Prisoner’s Dilemma

VOLUNTEER’S DILEMMA

Just as the prisoner’s dilemma has a multiperson version, so does chicken: the “volunteer’s dilemma.” You’re sitting at home one night and the lights go out. You look outside and see that all the lights in the neighborhood are out. The electric company will send someone out to fix the problem – provided, that is, someone calls to tell them about it. Should you call? Naw – let someone else do it.

In a volunteer’s dilemma, someone has to take on a chore that will benefit everyone. It doesn’t matter who does it – but everyone’s in trouble if no one does it.

In two-person chicken, it is desirable that one player “volunteer” to swerve for the common good. When no one volunteers, both get stung. When both volunteer, each player kicks himself for not driving straight. The n-person version looks something like this:

 At least one person volunteers Everyone says, let someone else do it You volunteer 1 – You say, let someone else do it 2 0

The “1” in the upper left cell signifies that you get the benefit of having the electric company notified (2) minus the slight inconvenience of phoning them. In fact, you might wonder what the fuss is about in the above anecdote: Why not just phone the power company and be done with it?

Let’s adjust the payoffs. If the phone lines were also out and you had to hike three miles in the snow to notify the electric company, the spread between volunteering and not volunteering would be greater. Then you’d be more inclined to let someone else notify the electric company. You’d also be more worried that no one else would do it.

You’re at a really strict boarding school. To defy the headmaster, all the students get together and steal the old school bell from the belfry. The next day, the headmaster is furious. He calls everyone into the auditorium and makes an offer: Provided that someone informs him of the whereabouts of the bell by the end of the day, that person or persons (who is clearly guilty) will receive a failing grade for the semester. If no one tells him where the bell is, everyone will receive a failing grade for the whole year. The students know that everyone is equally guilty, and all know where the bell is. Even the scapegoat(s) is better off than he would be if no one confessed. Do you volunteer?

Let’s turn up the juice a little more. The worst form of the volunteer’s dilemma occurs when the volunteer’s payoff is almost identical with the “catastrophe” payoff when no one volunteers. Then there is a lifeboat situation where one person must “sacrifice” himself or all are in trouble – but with the all-important difference that the persons involved cannot draw straws or otherwise confer with each other.

This is similar to one of the dilemmas mentioned in the first chapter. You and ninety-nine friends are held captive in a problem box. Every person is in a separate soundproof cubicle. Each cubicle has a button. If you push the button you die. But if no one pushes the button before the big clock of doom on the wall strikes twelve, everyone dies.

The worst possible outcome is for no one to push the button. To you, the next-to-worst outcome is for you to push the button. Then you die. a hero. Unfortunately, there is no guarantee that your death was necessary (someone else might push the button too) or even that it did any good (it is barely possible that everyone pushed the button and they all died anyway). The most desired outcome, of course, is for you to survive by having someone other than you push the button.

The volunteer’s dilemma is widespread. The classic example in American urban lore is the 1964 murder of Kitty Genovese, the New York woman who was stabbed to death in the courtyard of her Kew Gardens apartment house while thirty-eight neighbors watched and heard her cries but did not come to her aid. Game theorist Anatol Rapoport noted (1988), “In the U.S. Infantry Manual published during World War II, the soldier was told what to do if a live grenade fell into the trench where he and others were sitting: to wrap himself around the grenade so as to at least save the others. (If no one “volunteered,” all would be killed, and there were only a few seconds to decide who would be the hero.)” Another military example occurs in Joseph Heller’s war novel Catch-22. When Yossarian balks at flying suicide missions, his superiors ask “What if everybody felt that way?” Yossarian responds, “Then I’d certainly be a damned fool to feel any other way. Wouldn’t I?”

Rapoport notes that the Fuegian language of the natives of Tierra del Fuego contains the word mamihlapinatapai, meaning, “looking at each other hoping that either will offer to do something that both parties desire but are unwilling to do.”

William Poundstone, Prisoner’s Dilemma, Doubleday, NY 1992, pp. 201-203.