The Prisoners' Dilemma

Imagine I offer the following opportunity to Jill and Bob:

• If both of you give me a dollar, I will give each of you five dollars back.
• However, if one of you gives me a dollar and the other doesn't, I will give nothing to the one who gave me the dollar (the "sucker"), and will give 5 dollars to the one who gave me nothing.
• If both of you gives me nothing, neither of you will receive anything.

To analyze this problem, we can create a "payout table", which shows the net outcomes to each participant, for each of the four possible scenarios:

Clearly, the smartest thing for Jill and Bob to do is to both give me a dollar, and each will make a $4 profit.

However, if the two can't cooperate, and each of them is simply trying to maximize their own reward with no regards for the other, the only rational thing for each of them to do is to give me nothing. The irony, of course, is that this produces an undesirable outcome, where each of them make no profit at all.

Why is it rational for each to do something which causes an undesirable result? Let's look at Jill's situation. While she does not know and cannot influence what Bob will do, she does know that if Bob chooses to give a dollar, she will be better off if she gives nothing (making $5 profit rather than $4). She also knows that if Bob chooses not to give anything, she will be better off giving nothing as well (breaking even, rather than losing a dollar). So in all scenarios she should choose to hold on to her dollar in order to maximize her rewards, and Bob should as well.

This sort of seemingly paradoxical situation is known as a "Prisoners' Dilemma", based on a classic "game" where two captured partners in crime are separated and given a choice of implicating their partner, or saying nothing. They are offered varying jail terms depending on their choice and the other prisoner's choice. They would be better off keeping their mouths shut, but -- if they are rational -- will do as the police wish, and rat out their partner.

Many real life situations have elements of the Prisoners' Dilemma. For instance, overfishing of the world's oceans: fishermen are better off as a group if they cooperate and do not overfish. However, the individuals, unable to control what anyone else does, will maximize their rewards by taking as many fish as they can. This causes the ocean to be depleted and threatens the fishermen's livelihood. Again, individuals seeking to maximize their rewards make choices that cause them to be worse off than necessary.