The Game theory in 'Dr. Strangelove'

I was reading an introductory article on game theory today when I came across the phrase "doomsday device".. something that I'd heard in the movie 'Dr. Strangelove'. I didn't know this doomsday thing was for real! Apparently it was... the movie, ofcourse, is a satire.

The nuclear arms race that existed between the United States and the Soviet Union after WW II, led to the formation of an instance of a classic problem variant, known in Game theory, as the Prisoner's Dilemma. Both the USA and the USSR maintained the following policy: If one side launched a first strike, the other threatened to answer with a devastating counter-strike. This pair of reciprocal strategies, which by the late stages of the cold war would effectively have meant blowing up the world, was known as ‘Mutually Assured Destruction’, or ‘MAD’. Game theorists objected that MAD was mad, because it set up a Prisoner's Dilemma as a result of the fact that the reciprocal threats were incredible. Suppose the USSR launches a first strike against the USA. At that point, the American President faces the following situation. His country is already destroyed. He doesn't bring it back to life by now blowing up the world, so he has no incentive to carry out his threat, which has now manifestly failed to achieve its point. Since the Russians know this, they should ignore the threat and strike first! Of course, the Americans are in exactly the same position. Each power will recognize this incentive on the part of the other, and so will anticipate an attack if they don't preempt it. The expected outcome is therefore a race between the two powers to be the first to attack.

This game-theoretic analysis caused genuine consternation and fear on both sides during the Cold War, and produced some rather bizarre attempts at setting up strategic commitment devices. President Nixon, for example, had the CIA try to convince the Russians that he was insane, so that they'd believe that he'd launch a retaliatory strike even when it was no longer in his interest to do so. Similarly, the Soviet KGB leaked fabricated medical reports exaggerating Brezhnev's senility with the same end in mind. Ultimately, the Americans broke this deadly symmetry by using a ‘doomsday device’. They equipped a worldwide fleet of submarines with enough missiles to destroy the USSR, and arranged their communications technology in such a way that the President could not be sure to be able to reach the submarines and cancel their orders to attack if any Soviet missile crossed the radar ‘trigger line’. Of course, this strategy depended on making sure that the Russians were aware of the device.

In 'Dr. Strangelove', the world is destroyed by accident because the Russians build a doomsday machine but then keep it a secret! As a result, when the mad American colonel launches missiles at Russia on his own accord, and the American President tries to convince his Soviet counterpart that the attack was unintended, the Russian President sheepishly tells him about the secret doomsday machine. Now the two Presidents can do nothing but watch in dismay as the world is blown up - due to a game-theoretic mistake.

+

Update:

# Kubrick on game theory: "I started out being completely unfamiliar with any of the professional literature in the field of nuclear deterrence. I was at first very impressed with how subtle some of the work was -- at least so it seemed starting out with just a primitive concern for survival and a total lack of any ideas of my own. Gradually I became aware of the almost wholly paradoxical nature of deterrence or as it has been described, the Delicate Balance of Terror. If you are weak, you may invite a first strike. If you are becoming too strong, you may provoke a pre-emptive strike. If you try to maintain the delicate balance, it's almost impossible to do so mainly because secrecy prevents you from knowing what the other side is doing, and vice versa, ad infinitum . . .


## Peter Sellers played three different roles in the movie: President Merkin Muffley, RAF Group Captain Mandrake, and ex-Nazi scientist Dr. Strangelove. Kubrick originally envisioned Sellers playing a fourth role, as Major T. J. Kong (played by Slim Pickens in the film), but his inability to create the right Texan accent and a broken leg necessitated finding another actor.