The best books on Game Theory

What is game theory?

The way I think about game theory is that it’s a part of economic theory, a set of models and concepts that is supposed to capture the way we think about strategic interactive situations. These are situations when my reasonable behaviour depends on the way that I perceive or believe that the other participants in the situation will behave. I want to get into the shoes of the other player or players – I want to enter their mind. That’s crucial for my decision. It’s not like a situation where I’m trying to decide whether to take an umbrella or not, and all I have to think about is the chance it will rain this afternoon. But I can do it in many ways and I can respond in many ways. What is special about game theory is that until now it has been assumed that when the players respond to the other players they respond rationally.

People are presumed to be rational?

Yes, classical game theory deals with situations where people are fully rational. In principle we could think about interactive situations where players are not fully rational, but nevertheless take into account or anticipate other players’ behaviour. But the body of knowledge that is known as game theory, at least up to now, has focused mainly on situations where the players are rational.

What are the applications of game theory for real life?

That’s a central question: Is game theory useful in a concrete sense or not? Game theory is an area of economics that has enjoyed fantastic public relations. John Von Neumann, one of the founders of game theory, was not only a genius in mathematics, he was also a genius in public relations. The choice of the name “theory of games” was brilliant as a marketing device. The word “game” has friendly, enjoyable associations. It gives a good feeling to people. It reminds us of our childhood, of chess and checkers, of children’s games. The associations are very light, not heavy, even though you may be trying to deal with issues like nuclear deterrence. I think it’s a very tempting idea for people, that they can take something simple and apply it to situations that are very complicated, like the economic crisis or nuclear deterrence. But this is an illusion. Now my views, I have to say, are extreme compared to many of my colleagues. I believe that game theory is very interesting. I’ve spent a lot of my life thinking about it, but I don’t respect the claims that it has direct applications.

“The choice of the name ‘theory of games’ was brilliant as a marketing device. The word “game” has friendly, enjoyable associations – even though you may be trying to deal with issues like nuclear deterrence.”

The analogy I sometimes give is from logic. Logic is a very interesting field in philosophy, or in mathematics. But I don’t think anybody has the illusion that logic helps people to be better performers in life. A good judge does not need to know logic. It may turn out to be useful – logic was useful in the development of the computer sciences, for example – but it’s not directly practical in the sense of helping you figure out how best to behave tomorrow, say in a debate with friends, or when analysing data that you get as a judge or a citizen or as a scientist.

So the situation of the prisoner’s dilemma couldn’t arise in real life?

I didn’t say that. In game theory, what we’re doing is saying, “Let’s try to abstract our thinking about strategic situations.” Game theorists are very good at abstracting some very complicated situations and putting some elements of the situations into a formal model. In general, my view about formal models is that a model is a fable. Game theory is about a collection of fables. Are fables useful or not? In some sense, you can say that they are useful, because good fables can give you some new insight into the world and allow you to think about a situation differently. But fables are not useful in the sense of giving you advice about what to do tomorrow, or how to reach an agreement between the West and Iran. The same is true about game theory. A main difference between game theory and literature is that game theory is written in formal, mathematical language. That has advantages and disadvantages. The advantages are that the formal language allows us to be more precise, it allows us to get rid of associations that are not relevant and it allows us to better examine some arguments. The disadvantage of formal language is the level of abstraction, which has two main downsides. First of all, it makes the theory very far away from one minus epsilon of the population. Even among the academic community, most people who claim to use game theory hardly understand it. Secondly, abstraction has the negative side that once you abstract things, you miss a lot of the information and most of the details, which in real life are very relevant.

In general, I would say there were too many claims made by game theoreticians about its relevance. Every book of game theory starts with “Game theory is very relevant to everything that you can imagine, and probably many things that you can’t imagine.” In my opinion that’s just a marketing device.

Why do it then?

First, because it is interesting. And I’m not saying it isn’t useful in indirect ways. I believe that intellectual thinking – philosophy or logic or game theory – is very useful in the cultural sense. It’s part of the culture, it’s a part of our perpetual attempt to understand ourselves better and understand the way that we think. What I’m opposing is the approach that says, in a practical situation, “OK, there are some very clever game theoreticians in the world, let’s ask them what to do.” I have not seen, in all my life, a single example where a game theorist could give advice, based on the theory, which was more useful than that of the layman.

There is probably a confusion in the public between the personal abilities of game theorists and the power of the theory itself. The community of game theoreticians contains some brilliant people who have also “two legs on ground”. This rare combination is very useful. People like that can come up with interesting and original ideas. Not everyone – there are brilliant game theoreticians who I would not ask for any practical advice. But the advice of the other, even if it is good, should not lean on an authority.

Looking at the flipside, was there ever a situation in which you were pleasantly surprised at what game theory was able to deliver?

None. Not only none, but my point would be that categorically game theory cannot do it. Maybe somewhere in a Sherlock Holmes or Agatha Christie story there was a situation where the detective was very clever and he applied some logical trick that somehow caught the criminal, something like that. You know in America there was a programme on CBS, called Numbers, written Numb3rs, with the ‘e’ reversed. Numb3rs wanted to make people curious about mathematics through detective stories. I happened to hear about it because I had done some experimental work with Amos Tversky and Dana Heller, about the game of hide and seek. In one of the episodes they refer to the paper. Of course it was a joke, but the fact that my name was mentioned in such a programme made me very happy. But outside such programmes, I categorically cannot see any case where game theory could be helpful.

So if people study it, it should be just for love of the subject?

That’s my position about academic life in general. Universities and academic research are not supposed to be useful in a direct sense. I’m not talking about research like in medicine – that’s a completely different story – but I’m talking about social sciences and humanities, which I am more familiar with. The social sciences and humanities, in my opinion, should not have any pretension to be directly useful. We are part of the culture. We are useful as sculptures are. Maybe a sculpture that will be put in Central Park in New York will prove to have a lot of influence on people. So are our models.

The case of the computer sciences is interesting. For many years the Israeli computer scientists were criticised because the computer sciences were too abstract in Israel, whereas in other places they were thinking more in terms of practical applications. But I think that people will agree now that the big success of the Israeli hi-tech industry in the last 20 years is also the outcome of the abstract way computer sciences was taught in places like Jerusalem in the seventies and eighties. That created the cultural environment on which the unbelievable success and flourishing of the hi-tech industry of Israel since the 1990s is based. This is a case where abstraction led indirectly to something practical. Of course, I’m not against something practical coming out eventually of abstract studies but it is not the target. Of course I can give you examples where game theoreticians, because they were intelligent, gave good advice – and probably some examples where game theoreticians gave bad advice.

By the way, I don’t know enough about it, but it’s very interesting to investigate the role of game theoreticians in the development of American policy on nuclear deterrence. Thomas Schelling and John von Neumann and many other lions of game theory were connected to this effort. Some people, including John Nash, were working for a few months or years in RAND and thinking about strategic situations like that. From a historical point of view, I think it’s interesting whether indeed there was any real effect to game theorists in the 1950s. Now in Israel, again, given the situation with Iran, the question of whether game theory can tell us anything is in the air. I hope that the Israeli government will not consult game theorists regarding its hard strategic decisions.

Some of these people you’re talking about come up in the books you’ve chosen, so let’s talk start talking about those. What did you have in mind when you chose this list? Are these the classics of game theory?

The first one I chose was the Theory of Games and Economic Behavior, by John von Neumann and Oskar Morgenstern. There was game theory before von Neumann-Morgenstern, and, as with any field, people are now saying “in 1921 so and so did so and so”. I’m sure at the end of the day, someone will find something relevant also in the Talmud or Greek writings. But von Neumann-Morgenstern was the first comprehensive, systematic attempt to put many game theoretical ideas together. They set up the style, the concepts, some of the basic solution concepts and the level of abstraction.

Von Neumann was a brilliant mathematician and Morgenstern was an economist. I imagine if someone else had written the first book – for example a philosopher – game theory could have gone down a completely different path. It’s beautiful to see, the implicit or explicit decisions about the terms and the language. These decisions determined the content and the borders of the field. It’s very difficult to break those borders later.

The book does have pretensions. I read from page one: “The purpose of this book is to present a discussion of some fundamental questions of economic theory which require a treatment different from that which they have found thus far in the literature.” It’s an interesting sentence – what does it make us feel? First of all that it’s different, a different set of models than the previous economic models, and that it’s about fundamental questions of economic theory. It was different, we agree on that. It took another 30 years or so for it to be absorbed into the main body of economic theory. So I think this book is definitely on this list of five, because it set the tone and because of its brilliant ideas.

Do you still use this book?

These days I use it less and less. After JSTOR it became very easy to search in papers and journal articles but books are hard to search. This is changing now. More and more books are available on the web. The more they are searchable, the more we’ll use them again. It’s a book that has been referenced a lot, though I’m sure most of the references are from people who did not open it.

I cannot say I use it daily, and if a student comes and tells me, “I want to learn game theory,” it will not be the first book I’d recommend. That would be a more standard book, that teaches the concepts in a didactic way, summarising what was happening over the past almost 70 years. But in the second wave, I would advise him to read the book, especially if he really wants to get into the theory. People sometimes say, “Book X is the bible of a field.” This is not. I don’t actually know any bible of game theory, and probably it’s good that there isn’t one. Because once there’s a bible in the field, it’s very difficult to make a change. A “bible” might be the beginning and the end of a field.

Let’s talk about your next book, Games and Decisions.

This book is written by another two brilliant people, R Duncan Luce and Howard Raiffa. The book was written in the mid-1950s, so about 10 years after von Neumann-Morgernstern and of course it’s a book that was influenced a lot by von Neumann-Morgenstern. It’s a less formal book. It’s written beautifully. It’s a book about which I’m always saying to students, “There are many ideas in there that still have not been developed.”

Luce and Raiffa were thinking about elements of what we would probably now call modern choice theory. Standard classical choice theory deals with rationality, ways of applying rationality into decision problems. Their mode of thinking is natural, that’s what I like about this book (and much of game theory in general). It’s really on the bridge between natural thinking and formal thinking. Von Neumann-Morgenstern set the formal models, and Luce and Raiffa went one step back. You can see this in the subtitle of the book, Games and Decisions: Introduction and Critical Survey. The book is dedicated to the memory of von Neumann, but at the same time they did not shy away from criticising the rationality approach.

By the way, von Neumann-Morgenstern was not only the beginning of game theory. There is also a very important chapter about the expected utility model. This is the basic model which is still used by almost everybody in economics regarding decision-making under uncertainty. It’s the foundation not just of game theory, but of almost everything in economic theory which involves uncertainty. Luce and Raiffa criticised this theory and suggested some ideas and alternatives which are followed up 30 to 40 years later.

Let’s go on to your next book, a collection of papers by Robert Aumann, winner of the 2005 Nobel prize in economics, and, like you, an Israeli.

This collection is interesting for several reasons. Firstly, Bob Aumann is a very special man. I disagree with him about his political views – he is a right-wing person. I disagree with him about his current position on “what game theory is about”. From time to time he expresses views – about politics for example – backed with the authority of the great game theoretician. I don’t like those statements. In spite of this fact, I admire him for his academic work and personality. First of all, there is a beauty in his writing. He’s a master in the way he writes, whatever he writes, and the way he uses formal models to talk about game theory. It’s probably very difficult for someone outside the field to appreciate it, but there is an aesthetic to it. Aumann’s style contrasts the dominating style in current economics. It’s with a lot of – if I may use the word – bullshit, a lot of over-pretensions to be useful. In many current papers in economic theory models are not models, proofs are not proofs. The strive for generality is misleading as every model is not more than a tiny example.

Aumann has the ability to use sophisticated mathematical tools more than almost all other game theorists. But he is not tempted. He always tries to think in examples. He’s always striving for the most simple model. Aumann is really a master of using formal models.

People ask, “Why is game theory so popular in Israel?” One explanation is Aumann’s charming personality. His role in Israeli game theory reminds me of that of a rabbi in Jewish orthodox communities. Another explanation is the traditions among religious Jews – which have also had an effect on non-religious Jews – of the study of the Talmud. The study of the Talmud is not practical. For example, scholars of the Talmud were studying the question of what to do in the temple place during the entire 2,000 years we were disconnected from Jerusalem. One of the things that is beautiful about the Talmudic thinking is that it’s based on study of examples. The examples are very simple scenarios which demonstrate something deep. I believe that Aumann is influenced by this Talmudic way of thinking.

Time to talk about your next book, A Beautiful Mind.

This book is completely different. I picked it because when you think about the field you think also about the people who were involved. Of course the story of Aumann, the story of many other people, is interesting, but Nash’s story also has a message. The message is completely separate from game theory, but nevertheless, it happened around the development of game theory. Sylvia Nasar’s book is a brilliant book because she made a deliberate decision not to explain game theory. What she describes is a human drama.

Sylvia Nasar was a reporter for the New York Times when she covered the success of the telecommunications spectrum auctions in 1994. The auction was described – in my opinion wrongly – by the popular press and by some game theoreticians as the glorious success of the field of game theory, in terms of making it applicable. But in any case, the success was in contrast to the misery of one of its important contributors, John Nash.

In case – despite the movie starring Russell Crowe – anyone doesn’t know the story, John Nash suffered from paranoid schizophrenia and spent years just wandering around the campus of Princeton University, where he’d been a graduate student.

The story of John Nash is really a human story – I don’t think it sheds much light on game theory. In a field like economic theory the personality of the author is not relevant to understanding the subject matter. You might not know that Aumann is a religious Jew, you might think he is a Chinese Buddhist, but nevertheless whatever he wrote will still have the same meaning. That’s probably less true about philosophers or writers. That’s both the power and the weakness of formal models. So this book does not help to understand the field better, but it has a human message. It gives hope to people dealing with this terrible mental disease. Because of my involvement in the story of Nash, I came to talk to many people about it, and I feel that the story of Nash gave them a lot of hope.

Just to be clear, you feature a bit in the book because you fought to get Nash recognised by the field. I love the line in the book, your response when you fail to get Nash elected to one of these societies: “Ariel had a fit.”

I was marginally involved in the story of Nash in a couple of ways described in the book. One was making him a fellow in the Econometric Society. This was at the time I was at the London School of Economics, in the mid- to late 1980s. The other nominating committee members were open-minded, famous economists. Nevertheless, I was outvoted four to one against making John Nash a fellow. It’s just an honour. But his mental state influenced even that. A year after it was, of course, corrected.

There’s a big contrast between the attitude to Nash then and now, when Nash is invited to give lectures around the world. His lectures and recovery are important as they give hope to the very large community of people that have family who are sick. He gives an opportunity to people to discuss society’s attitude to mental illness. So I chose A Beautiful Mind as an important human story behind the story of game theory.

And his contribution to economics is absolutely central, isn’t it? You use Nash equilibrium all the time.

Yes, but it is not that Nash was the first to use Nash equilibrium. People were using the concept before Nash. But he put it into an elegant framework and showed about it whatever he showed. He did a crucial move but I would be very careful not to say, “Without Nash game theory would not develop.” Without diminishing the importance of it, I don’t think Nash contributed much to the discussion of what Nash equilibrium is.

So, your last book. You told me it was going to be a surprise.

Yes, I promised you a surprise as the fifth book. The fifth book is a book that has not been written yet. That’s the point. The fifth book is a lacuna, it’s a space that has to be filled. The book which, in my opinion, is so much waiting to be written is a book that will criticise game theory. Not from a sociological point of view, not a personality analysis of people like Aumann or Shapley or Schelling or whoever, but a purely intellectual analysis. There is a need for a book that counters the natural tendency of people to find in game theory solutions to problems that in my opinion game theory doesn’t say anything about. I’ve tried to do something small in this direction, in a book – Economic Fables. But my book is not more than a call for such a book.

I think people reading this interview would enjoy it a lot. It’s pretty funny – about the bar scene in A Beautiful Mind, for example, and how that’s got nothing to do with any idea of Nash’s. But also, your discussions of experiments, and how a knowledge of game theory would actually make you worse off if you were playing these games in real life.

Yes, many of the ideas that we talked about you’ll find in the book. But, again, I’m not recommending my book. The challenge is to take a chapter like my chapter two – which discusses game theory – and develop it into a full book, which will explain the limitations of game theory. This is the missing book.

You’ve spent so much of this interview talking about the limitations of game theory. It makes me wonder, what motivated you to become a game theorist in the first place? What attracted you to it?

I studied mathematics, though actually I wasn’t so interested in mathematics per se. I had this naive feeling that behind the symbols there was something more, which is connected with life. It’s a little bit like going to a zoo. You see animals, but you don’t think about the animals, you think about situations in life. You think, “Ah! The situation among the elephants is something that I recognise in my personal life.” That may not be the best analogy, but that’s the kind of feeling I had when I was a student. It’s not that I wanted to be practical – I never had the illusion that what I did had any practical value – but I wanted to understand argumentation better. Human argumentation was always something I was interested in. I wanted to be a lawyer. As a child I thought of a lawyer as someone who goes to court, makes arguments in favour of justice and wins over evil. My thinking was that formal models could help in this respect, from an intellectual point of view. And that’s all. If you ask me now whether I would repeat my life in this way, I don’t think so. If I could repeat my life, I would probably follow my unfulfilled dream to be a lawyer.