Excerpts from

Prisoner’s Dilemma

William Poundstone


Of the practical dilemmas in Flood’s paper, by far the most important was the third, dubbed “A Non-cooperative Pair.” The first scientific discussion of a prisoner’s dilemma, this part of the paper describes an experiment done in January 1950 in collaboration with RAND colleague Melvin Dresher.

The original experiment is probably not the best way to introduce the prisoner’s dilemma. Instead, let’s jump to a modern version of the prisoner’s dilemma, in the form of a story.

Suppose you have stolen the Hope Diamond and are trying to sell it. You learn of a potential buyer, an underworld figure called Mr. Big – the most ruthless man on earth. Though extremely intelligent, Mr. Big is notoriously greedy and equally notorious for double-crossing. You have agreed to exchange the diamond for an attaché case full of $100 bills. Mr. Big suggests that you meet out in a deserted wheat field somewhere to make the exchange. That way there are no witnesses.

You happen to know that Mr. Big has negotiated with many other sellers of contraband in the past. Each time he has suggested a remote locale for the exchange. Every time, Mr. Big showed up and opened the attaché case to show his good will. Then Mr. Big pulled out a tommy gun, shot the other person dead, and left with both the money and the goods.

You say you don’t think the wheat-field plan is such a good idea.

You suggest the two-wheat-field plan. Mr. Big hides his attaché case of money in a wheat field in North Dakota, while you hide the diamond in a wheat field in South Dakota. Then both parties go to the nearest public phone and exchange directions on how to find the hidden goods.

This plan has built-in safeguards (tactfully, you don’t mention that). You need have nothing of value on you when you go to recover Mr. Big’s attaché case. Mr. Big (who is no homicidal maniac, just a shrewd businessman) will have no reason to wait in the North Dakota field to ambush you. Mr. Big agrees to the two-wheat-field plan.

You find a wheat field in South Dakota. As you are about to hide the attaché case with the diamond, an idea pops into your head. Why not just keep the diamond? Mr. Big will have no way of knowing that you betrayed him until he gets to South Dakota (you would wait for his phone call and give him directions as if nothing were wrong). By that time, you would be in North Dakota to pick up the money. Then you would hop on a plane to Rio. You would never see Mr. Big again.

A worse thought pops into your head. Mr. Big must be thinking the exact same thing! He’s just as smart as you are, and probably ten times greedier. He has equal incentive to betray you, and you wouldn’t be able to retaliate any more than he will. The dilemma looks like this:

  Mr. Big sticks to agreement Mr. Big cheats
You stick to agreement Deal goes through: You get money, Mr. Big gets diamond You get nothing, Mr. Big walks away with diamond and money
You cheat You walk away with money and diamond, Mr. Big gets nothing A lot of trouble for nothing: you keep diamond, Mr. Big keeps money

The problem is that you have to make a decision in ignorance of Mr. Big’s decision and then live with it. You would most prefer to get the money without surrendering the diamond. Mr. Big would most prefer to get the diamond for nothing. Make no mistake about it, though, you both would be sincerely happy to have the deal go through to the letter of the agreement. Mr. Big really wants that diamond for his trophy case – not just any diamond, but the one-and-only Hope Diamond. He knows that you’re his only chance to get it. Likewise, you really want the money. Mr. Big has offered a fabulous price, far more than anyone else would.

The best outcome all around is the upper left cell – the result when both comply with the bargain. But the best outcome for any individual is to be the lone cheater. The worst outcome is to be a sucker who sticks to the agreement while the other person cheats.

Here’s one way of looking at it. Your actions in South Dakota cannot possibly influence Mr. Big’s actions in North Dakota. No matter what Mr. Big does, you are better off keeping the diamond for yourself. If Mr. Big leaves the money, you end up with the money and the diamond. If Mr. Big leaves nothing, at least you still have your diamond to sell to someone else. So you should cheat and leave nothing.

Here’s another way of looking at it. You’re both in the same boat. Take the reasoning of the previous paragraph a step further. Mr. Big is perfectly capable of coming to the same conclusion, that it is “rational” to cheat. Then both of you will cheat, and both will go to a lot of trouble for nothing. Logic (?) blocks a deal beneficial to both parties. There’s nothing logical about that! Therefore you should stick to the agreement. You should be sensible enough to realize that cheating undermines the common good.

This is a prisoner’s dilemma, and now is a good time to ask yourself, what would you do?

This formulation of the dilemma was popularized by cognitive scientist Douglas Hofstadter. Here the dilemma is particularly easy to appreciate. Even among the law-abiding, most transactions are potential prisoner’s dilemmas. You agree to buy aluminum siding: how do you know the salesman won’t skip town with your down payment? How does he know you won’t stop payment on the check? In my grade school, the accepted way to swap toys was for each child to set his toy down on the ground in plain sight some distance from the other, and then to run to the other toy. (If they just handed the toys over, one child could grab both.) With this arrangement, each child could see that the other had surrendered his toy, avoiding the cheating dilemma above! The slightly more adult equivalent of this is the escrow in real estate transactions. And speaking of crime, newspaper accounts of soured drug deals often report that someone tried to cheat more or less as above (not always with impunity).

William Poundstone, Prisoner’s Dilemma, Doubleday, NY 1992, pp. 103-105.

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