a non-cooperative situation where the best all-around situation is for both to cooperate, but the worst individual outcome is to be cooperating player while the other player defects.

On the one hand, it is tempting to defect, or confess. Since you have no way of influencing the other player's decision, no matter what he does, you're better off confessing. But on the other hand, you're both in the same boat. Both of you should be sensible enough to realize that cheating undermines the common good.

There is no single "right" solution to the Prisoner's Dilemma (that's why it's a dilemma). Its implications carry into psychology, economics, and many other fields.

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