Excerpts from

Prisoner's Dilemma

William Poundstone


Like the prisoner's dilemma, "chicken" is an important model for a diverse range of human conflicts.

The adolescent dare game of chicken came to public attention in the 1955 movie Rebel Without a Cause. In the movie, spoiled Los Angeles teenagers drive stolen cars to a cliff and play a game they call a "chickie run." The game consists of two boys simultaneously driving their cars off the edge of the cliff, jumping out at the last possible moment. The boy who jumps out first is "chicken" and loses.

The plot has one driver's sleeve getting caught in the door handle. He plunges with his car into the ocean. The movie, and the game, got a lot of publicity in part because the star, James Dean, died in a hot-rodding incident shortly before the film's release. Dean killed himself and injured two passengers while driving on a public highway at an estimated speed of 100 mph.

For obvious reasons, chicken was never very popular – except in Hollywood. It became almost an obligatory scene of low-budget "juvenile delinquent" films in the years afterward. Wrote film critic Jim Morton (1986), "The number of subsequent films featuring variations on Chicken is staggering. Usually it was used as a device to get rid of the 'bad' kid – teens lost their lives driving over cliffs, running into trains, smacking into walls and colliding with each other. The creative abilities of Hollywood scriptwriters were sorely taxed as they struggled to think of new ways to destroy the youth of the nation."

Bertrand Russell saw in chicken a metaphor for the nuclear stalemate. His 1959 book, Common Sense and Nuclear Warfare, not only describes the game but offers mordant comments on those who play the geopolitical version of it. Incidentally, the game Russell describes is now considered the "canonical" chicken, at least in game theory, rather than the off-the-cliff version of the movie:

‘Since the nuclear stalemate became apparent, the Governments of East and West have adopted the policy which Mr. Dulles calls "brinkmanship." This is a policy adapted from a sport which, I am told, is practised by some youthful degenerates. This sport is called "Chicken!" It is played by choosing a long straight road with a white line down the middle and starting two very fast cars towards each other from opposite ends. Each car is expected to keep the wheels of one side on the white line. As they approach each other, mutual destruction becomes more and more imminent. If one of them swerves from the white line before the other, the other, as he passes, shouts "Chicken!" and the one who has swerved becomes an object of contempt....’

‘As played by irresponsible boys, this game is considered decadent and immoral, though only the lives of the players are risked. But when the game is played by eminent statesmen, who risk not only their own lives but those of many hundreds of millions of human beings, it is thought on both sides that the statesmen on one side are displaying a high degree of wisdom and courage, and only the statesmen on the other side are reprehensible. This, of course, is absurd. Both are to blame for playing such an incredibly dangerous game. The game may be played without misfortune a few times, but sooner or later it will come to be felt that loss of face is more dreadful than nuclear annihilation. The moment will come when neither side can face the derisive cry of "Chicken!" from the other side. When that moment is come, the statesmen of both sides will plunge the world into destruction.’

Russell, of course, is being facetious in implying that Dulles's "brinkmanship" was consciously adapted from highway chicken. Herman Kahn's On Thermonuclear War (1960) credits Russell as the source of the chicken analogy.

Chicken readily translates into an abstract game. Strictly speaking, game theory's chicken dilemma occurs at the last possible moment of a game of highway chicken. Each driver has calculated his reaction time and his car's turning radius (which are assumed identical for both cars and both drivers); there comes a moment of truth in which each must decide whether or not to swerve. This decision is irrevocable and must be made in ignorance of the other driver's decision. There is no time for one driver's last-minute decision to influence the other driver's decision. In its simultaneous, life or death simplicity, chicken is one of the purest examples of von Neumann's concept of a game.

The way players rank outcomes in highway chicken is obvious. The worst thing that can happen is for both players not to swerve. Then – BAM!! – the coroner picks both out of a Corvette dashboard.

The best thing that can happen, the real point of the game, is to show your machismo by not swerving and letting the other driver swerve. You survive to gloat, and the other guy is "chicken."

Being chicken is the next to worst outcome, but still better than dying.

There is a cooperative outcome in chicken. It's not so bad if both players swerve. Both come out alive, and no one can call the other a chicken. The payoff table might look like the following. The numbers represent arbitrary points, starting with 0 for the worst outcome, 1 for the next-to-worst outcome, and so on.

  Swerve Drive straight
Swerve 2,2 1,3
Drive straight 3,1 0,0

How does chicken differ from the prisoner's dilemma? Mutual defection (the crash when both players drive straight) is the most feared outcome in chicken. In the prisoner's dilemma, cooperation while the other player defects (being the sucker) is the worst outcome.

The players of a prisoner's dilemma are better off defecting, no matter what the other does. One is inclined to view the other player's decision as a given (possibly the other prisoner has already spilled his guts, and the police are withholding this information). Then the question becomes, why not take the course that is guaranteed to produce the higher payoff?

This train of thought is less compelling in chicken. The player of chicken has a big stake in guessing what the other player is going to do. A curious feature of chicken is that both players want to do the opposite of whatever the other is going to do. If you knew with certainty that your opponent was going to swerve, you would want to drive straight. And if you knew he was going to drive straight, you would want to swerve – better chicken than dead. When both players want to be contrary, how do you decide?

The game of chicken has two Nash equilibriums (boldface, lower left and upper right cells). This is another case where the Nash theory leaves something to be desired. You don't want two solutions, any more than you want two heads. The equilibrium points are the cases where one player swerves and the other doesn't (lower left and upper right).

Take the upper right cell. Put yourself in the place of the row player, who swerves. You're the chicken (1 point). Do you have any regrets? Well, looking at the big picture, you wish you had driven straight and. the other player had been the chicken (3 points for you). But the first rule of Monday-morning quarterbacking is that you can regret your strategy only, not your opponent's. You wouldn't want to have driven straight while the other player did. Then both of you would have crashed (0 points). Given the other player's choice, your choice was for the best.

But look: The outcome where you drive straight and the other swerves is also an equilibrium point. What actually happens when this game is played? It's hard to say. Under Nash's theory, either of the two of the equilibrium points is an equally "rational" outcome. Each player is hoping for a different equilibrium point, and unfortunately the outcome may not be an equilibrium point at all. Each player can choose to drive straight – on grounds that it is consistent with a rational, Nash-equilibrium solution – and rationally crash.

Consider these variations:

(a) As you speed toward possible doom, you are informed that the approaching driver is your long-lost identical twin. Neither of you suspected the other's existence, but you are quickly briefed that both of you dress alike – are Cubs fans – have a rottweiler named Max. And hey, look at the car coming toward you – another 1957 firecracker-red convertible. Evidently, the twin thinks exactly the way you do. Does this change things?

(b) This time you are a perfectly logical being (whatever that is) and so is the other driver. There is only one "logical" thing to do in a chicken dilemma. Neither of you is capable of being mistaken about what to do.

(c) There is no other driver, it's a big mirror placed across the highway. If you don't swerve you smash into the mirror and die.

All these cases stack the deck in favor of swerving. Provided the other driver is almost certain to do whatever you do, that's the better strategy. Of course, there is no such guarantee in general.

Strangely enough, an irrational player has the upper hand in chicken. Take these variations:

(d) The other driver is suicidal and wants to die.

(e) The other driver is a remote-controlled dummy whose choice is made randomly. There is a 50 percent chance he will swerve and a 50 percent chance he will drive straight.

The suicidal driver evidently can be counted on to drive straight (the possibly fatal strategy). You'd rationally have to swerve. The random driver illustrates another difference between chicken and the prisoner's dilemma. With an opponent you can't second-guess, you might be inclined to play it safe and swerve. Of the two strategies in chicken, swerving (cooperation) has the maximum minimum. In the prisoner's dilemma, defection is safer.

William Poundstone, Prisoner's Dilemma, Doubleday, NY 1992, pp. 197-201.

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