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Finance Feature: Game Theory in Economics and Talmud

A7 Radio: Nobel Laureate Robert Aumann talks about game theory and how it can suit economics and even Talmudic problems.
By Douglas Goldstein, Financial Advisor
First Publish: 7/19/2011, 5:05 PM / Last Update: 7/19/2011, 9:34 PM

Douglas Goldstein, Financial Planner & Investment Advisor, interviews Nobel Laureate Robert Aumann on Arutz Sheva Radio. 

Douglas Goldstein:  Professor Robert Aumann, was born in Germany. He fled Nazi prosecution when he was about 8 years old and ended up in the United States with his family. He received the 2005 Nobel Prize in Economics.

Professor Aumann, 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 briefly what Game Theory is all about?

Robert Aumann:  Game Theory is about the strategic analysis of situations in which different entities are involved interacting with each other but striving towards different goals. Now, those goals may be diametrically opposedas in a game like chess, but usually they are not.

For example, in commercial enterprises – in a commercial transaction when somebody 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 consummated.

Game Theory is about that kind of situation, where two or more entities are interacting with each other but striving towards different goals. The reason that it is called Game Theory can be seen from such situations in real games.

They could be games like chess, in which the interests are diametrically opposed, but they also could be games like poker in which more than two people are involved, and you can have more than two things being diametrically opposed. 

Robert Aumann:   Game Theory has applications to economics, politics, international relations, warranties, and law, in which often players are the plaintiff and the defendant and you also have the judge as a player in this game. Even biology, in which you have living species compete with each other for the resources that nature has to offer.

Douglas Goldstein: 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.

Game Theory has a lot of practical applications, but ifyou’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 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, not really Game Theory.

Besides I want to warn you that I am not an expert in finance. I myself have to make decisions of that kind and sometimes they are very, very complex.

For example, 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 really is going on and what the options are from the people that served me in this pension fund. 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.

I think sometimes in the financial institutions, pension funds and places like that, the people up there would do the planning and 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. It’s not an economics question anymore; it’s a practical question of the service you’re getting.

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, 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.

If you’re a broker in Wall Street, if you work for some kind of hedge fund, or if you’re in fact an investor who spends 40, 50 or 60 hours a week thinking about these investments, then you will understand these products 

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 time thinking about financial instruments. So I think there’s a real problem there which has to be fixed.

Douglas Goldstein:  You used 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, we 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 the sages of the Talmud knew about this.

So we had to get to the bottom of the logic and this took us a few more months and finally we did arrive at it.

The sages of the Talmud were very smart and sophisticated. Obviously, they didn’t know modern mathematics but they did know logic. 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.”

It’s hard to believe, 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, CFP®, is the director of Profile Investment Servicesand the host of the Goldstein on Gelt radio show (Monday nights at 7:00 PM on www.israelnationalradio.com. He is a licensed financial professional both in the U.S. and Israel. Securities offered through Portfolio Resources Group, Inc., Member FINRA, SIPC, MSRB, NFA, SIFMA. Accounts carried by National Financial Services LLC. Member NYSE/SIPC, a Fidelity Investments company. His book Building Wealth in Israelis available in bookstores, on the web, or can be ordered at: www.profile-financial.com