How We Learned to Stop Worrying and Love the Game.
Posted: June 19, 2011 Filed under: Canonical Games, Chicken, Normal-Form Games, Nuclear Chicken 2 Comments
It is the mid-1950s, and the United States and Soviet Union are in the midst of a nuclear arms race. In the “War Room,” the President, a general, and an eccentric, wheelchair-bound genius with a thick European accent debate the merits of a first-strike attack that would obliterate all of the Soviet Union before it can retaliate. Here, fiction diverges from reality.
Indeed, a Hungarian wheelchair-confined mathematician on the verge of chemotherapy-induced dementia, John von Neumann, was transported to the White House to advise President Eisenhower[1]. Von Neumann, a founding father of game theory, believed that a first-strike that destroyed the Soviets before they could build an H-bomb was the key to ending the nuclear threat as well as allowing the US to maintain its position as the only nuclear superpower[2].
In Stanley Kubrick’s Dr. Strangelove, the Soviets have a deterrence plan — a Doomsday Device that automatically activates and destroys life on Earth for 100 years if Russia is bombed. The device also cannot be disarmed, and so by building such a machine, the Soviets have made a “completely credible and convincing” threat for deterrence[3]. However, it is revealed by the Soviet ambassador that no one yet knows of the device, since the Soviet Premier had wanted to unveil it with fanfare.
The Americans also have a retaliatory measure in place, “Wing Attack Plan R,” which allows Field Commanders to bomb the Soviet Union in the case that Washington is destroyed by a Soviet first attack. It happens that Brigadier General Jack D. Ripper believes that Communists are poisoning the water and, knowing nothing of the Doomsday Device, orders his nuclear-armed B-52s to attack. He too has effected measures to prevent the recall code from being obtained — and even when it is finally obtained and broadcasted, one of the bombers has a defective radio and was beyond contact. Major Kong rides the bomb as it falls from the plane, and mushroom clouds erupt around the globe.
“The whole point of having a Doomsday Machine is lost if you keep it a secret. Why didn’t you tell the world?”
The nuclear game of Dr. Strangelove shares characteristics with the game of Chicken, where two vehicles accelerate toward each other and the loser is the driver who swerves. If neither swerves, mutual destruction results:
| Swerve | Straight | |
| Swerve | Tie, Tie | Lose, Win |
| Straight | Win, Lose | Crash, Crash |
| Fig. 1: A payoff matrix of Chicken | ||
| Swerve | Straight | |
| Swerve | 0, 0 | -1, +1 |
| Straight | +1, -1 | -10, -10 |
| Fig. 2: Chicken with numerical payoffs[4] | ||
The only pure strategy equilibria for Chicken are (straight, swerve) and (swerve, straight). Likewise, inDr. Strangelove‘s game of nuclear chicken, the pure strategy equilibrium is to allow one country to be the nuclear power and for the other not to threaten:
| Disarm | Bomb | |
| Disarm | Tie, Tie | Lose, Win |
| Bomb | Win, Lose | Armageddon, Armageddon |
| Fig. 3: Nuclear Chicken | ||
As can be seen, the game might be won by either the US or USSR by striking first. One strategic move that can be made in Chicken is commitment to a credible threat (called Brinkmanship) — e.g. you could rip out your steering wheel and throw it out the window, demonstrating that your car must go straight and that your opponent must swerve to avoid mutually assured destruction.
This is the strategy that the USSR attempts to play in Dr. Strangelove, and it would have been effective if only the US and USSR both had known that the other had effectively ripped out their steering wheels. And even so, destruction of all life would not have been assured but for one deranged General Ripper’s conspiracy theories.
Game theory is often criticized for its flippance toward irrationality. What about the General Rippers of the humanity, they ask? The whole point is far from lost if we keep it a secret, because rational choices are by their nature not a secret; they can be teased out and brought out into the light. Why not tell the world?
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