Matrix 6.5 depicts the ordinal structure of Chicken, the prototype of the dangerous game (P.G. Swingle, Dangerous games. In P.G. Swingle (Ed.), The Structure of Conflict, New York: Academic Press, 1970, pp. 235-276). Its name derives from various versions of a gruesome pastime that originated among Californian teenagers in the 1930s and became notorious in 1955 through Nicholas Ray’s powerful film, Rebel Without a Cause, starring James Dean. The game itself is, of course, as old as time. T.C. Schelling, (Arms and Influence, New Haven, CT: Yale University Press, 1966, p. 117) cites an example from Homer’s Iliad in which Antilochos won a game of Chicken against Menelaos 3000 years ago. The most familiar version is this: two two motorists speed towards each other. Each has the option of swerving to avoid a head-on collision and thereby being “chicken” (C) or of resolutely driving straight ahead (D). If both players are “chicken”, the outcome is a draw with payoffs of (3, 3), and if both drive straight ahead, they risk death or serious injury (1, 1). But if one chickens out by swerving while the other exploits this cautious choice by driving straight on, the “chicken” loses face (but is not killed), and the “exploiter” wins a prestige victory based on courage or machismo, (2, 4) or (4, 2) depending on who is chicken.
Once again, there are no dominant strategies and the maximin strategies intersect in the (C, C) outcome. This outcome is not a Nash equilibrium, so a player can benefit by deviating unilaterally from it. The pure-strategy Nash equilibria in Chicken are the asymmetric (C, D) and (D, C) outcomes. The “exploiter” who deviates unilaterally from maximin gains an advantage and, in contrast to the games examined above, invariably affects the other player adversely by so doing. By trying to get the maximum payoff, the “exploiter” not only harms the other player but also exposes both players to the risk of a disastrous outcome. This is what makes Chicken a dangerous game.
The game of Chicken has some very peculiar properties. The first is its compulsive character: it is impossible to avoid playing with someone who is insistent. A person who has refused a challenge to play Chicken has effectively played and lost. The second peculiarity concerns the effects of commitment. A player who succeeds in making a credible commitment to choose the risky D strategy is bound to win at the expense of the other player, provided the other player is rational. This provides a game theory interpretation of the motto “Who dares wins” of the dreaded British Special Air Service (SAS). A person who enjoys a reputation of recklessness is at a decided advantage in a game of Chicken on account of the fear that this induces in any rational opponent. For this very reason, long-term prisoners often cultivate reputations for recklessness, as the following quotation from a famous ex-convict illustrates:
A con like “Harry”, who had a record of violent assaults on both warders and other prisoners, could come into the T.V room and virtually dictate what programme would be watched. With no more than a perfunctory remark such as, “What, we having the film on?” as he switched to the programme of his choice, he could control what thirty other cons were going to watch. On one occasion when I observed him do this, I’d just witnessed a show of hands which had voted for the programme which Harry had turned off. Nobody, however, protested at Harry’s action. The next day I casually questioned some of the cons who’d acquiesced to Harry’s demands. A few gave an account of what happened which accorded with the reality of the incident. “Well, Harry gets his own way ’cause he can have a right row”, one replied. Other cons, though, rationalized explanations for what happened in order to protect their self-image from the implication that they’d backed down. … Another commented, “I couldn’t give a fuck what was on. Like the film or the football, what’s the difference?” Yet this con, like the others, had voted for the football which Harry had decided wouldn’t be watched.If a game of Chicken is repeated a number of times, a player who gains an early advantage is likely to maintain and increase it: nothing succeeds like success in the field of brinkmanship. Players who have successfully exploited others gain confidence in their ability to get away with the risky strategy in the future, and this makes their opponents all the more fearful of deviating from the cautious maximin strategy.
(J. McVicar, Postscript, pp. 225-226. In S. Cohen & L. Taylor, Psychological Survival: The Experience of Long-Term Imprisonment, 2nd ed., 1981, pp. 221-229.)
A third peculiarity of Chicken revolves around what Daniel Ellsberg (cited in Schelling, 1960, p. 13) called “the political uses of madness”. A player who is seen to be irrational, not in control, or frankly “crazy”, gains a paradoxical advantage in a game of Chicken: people tend to give a wide berth to a lunatic. The following imaginary example, in which a player of automobile Chicken deliberately acts irrationally in order to create fear in the opponent and thereby gain a strategic advantage, is taken from Herman Kahn’s book On Escalation, New York: Praeger, 1965:
The “skilful” player may get into the car quite drunk, throwing whisky bottles out of the window to make it clear to everybody just how drunk he is. He wears very dark glasses so that it is obvious that he cannot see much, if anything. As soon as the car reaches high speed, he takes the steering wheel and throws it out of the window. If his opponent is watching, he has won. If his opponent is not watching, he takes the steering wheel and throws it out of the window. If his opponent is watching, he has won. If his opponent is not watching, he has a problem; likewise if both players try this strategy. (p. 11)The American president Richard Nixon reportedly used the same principle during the Vietnam war. He told his aide H.R. Haldeman: “I call it the Madman Theory, Bob. I want the North Vietnamese to believe that I’ve reached the point where I might do anything to stop the war. Well just slip the word to them that ‘for God’s sake, you know Nixon is obsessed about Communism. We cant restrain him when he’s angry — and he has his hand on the nuclear button’ and Ho Chi Minh himself will be in Paris in two days begging for peace” (H.R. Haldeman and J. DiMona, The Ends of Power. New York: Times Books, 1978, p. 83).
Small children are remarkably adept at the political uses of madness, and so are some inmates of psychiatric hospitals. Even at the level of international politics, Adolf Hitler won a series of important games of Chicken largely on account of his carefully cultivated reputation for irrationality. It is ironical that game theory, a discipline devoted to the logic of rational decision making, should provide a strategic justification for irrationality.
The game of Chicken has been used to model a variety of incidents involving bilateral threats in national and international politics. One encounter with the strategic structure of Chicken was the Cuban missile crisis of October 1962, involving the United States and the Soviet Union (as it then was), which brought the world to the brink of a nuclear holocaust. The crisis was precipitated by the discovery of Soviet nuclear missile emplacements in Cuba. The two major strategies considered by the United States were (a) to mount a naval blockade of the island, and (b) to launch a “surgical” air strike to knock out the missiles. The Soviet leaders had to choose between (a) withdrawing, and (b) maintaining their missiles. A model of this situation, based on game theory analyses by N. Howard, (Paradoxes of Rationality: Theory of Metagames and Political Behavior, Cambridge, MA: MIT Press, 1971, pp. 181-184) and S. J. Brams (Game Theory and Politics, New York: Free Press, 1975, pp. 39-47; S. J. Brams, Paradoxes in Politics: An Introduction to the Nonobvious in Political Science, New York: Free Press, 1976, pp. 114-126) is shown in Matrix 6.6.
— Andrew M. Colman, Game Theory and Its Applications: In the Social and Biological Sciences, Routledge; 2nd Rev edition, 1995, pp. 111-115
Finally we were taken to a small patio for lunch with Kissinger. His aide Alexander Haig, now a general, was at the table. As we all said hello, Kissinger turned to Lloyd and said, in his ingratiating manner, “You know, I have learned more from Dan Ellsberg than from any other person—” I assumed he was about to repeat what he’d said about me at Rand two years earlier: “in Vietnam.” But instead he said, “—about bargaining.”
I was taken aback. Bargaining? For a moment I didn’t have any idea what he was referring to. Then I remembered the talks I had given to his seminar at Harvard in 1959, from my Lowell Lecture series, “The Art of Coercion.” That had been eleven years earlier. I said, “You have a very good memory.”
Guttural drawl: “They were very good lectures.”
Nice. Except that when I thought about it later, it made the hair on the back of my neck stand up. The lectures I had given to his class had had to do with Hitler’s blackmail of Austria and Czechoslovakia in the late thirties that had allowed him to take over those countries just by threatening their destruction. One of the talks was titled “The Theory and Practice of Blackmail,” and the other was “The Political Uses of Madness.” Hitler had deliberately cultivated among his adversaries the impression of his own irrational unpredictability. He couldn’t be counted on not to carry out a threat to do something crazy, mutually destructive. It worked for him, up to a point, because he was crazy, madly aggressive, and reckless. But after a certain point it brought the world down around him. It wasn’t a tactic I was recommending for the United States, or anyone else, for that matter. Far from it. For someone to imitate Hitler in this respect was to cultivate madness and court disaster.
— Daniel Ellsberg, Secrets: A Memoir of Vietnam and the Pentagon Papers, Penguin Books, 2002, p. 344