GT #6

1. Sometimes, confronted with an efficient outcome that can't be reached because it isn't a NE, one or more players can take actions that change the game. This must always involve at least one player doing something that makes a move she could have had, and would have chosen, in the original game impossible, thus forcing the game onto another path – which might have a better outcome for all. This is called commitment.

2. This sort of case exposes one of many fundamental differences between the logic of non-parametric and parametric maximization. In parametric situations, an agent can never be made worse off by having more options. But where circumstances are non-parametric, one agent's strategy can be influenced in another's favour if options are visibly restricted. We'll look at some examples.

3. Suppose you own a piece of land adjacent to mine, and I'd like to buy it so as to expand my lot. Unfortunately, you don't want to sell at the price I'm willing to pay. If we move simultaneously – you post a selling price and I independently give my agent an asking price – there will be no sale. So I might try to change your incentives by playing an opening move in which I announce that I'll build a putrid-smelling sewage disposal plant on my land beside yours, thereby lowering your price. I've now turned this into a sequential-move game. However, this move so far changes nothing, and here's why. If you refuse to sell in the face of my threat, it is then not in my interest to carry it out, because in damaging you I also damage myself. In game theory we say that this threat is incredible.

4. However, I could make my threat credible by committing myself. I could sign a contract with some farmers promising to supply them with treated sewage (fertilizer) from my plant, with a escape clause releasing me from my obligation only if I can double my lot size and so put it to some other use. Now my threat is credible: if you don't sell, I'm committed to building the sewage plant. Since you know this, you now have an incentive to sell me your land in order to escape its ruination.

5. Here's another example. Two of us wish to poach a rare antelope from Kruger Park in order to sell the trophy. One of us must flush the animal down towards the second person, who waits in a blind to shoot it and load it onto a truck. You promise, of course, to share the proceeds with me. However, your promise is not credible. Once you've got the buck, you have no reason not to drive it away and pocket the full value from it. After all, I can't very well complain to the police without getting myself arrested too. But now suppose I add the following opening move to the game. Before our hunt, I rig out the truck with an alarm that can be turned off only by punching in a code. Only I know the code. If you try to drive off without me, the alarm will sound and we'll both get caught. You, knowing this, now have an incentive to wait for me.

6. Notice that in both of these cases I take an action that increases my risk of a penalty and limits my freedom of action. As noted earlier, in pre-game-theoretic economics, such actions can never be rational: for an agent facing a non-interactive environment, more freedom of action is always preferable to less. However, in the interactive context I can increase my expected utility by decreasing my freedom of action. In the first case, I won't be able to refrain from wrecking my property if you don't do as I want, and since you know this you have reason to respect my threat. In the second case, I can't refrain from turning myself over to the police if you try to cheat me, and since you know this, it's in your interest to keep your promise.

10. Notice something further about the poaching case. You prefer that I rig up the alarm, since this makes your promise to give me my share credible. If I don't do this, leaving your promise incredible, we'll be unable to agree to try the crime in the first place, and both of us will lose our shot at the profit from selling the trophy. Thus, you benefit from my binding you.

11. The nuclear stand-off between the superpowers during the Cold War was carefully studied by game theorists (who were employed by both sides). 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. (By the late 1960s, this would have meant blowing up the world.) Game theorists objected that this set up a Prisoner's Dilemma because the reciprocal threats were incredible. Suppose the USSR launched a first strike against the US. 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; he has no incentive to carry out his threat. Since the Russians know this, they should ignore the threat and strike first! Of course, the Americans are in the same position. So what we should get is a race between the two powers to be the first to attack.

12. 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 fake medical reports exaggerating Brezhnev's senility with the same end in mind. Ultimately, the Americans broke this scary symmetry by using a `doomsday device'. They equipped a worldwide fleet of submarines with enough missiles to destroy the USSR, and arranged they communications technology in such a way that the President couldn’t be guaranteed to be able to reach all 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 the classic film 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 a mad American colonel launches missiles at Russia on his own accord, and the American President offers to destroy two of his own cities as proof that the attack was an accident, 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.)