Game Theory

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• JEFFREY BROWN:

  In the late 1940s, Thomas Schelling worked as a government economist negotiating international treaties as part of the Marshall Plan. The experience led him to the study of how nations and individuals negotiate all types of conflict, whether a rush-hour traffic jam, or a Cold War nuclear arms race.

  Yesterday, the Royal Swedish Academy awarded the Nobel Prize in economics to Thomas Schelling for his work in what's known as game theory. He shared the award with Robert Aumann, a professor at the Hebrew University in Jerusalem.

  Thomas Schelling is 84 and the author of numerous books exploring strategy and decision-making. He taught at Harvard for many years before coming to the University of Maryland, where he's an emeritus professor.

  We spoke this morning at his home in suburban Washington DC.

• JEFFREY BROWN:

  What's a simple way of explaining to the layman what is meant by game theory?

• THOMAS SCHELLING:

  The simplest explanation is that game theory is the study of any situation in which two or more people make decisions that impinge on each other. And each individual must take into account what the other is likely to do either simultaneously or in succession.

• JEFFREY BROWN:

  You and I might want something or be competing for something.

• THOMAS SCHELLING:

  That's right.

• JEFFREY BROWN:

  And we would have to take into account what each other thinks?

• THOMAS SCHELLING:

  Well, take a simple example. We're maneuvering in a traffic jam. I have to anticipate whether you are going to try to go first or are you going to let me go first. Sometimes we signal, as if I want to go first. Sometimes we try to intimidate each other and influence each other. But if we both do the wrong thing, we're both in trouble. And there are certain outcomes we can achieve if we take into account each other's intentions, motives and alternatives.

• JEFFREY BROWN:

  In your press conference yesterday you described yourself as a user of game theory. What did you want to use it for? What were you trying to do?

• THOMAS SCHELLING:

  I'll give you an example. I once got interested in the question: if there is some weapon that may be susceptible to an arms limitation, let's say it is an alternate weapon – you either have it or you don't — anti-ballistic missile system, bombs in orbit, gas weapons, something of that sort — how many different ways are there that the two parties to a negotiation might rank possible outcomes?

  You would say well, there are four possible outcomes. We both have the weapons. Neither has the weapons, I have it and you don't. You have it and I don't. Each has a choice between two alternatives, have it or not. There are four possible outcomes. And then the question: how many different bargaining situations are there?

  Well, it turns out that there are at least 16 importantly different configurations of preferences that the two parties can have. If you show these 16 outcomes to people in a 4 x 4 matrix it becomes perfectly clear what you are talking about. You can see that here's an outcome that both prefer compared with that one. Here's an outcome that I prefer but you don't. You can find certain situations in which it makes sense to reach an agreement, certain situations in which no agreement is needed, certain situations in which if one can choose before the other, it's an advantage to go first — other situations in which it's an advantage to go second.

  All of these things are hard to think about when I try to describe them verbally but if I had a blackboard and could show you on the blackboard, I could teach you in an hour how to use elementary game theory as a kind of accounting system to keep track of all the possible choices and all the possible outcomes.

• JEFFREY BROWN:

  You talked about how this kind of thinking can be used in a whole variety of things, climate change and trying to stop smoking. You even said it helped in disciplining children.

• THOMAS SCHELLING:

  Oh, sure. The kind of problem or one kind of problem that game theory deals with is, how do you make a threat that is credible, believable.

• JEFFREY BROWN:

  Whether you are a nation or a parent.

• THOMAS SCHELLING:

  Or a parent. How do you make a promise that is believable? How do you identify compromises when you're bargaining over something that seems to be indivisible? And I think, for example, early in NATO the question arose: how would the United States ever persuade western European governments that it would attack Russia with nuclear weapons if the Soviets attacked Western Europe? And this was known as the credibility problem. Was it believable that the United States would go to nuclear war to save Western Europe?

  And to a game theorist, that's the kind of issue that excites the search for ways to commit yourself, and the way the United States committed itself was very simple: The United States, the secretary of state went to Congress and wanted authorization to send seven American infantry divisions to Europe. And the question arose: What can seven infantry divisions do against a Soviet attack? And the answer given, really, was they can guarantee that the war can't stop there. The Americans will never allow seven divisions of young American men to be either killed or captured without raising the war to a higher level.

  And therefore, those seven divisions are there to convince the French that the Russians are convinced that the United States would respond to an attack on Western Europe. Well, that doesn't require game theory but it is the kind of thing that game theorists think about.

• JEFFREY BROWN:

  Now forgive this layman's question, but what does all that have to do with economics?

• THOMAS SCHELLING:

  Well, I might answer not much because most of my use of game theory has been applied to things outside economics but in economics, I will give you another example. How does a union that wants to threaten a strike make the threat believable? And if it's on strike, how does it manage to make a credible threat that we can stay on strike longer than you can stand?

• JEFFREY BROWN:

  Let me ask you a personal question about your scholarship. What is it that drove you as an economist to venture into these big issues of the day?

• THOMAS SCHELLING:

  Oh, in 1948 I was just finishing graduate study. And I had an opportunity to go to Washington to join the new Marshall Plan which began in April of 1948. And I continued working on foreign aid negotiations until 1953, at which time I went off to Yale University on a faculty but decided I think negotiation is the most interesting thing I've ever been involved in, and I'm going to make that my study, so that bargaining, conflict, cooperation, all led me into the studies of strategy. And eventually I got into game theory.

• JEFFREY BROWN:

  I read that you thought that perhaps because of your age you were not going to receive a Nobel Prize.

• THOMAS SCHELLING:

  That's right.

• JEFFREY BROWN:

  What do you mean, your time, you thought your time had passed?

• THOMAS SCHELLING:

  I figured that when — when the committee began giving prizes to people in their 50s, and I was in my 80s, if they really wanted ever to give me the prize, they'd better hurry up. And I decided clearly if they were ever going to give it to me they would have given it to me already. That was my reasoning. And my wife didn't believe me when I —

• JEFFREY BROWN:

  But you had a happy surprise.

• THOMAS SCHELLING:

  Yeah, I had a happy surprise.

• JEFFREY BROWN:

  All right. Thomas Schelling, thanks for talking to us. And congratulations.

• THOMAS SCHELLING:

  Thank you for inviting me.