When the three winners of the Nobel Prize in Economics were announced, I remembered a heady time when I encountered game theory, along with the Man with a Gun and the Crafty Burglar. The Nobel was given for work in this playful-sounding discipline, which has many applications -- economics, politics, military strategy, and, as parents intuitively understands, the rearing of children.

Many years ago, I dabbled in game theory.

I wish there were another way to put it, but that is what it was. This was at Harvard, where, as a Neiman Fellow, I took a course from an economist named Thomas C. Schelling. Schelling was not among the Nobel laureates, but in its article about the prize, the New York Times described him as being "in a class by himself in applied game theory."

A Nieman experience is one of the world's great intellectual smorgasbords. The journalists selected for it are permitted to take any courses they wish out of Harvard's vast offerings.

As with most things, the possibilities actually are not unlimited. A gentle nudge discourages the applicant who would be in over his or her head. There was an advanced course I fancied in the history of science, but the professor politely observed that unless I already appreciated the elegance of James Clerk Maxwell's great equations in electromagnetism, it might be a waste of everybody's time. But Schelling raised no such objection, and I stayed with his classes in game theory, even after the mathematics put me in water that was too deep.

Formalized

Game theory was formalized in as epochal book titled Theory of Games and Economic Behavior, published in 1944 by Oskar Morgenstern, an economist, and John Von Neumann, a mathematician who later became an inventor of the hydrogen bomb. In this, they complained that classical mathematics was of little help in solving problems involving several participants, all of whom are out to improve their positions, but none of whom controls all the variables.

Game theory offered a way to go about it, and the authors introduced the concept of the zero-sum and non-zero-sum games. In the former, it is winner takes everything, loser loses all. A hand of stud poker is a good example.

In non-zero-sum games, the sides understand that their opponents need to win something. Labor negotiations are a classic example. The workers ultimately lose if they triumph, but their employer goes out of business. If the company wins by destroying an experienced work force, it may fatally lose its competitive position.

If the two sides use game theory, they may be able to calculate quite accurately their possible gains and losses under a variety of scenarios subjected to a mathematical matrix. It is a way of approaching rigorous analysis to one's self-interest to determine how it can be both maximized and rationally achieved.

Political parties can use game theory in cases where certain numbers of votes will be won or lost depending on whether they, or their opponents, support, oppose or evade a particular issue. Though hawks had trouble appreciating this, in the balance of terror with the old Soviet Union, it was important not to get trapped into a zero-sum situation.

Outcome of War

Under that condition, the outcome of war for both sides was either "victory" or ashes. In such a situation, the dangers of an all-or-nothing preemptive nuclear strike would rise dramatically.

And, as I was able to see years later as a father, while it was important for me to prevail in matters of household conduct or the use of bad language or rules for bicycle safety, I could not win absolutely all the time without harming my sons. They needed a process, a security in parental love and an opportunity to have opinions taken seriously that left them feeling they had not been destroyed. Parents and children should not have zero-sum relationships.

Whether it is economics or strategic policy or a simple disagreement between a father and son, game theory has pertinent lessons. It teaches that in many situations, "winning" -- the attainment of a particular objective -- requires communication and sharing information as well as the negotiation of agreements that the parties understand are in their rational self-interest to honor.

I took these things away from Professor Schelling's course, along with memories of the Man with a Gun and the Crafty Burglar. These are simple zero-sum exercises and I shall leave them with you.

Man With a Gun

In the first, imagine yourself with a pistol, facing an armed opponent 100 paces away who intends to kill you. Each of you has one lethal bullet. At that distance the chance of hitting each other is one in 100. You advance upon each other, one step at a time.

The odds improve with each step. At half way, they are 50-50; at point blank a hit is certain. If you fire and miss, he will walk up to you and kill you. You will do the same if he misses. At what point do you shoot?

Now imagine that the guns are silent and you cannot tell if your opponent has already fired. Game theory tells you when to pull the trigger.

The Crafty Burglar

The Crafty Burglar plans to steal your diamonds tonight. You can lock them in your desk at work or your safe at home. The distance between the two is such that the burglar can only strike once. If you guess right, you save your diamonds. If you guess wrong, he succeeds. Where do you put them?

Now also consider this. This burglar is precisely intelligent as you. If you think he will go to the office and so you hide the jewels at home, he will also reason thus and go there. And he will follow your thinking, no matter how convoluted or extended it may be, coming to the exact same conclusion as you. How can you make a decision that takes away his power to reason?

Tom Schelling had an answer. He said, flip a coin.