Game theory: The nuclear button

BACKGROUND

Perhaps the simplest tactical/moral dilemma is that in which each player can wipe out the other if he strikes first: ie, the leaders of two countries each have a finger on the nuclear button. The "best" advice is of course to push your own button as soon as possible.

DIALOGUE

(Charlotte 9, Owen 13)

Suppose you children were each in charge of a different country, and each commanded a strong force of nuclear missiles. Suppose whichever sent the missiles out first would destroy the other country and enjoy peace and prosperity. What would you do?

Owen: I'd wait for a little while.

Why?

Owen: Um...to see what happened.

But while you were waiting Charlotte might seize the opportunity to wipe you out.

Charlotte: I'd send the missiles off straight away.

Is that kind?

Charlotte: No, but I don't trust Owen.

OK. But suppose you had armies instead of missiles. Whoever moved first was bound to win in the end because of the advantage of surprise, but could expect to lose half their army and some of their cities in the course of the war.

Charlotte: I'd still move as soon as I could. Otherwise Owen's side might.

What if the situation was like this: You both have powerful armies and missiles. If one side starts a war and the other side is a bit slow responding, then the first side will probably win, and if it is lucky will suffer much less damage than the second side. But if one side starts a war and the other side is ready, both will be completely wiped out.

Owen: It would be better not to start a war.

Charlotte: Yes, but I would be on guard all the time in case he did start one.

Yes. Well that's the way it is at the moment.

COMMENT

Game theory does not necessarily provide the complete answer in any tactical situation. It may for example neglect moral aspects. Following the Second World War, the mathematical genius John Von Neumann, a pioneer in the theory of games, repeatedly advised the President of the USA to make a full scale pre-emptive nuclear strike against the Soviet Union, seeing this as the "best strategy" for the USA at the time. His advice was rejected.

Chooks, on the other hand, who are apparently lacking in moral scruple, tend to adopt the pre-emptive strike whenever it is the best strategy. In general, all other chooks in the coop represent a threat. If there is a fight in the coop, the chooks which are not initially involved tend to join in on the side of those who are winning, seizing the opportunity to kill without risk to themselves the one which is getting the worst of it. In fact animal behaviour illustrates many of the principles of game theory. See Dawkins' The Selfish Gene.

For more on game theory and nuclear war, see Nicholas Measor's essay "Games Theory and the Nuclear Arms Race". [An accessible source for Measor's essay is Singer's Applied Ethics, in which it is reprinted as chapter XIV.]

Bibliography

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