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Stardate
20020219.2113 (On Screen): More on game theory's "tit for tat". In the drug-deal game, note that what keeps each guy honest is the knowledge that there may be consequences tomorrow for cheating today. But when the relationship is about to end, there is no tomorrow and thus no incentive to be fair today. And it's not at all uncommon in such a case for one side or both sides to cheat on the last day.
By the same token, something like that can happen in war, and it's one reason to fear doomsday weapons. In the "war" game, I deter you from using poison gas by having poison gas of my own. But if you're near losing the war, and if there's no tomorrow, then there's no longer any deterrent to keep you from using gas against me.
That's why it is dangerous to invade nations with weapons of mass destruction; when all is lost, there is now a rational game-theory incentive for them to blast you with them. Tit-for-tat doesn't solve that because it doesn't solve the end-of-sequence problem. In the real world, all you can do is to be really careful and hope that by the time you get to that point you've already eliminated his ability to use the doomsday option.
In principle, the end-game problem can be solved by a situation where neither side actually knows when the game will end. If they only find out that a given exchange was the last one after it takes place, then they can't use that knowledge to cheat. On the other hand, if one side knows that it is the last exchange but the other side does not, the side that knows has the advantage and will screw the other guy. In the real world, there's no easy way to arrange it so that neither side knows when the relationship will end. Therefore, if the game must end then you want to be the guy who decides when it ends.
Update: David Janes and I have been exchange emails about this; he summarizes a couple of them here and here.
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