Doomsday Machines and Bluff

On Bilateral Monopolies: […] Mary has the world’s only apple, worth fifty cents to her. John is the world’s only customer for the apple, worth a dollar to him. Mary has a monopoly on selling apples, John has a monopoly (technically, a monopsony, a buying monopoly) on buying apples. Economists describe such a situation as bilateral monopoly. What happens? Mary announces that her price is ninety cents, and if John will not pay it, she will eat the apple herself. If John believes her, he pays. Ninety cents for an apple he values at a dollar is not much of a deal but better than no apple. If, however, John announces that his maximum price is sixty cents and Mary believes him, the same logic holds. Mary accepts his price, and he gets most of the benefit from the trade. This is not a fixed-sum game. If John buys the apple from Mary, the sum of their gains is fifty cents, with the division determined by the price. If they fail to reach an agreement, the summed gain is zero. Each is using the threat of the zero outcome to try to force a fifty cent outcome as favorable to himself as possible. How successful each is depends in part on how convincingly he can commit himself, how well he can persuade the other that if he doesn’t get his way the deal will fall through. Every parent is familiar with a different example of the same game. A small child wants to get her way and will throw a tantrum if she doesn’t. The tantrum itself does her no good, since if she throws it you will refuse to do what she wants and send her to bed without dessert. But since the tantrum imposes substantial costs on you as well as on her, especially if it happens in the middle of your dinner party, it may be a sufficiently effective threat to get her at least part of what she wants. Prospective parents resolve never to give in to such threats and think they will succeed. They are wrong. You may have thought out the logic of bilateral monopoly better than your child, but she has hundreds of millions of years of evolution on her side, during which offspring who succeeded in making parents do what they want, and thus getting a larger share of parental resources devoted to them, were more likely to survive to pass on their genes to the next generation of offspring. Her commitment strategy is hardwired into her; if you call her bluff, you will frequently find that it is not a bluff. If you win more than half the games and only rarely end up with a bargaining breakdown and a tantrum, consider yourself lucky.

Herman Kahn, a writer who specialized in thinking and writing about unfashionable topics such as thermonuclear war, came up with yet another variant of the game: the Doomsday Machine. The idea was for the United States to bury lots of very dirty thermonuclear weapons under the Rocky Mountains, enough so that if they went off, their fallout would kill everyone on earth. The bombs would be attached to a fancy Geiger counter rigged to set them off if it sensed the fallout from a Russian nuclear attack. Once the Russians know we have a Doomsday Machine we are safe from attack and can safely scrap the rest of our nuclear arsenal. The idea provided the central plot device for the movie Doctor Strangelove. The Russians build a Doomsday Machine but imprudently postpone the announcement they are waiting for the premier’s birthday until just after an American Air Force officer has launched a unilateral nuclear attack on his own initiative. The mad scientist villain was presumably intended as a parody of Kahn. Kahn described a Doomsday Machine not because he thought we should build one but because he thought we already had. So had the Russians. Our nuclear arsenal and theirs were Doomsday Machines with human triggers. Once the Russians have attacked, retaliating does us no good just as, once you have finally told your daughter that she is going to bed, throwing a tantrum does her no good. But our military, knowing that the enemy has just killed most of their friends and relations, will retaliate anyway, and the knowledge that they will retaliate is a good reason for the Russians not to attack, just as the knowledge that your daughter will throw a tantrum is a good reason to let her stay up until the party is over. Fortunately, the real-world Doomsday Machines worked, with the result that neither was ever used.

For a final example, consider someone who is big, strong, and likes to get his own way. He adopts a policy of beating up anyone who does things he doesn’t like, such as paying attention to a girl he is dating or expressing insufficient deference to his views on baseball. He commits himself to that policy by persuading himself that only sissies let themselves get pushed around and that not doing what he wants counts as pushing him around. Beating someone up is costly; he might get hurt and he might end up in jail. But as long as everyone knows he is committed to that strategy, other people don’t cross him and he doesn’t have to beat them up. Think of the bully as a Doomsday Machine on an individual level. His strategy works as long as only one person is playing it. One day he sits down at a bar and starts discussing baseball with a stranger also big, strong, and committed to the same strategy. The stranger fails to show adequate deference to his opinions. When it is over, one of the two is lying dead on the floor, and the other is standing there with a broken beer bottle in his hand and a dazed expression on his face, wondering what happens next. The Doomsday Machine just went off. With only one bully the strategy is profitable: Other people do what you want and you never have to carry through on your commitment. With lots of bullies it is unprofitable: You frequently get into fights and soon end up either dead or in jail. As long as the number of bullies is low enough so that the gain of usually getting what you want is larger than the cost of occasionally having to pay for it, the strategy is profitable and the number of people adopting it increases. Equilibrium is reached when gain and loss just balance, making each of the alternative strategies, bully or pushover, equally attractive. The analysis becomes more complicated if we add additional strategies, but the logic of the situation remains the same.

This particular example of bilateral monopoly is relevant to one of the central disputes over criminal law in general and the death penalty in particular: Do penalties deter? One reason to think they might not is that the sort of crime I have just described, a barroom brawl ending in a killing more generally, a crime of passion seems to be an irrational act, one the perpetrator regrets as soon as it happens. How then can it be deterred by punishment? The economist’s answer is that the brawl was not chosen rationally but the strategy that led to it was. The higher the penalty for such acts, the less profitable the bully strategy. The result will be fewer bullies, fewer barroom brawls, and fewer “irrational” killings. How much deterrence that implies is an empirical question, but thinking through the logic of bilateral monopoly shows us why crimes of passion are not necessarily undeterrable. […]

in Chapter 8, David D. Friedman, “Law’s Order: What Economics Has to Do With Law and Why it Matters“, Princeton University Press, Princeton, New Jersey, 2000.

Note – Further reading should include David D. Friedman’s “Price Theory and Hidden Order“. Also, a more extensive treatment could be found on “Game Theory and the Law“, by Douglas G. Baird, Robert H. Gertner and Randal C. Picker, Cambridge, Mass: Harvard University Press, 1994.