Winner Take Less

It is so hard to make important decisions that we have a great urge to reduce them to rules. Every moral teacher or spiritual adviser gives injunctions about how to live wisely and well. But life is so complicated and full of uncertainty that rules seldom tell us quite what to do. Even the more analytically minded philosophers leave us in quandaries. Utilitarians start with Jeremy Bentham’s maxim, that we should strive for the greatest happiness of the greatest number of people. How do we achieve that? Kant taught us that we should follow just those rules of conduct that we would want everybody to follow. Few find this generalization of the golden rule a great help. It may seem that there is one kind of person or group that has no problem: the entirely selfish. Utilitarians find selfish people more interesting than one might expect, for it has been argued that the way to “maximize everyone’s utility” is to have a free market in which everyone acts in his own interests.

Even if you are entirely selfish and know what you want, you still live in a world full of uncertainties and won’t know for sure how to achieve what you want. The problem is compounded if you are interacting with another selfish person with desires counter to yours. Long ago Leibniz said we should model such situations on competitive games. Only after World War II was the idea fully exploited by John von Neumann. The result is called game theory, which quickly won a firm foothold in business schools and among strategic planners. In a recently reprinted essay, “What is Game Theory?” Thomas Schelling engagingly reminds us that we reason “game-theoretically” all the time. He starts with an example of getting on the train, hoping to sit beside a friend, or to evade a bore. Given some constraints about reserved seats and uncertainties about what the other person will do, should one go, he asks, to the dining car or the buffet car? You’ll see by the example that this is a vintage piece from 1967, when people were a little more optimistic about game theory than they are now.

The simplest games have two players, you and your friend, perhaps. Each has some strategies; go, for example, to the dining car or to the buffet car. Each has some beliefs about the world, about seating, reservations, and so forth, and each has some uncertainties. Each has some preferences—company over isolation, and dinner with wine, perhaps, over sandwich with beer. The “rational” player tries to maximize his utility by calculating the most effective way to get what he wants. Schelling’s first game is not even competitive; it becomes so when one is trying to avoid the bore.

Game theory is quite good for those games in which winners take everything that is staked, and losers lose all that they stake. The solution—the optimum strategy—is crisply defined for some classes …

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