Game Theory and the Nobel Prize

Interview with Robert Aumann

Professor Robert Aumann, who won the Nobel Prize for Economic Sciences in 2005, explains game theory and its applications. Find out how it can even be applied to the study of the Talmud, and how sophisticated the logic of the ancient Sages really is.

Douglas Goldstein: We are talking to Professor Robert Aumann, who was born in Germany. He fled Nazi persecution when he was about 8 years old and ended up in the United States with his family. In the process, his parents basically lost everything, but strove to give their two children an excellent Jewish and general education. He is joining us here today to talk to us about some of the work he has done that also led to his winning the 2005 Nobel Prize in Economics. Professor, it’s an honor to have you with us.

Robert Aumann: Great to be here now.

Douglas Goldstein: You’re probably best known for the work you’ve done on Conflict and Cooperation through Game Theory Analysis. Before we may begin with that, could you just describe a little bit what Game Theory is all about?

Robert Aumann: Yes, I’d be glad to. Game Theory is about the strategic analysis of situations in which different entities are involved interacting with each other, but they are striving towards different goals. Now, those goals may be diametrically opposed like in a game of chess, but usually they are not diametrically opposed in more important situations. For example, in commercial enterprises – in a commercial transaction when someone is buying something from somebody else, the buyer is interested in getting a low a price as possible and the seller is interested in getting as high a price as possible. So they are striving for different goals, but those goals are not diametrically opposed because both sides are usually interested in the transaction being consummate. So Game Theory is about that kind of situation, where two or more entities are interacting with each other but are striving towards different goals. The reason that it is called Game Theory can be seen from an obvious and clean example of such situations in real games. They could be games like chess, in which as I said the interests are diametrically opposed, but they also could be games like poker, in which more than two people are involved, and of course you can have more than two things being diametrically opposed. So that is what Game Theory is about, and it has applications to many different areas, like economics.

Game Theory and Economics

Douglas Goldstein: So economics is a good topic for us.

Robert Aumann: Yes. Economics, politics, international relations, warranties, and law, in which often the players are the plaintiff and the defendant, and you also have the judge as a player in this game. It even exists in biology, in which you have living species compete with each other for the resources that nature has to offer. So it has a very broad range of applications, and if economics interests you especially then let’s talk about economics.

Douglas Goldstein: Because we’re on The Goldstein on Gelt Show, the show is really an investment show, and we try to talk about financial planning issues. My day job is that I’m a financial advisor here in Jerusalem, so I only get this once-a-week gig when I get to talk to people on the radio. I think the concept of Game Theory is very important when people are doing financial planning because they need to develop a long-term strategy on how they will have enough money to retire, and they’re dealing with so many other obstacles that, like you said, are not are necessarily diametrically opposed. But can normal people use Game Theory to come up with practical decisions?

Robert Aumann: Actually, Game Theory is more about situations in which there are several entities involved in the situation and they are playing strategically with each other. Subsequently, Game Theory has a lot of very, very practical applications, but if you’re talking about looking at your financial options and asking yourself where is the best place to put your money, that is not explicitly a game theoretic problem. This is because in Game Theory, you have to have at least two entities that are striving towards different goals. When you’re looking at your financial options, you don’t have two entities, you have just one – you just have the person who wants to put his money in the best possible place. That is what we call a decision problem, but that’s not really a Game Theory.

Besides, I want to warn you that I am not an expert in finance. That is not my special area of expertise. I realize that there are decisions to be made over there and I myself have to make decisions of that kind and sometimes they are very, very complex. For example, there’s the pension fund that I was unable to get explanations for, although I tried for half a year. I was unable to get explanations of what is really going on and what the options really are from the people that served me in this pension fund on the telephone. I repeatedly asked these people several questions, but they were unable to give me answers. I asked for their supervisors, and the supervisors were also unable to give me answers. Some of these financial instruments are extremely complicated, to the extent that the consumer doesn’t really know what’s going on. Although it’s not my area of expertise, I do have a little bit of mathematical training and economic training. I know what an interest rate is and I know what an annuity is, but I was unable to get satisfactory answers. So I think sometimes in the financial institutions, pension funds and places like that, the people up there would do the planning and they want to give the consumer as many choices as possible, but they missed the mark because they make their plans so complicated that nobody even in their organization can understand it and when you can’t understand it, it’s useless.

Douglas Goldstein: That’s a real problem in what you’re describing. We’re talking to Professor Robert Aumann, who won the 2005 Nobel Prize in Economics and is noting on the show here a real difficulty in practical economics of simply getting the information that you need in order to make a wise financial decision. It’s not an economics question anymore; it’s just a practical question of the service you’re getting.

Why It’s Important to Understand Financial Products

Robert Aumann: It’s a practical question, but I think it has policy implications and that policy implication is what we call peace. Peace means keep it simple, because if you don’t keep it simple, people won’t understand it and they won’t be able to make an appropriate decision. You know in the end, I threw up my hands and I just made an arbitrary decision. I had to decide something and since nobody could explain it to me, I just made an arbitrary decision. I’m doing not badly, but maybe I could be doing better. The people up there, the bosses, they think that if they make very complicated plans and financial products available, they’re doing people a favor, but actually they’re not. Now, I have to be careful because you make a living from financial transactions. If you’re a broker there in Wall Street, if you work for some kind of hedge fund or something like that, or if you’re in fact an investor who spends 40, 50 or 60 hours a week thinking about these investments, and there are people like that, then you will understand these products.

Douglas Goldstein: Okay, I’m not so sure that everyone –

Robert Aumann: You will understand them but most of us are not like that. Most of us have work to do and we’re really tired. We have our families, our travel or whatever it is that we do. We have a retirement to see to and we don’t spend all our time thinking about financial instruments. So I think there’s a real problem there which has to be fixed.

Douglas Goldstein: Yes, it is an issue. When I do financial plans for people, I ask them, “Do you have a pension plan? How much will you get when you retire?” They say, “Well, I’ve no idea,” and then I say, “What if you die? Does your wife get a piece of it?” They say, “I have no idea,” and I say, “Why don’t you go ask the pension company?” And they say, “Well, they give me all these answers and these forms.” So, I put together a few years ago a simple questionnaire to ask those questions: how much will I get, what’s the tax on it.

Robert Aumann: It justifies that we’re right. You ask them about interest rates, and the point is that people don’t really understand anything. They understand much less. The other people you talk to about interest rates, the real interest rate, and something a little more complex, don’t know what you’re talking about.

Game Theory and the Talmud

Douglas Goldstein: We know we’ve diverged off the subject. I’m so happy to be talking to Nobel Prize winner Professor Robert Aumann about Game Theory. We digressed a little bit into some practical financial issues. But let me just ask you the last question before we run out of time. You apparently used some Game Theory to solve certain Talmudic problems in the Gemara and the Talmud. How does that work?

Robert Aumann: I will tell you the story. There is a passage in the Talmud in Ketubot 93a, and it has generated a tremendous amount of ink over thousands of years, and really there was great difficulty in understanding it. My son was killed in Lebanon in 1982. I wrote him a letter once about a certain Talmudic issue and he wrote back Ketubot 93a and to look over there. I looked at this passage in the Talmud and I couldn’t figure it out. I, together with a colleague of mine, looked at the numbers over there and they looked really, really odd. Then we decided to apply some game theoretic tools to try to understand this. Eventually we found one of those tools which really fit the number perfectly, but this didn’t satisfy us yet because it’s a sophisticated modern mathematical concept and it’s unlikely that the sagesof the Talmud knew about it. So we had to get to the bottom of the logic. This took us a few more months, and finally we did arrive at it. We understood the logic and it’s very sophisticated. The sages of the Talmud were very smart people. They were very savvy and very sophisticated. They didn’t know modern mathematics, obviously, but they were smart and sophisticated people. It’s quite possible that the logic that we found behind these numbers really was in the minds of the Talmudic sages. It was also published in the Journal of Economic Theory in 1985 under the title, “Game Theoretic Analysis of a Bankruptcy Problem from the Talmud.” So anybody who wants to look at that article, which is slightly mathematical, will find it there. But if you don’t understand the mathematics, just skip it because there’s a lot of verbal analysis there also and that should be fine. That’s all what I have to say about that. What I’m saying really is that the sages of the Talmud were savvy people and it’s not to be imagined, but they worked out a Game Theoretic approach. They did reach the conclusions, which were not at all obvious, so I take off my hat to them.

Douglas Goldstein: That’s amazing, and I take off my hat to you and to all the work you’ve done, especially traveling around, speaking and teaching. We’ve been talking to Professor Robert Aumann, who won the Nobel Prize in 2005 and has expertise not only in Economics, but also in the Talmud. Professor, it was a pleasure talking to you. Thank you very, very much for your time.

Robert Aumann: Thank you very, very much and good evening. Bye.