Excerpts from

Prisoner’s Dilemma

William Poundstone


The stag hunt is more of a dilemma. Like chicken, it recalls dilemmas of adolescence. It’s late May, next to the last day of school. You and a friend decide it would be a great joke to show up on the last day of school with some ridiculous haircut. Egged on by your clique, you both swear you’ll get the haircut.

A night of indecision follows. As you anticipate your parents’ and your teachers’ reactions to the haircut, you start wondering if your friend is really going to go through with the plan.

Not that you don’t want the plan to succeed: the best possible outcome would be for both of you to get the haircut.

The trouble is, it would be awful to be the only one to show up with the haircut. That would be the worst possible outcome.

You’re not above enjoying your friend’s embarrassment. If you didn’t get the haircut, but the friend did, and looked like a real jerk, that would almost be as good as if both of you got the haircut.

After mulling things over, you conclude that it wouldn’t really be so bad if no one got the haircut. Maybe everyone will just forget about it. (This is what your mother says will happen.)

Of the possible outcomes, your first choice is for mutual cooperation (both get the haircut), second is unilateral defection (you don’t get the haircut, your friend does), third is mutual defection (both chicken out), and fourth is unilateral cooperation (you get the haircut, the friend doesn’t). Assume that your friend has the same preferences. The barbershop at the mall closes at nine. What do you do?

The peculiar thing about the stag hunt is that it shouldn’t be a dilemma at all. You should certainly cooperate – that is, get the hair-cut. If both of you do, both will get the best possible payoff. What spoils things is the possibility that the friend won’t be so rational. If the friend chickens out, you want to chicken out, too.

The game of stag hunt has been known by many names in the literature of game theory, among them “trust dilemma,” “assurance game,” and “coordination game.” These colorless terms have been firmly superseded by the more poetic “stag hunt,” which derives from a metaphor in Swiss-born philosopher Jean-Jacques Rousseau’s A Discourse on Inequality (1755).

The writings of Rousseau idealized primitive man and held that most social ills were the product of civilization itself. He based his philosophy on a speculative and inaccurate conception of prehistory. In A Discourse on Inequality Rousseau attempted to offer “scientific” support for his arguments with traveler’s tales that have an almost magic-realist quality today. He tells of the orangutan presented to the Prince of Orange, Frederick Henry. It slept in a bed with its head on the pillow and could drink from a cup. From reports of orangutans forcing unwanted sexual attention on women, Rousseau speculates that they were the satyrs of Greek mythology.

Part Two of the Discourse theorizes that the first human societies began when people forged temporary alliances for hunting. The “stag” is a deer in Maurice Cranston’s translation:

If it was a matter of hunting a deer, everyone well realized that he must remain faithfully at his post; but if a hare happened to pass within the reach of one of them, we cannot doubt that he would have gone off in pursuit of it without scruple and, having caught his own prey, he would have cared very little about having caused his companions to lose theirs.

The point is that no individual is strong enough to subdue a stag by himself. It takes only one hunter to catch a hare. Everyone prefers stag to hare, and hare to nothing at all (which is what the stag party will end up with if too many members run off chasing hares).

The payoffs, in arbitrary points, look like this:

  Hunt stag Chase hare
Hunt stag 3,3 0,2
Chase hare 2,0 1,1

Obviously, mutual cooperation is a Nash equilibrium. The players can’t do any better no matter what. Temptation to defect arises only when you believe that others will defect. For this reason the dilemma is most acute when one has reason to doubt the rationality of the other player, or in groups large enough that, given the vagaries of human nature, some defections are likely.

A mutiny may pose a stag hunt (“We’d all be better off if we got rid of Captain Bligh, but we’ll be hung as mutineers if not enough crewmen go along.”) Elected representatives sometimes favor a bill but are reluctant to vote for it unless they are sure it will pass. They don’t want to be in the losing minority. This was apparently the case with some of the U.S. senators voting on President Bush’s 1989 constitutional amendment to make burning of the U.S. flag a federal crime. Most opponents of the bill objected to it as a violation of freedom of expression. At the same time, they feared that if they voted against it and it passed, their opponents would brand them unpatriotic or “in favor of flag burning” in the next election. Senator Joseph R. Biden, Jr., an opponent of the bill, made the striking claim, “More than 45 senators would vote ‘no’ if they knew they were casting the deciding vote.”

Arguably, the stag hunt describes the ethical dilemma of the scientists who built the atomic bomb. Roughly: The world would be better off without the bomb (“I personally hope very much that the bombs will not explode, no matter how much effort is put into the project,” Harold Urey said of the hydrogen bomb in his 1950 speech). But we have to try to build it because our enemy will. Better we have the bomb than our enemy; better both sides have the bomb than just our enemy.

In the wake of professional hockey player Teddy Green’s 1969 head injury, Newsweek stated:

Players will not adopt helmets by individual choice for several reasons. Chicago star Bobby Hull cites the simplest factor: “Vanity.” But many players honestly believe that helmets will cut their efficiency and put them at a disadvantage, and others fear the ridicule of opponents. The use of helmets will spread only through fear caused by injuries like Green’s – or through a rule making them mandatory.... One player summed up the feelings of many: “It’s foolish not to wear a helmet. But I don’t – because the other guys don’t. I know that’s silly, but most of the players feel the same way. If the league made us do it, though, we’d all wear them and nobody would mind.”

William Poundstone, Prisoner’s Dilemma, Doubleday, NY 1992, pp. 218-221.

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