what is game theory?
The way I think about game theory is that it’s part of economic theory, a set of models and concepts that are supposed to capture the way we think about interactive strategic situations. these are situations in which my reasonable behavior depends on how I perceive or believe that other participants in the situation will behave. I want to put myself in the place of the other player or players, I want to get into their mind. that’s crucial to my decision. It’s not like a situation where I’m trying to decide whether or not to bring an umbrella, and all I have to think about is the possibility of rain this afternoon. but I can do it in many ways and I can respond in many ways. The special thing about game theory is that until now it has been assumed that when players respond to other players they respond rationally.
You are reading: Books on game theory
Are people supposed to be rational?
Yes, classical game theory deals with situations where people are completely rational. in principle we could think of interactive situations where the players are not completely rational, but nevertheless take into account or anticipate the behavior of other players. but the body of knowledge known as game theory, at least until now, has focused primarily on situations in which the players are rational.
what are the applications of game theory in real life?
that is 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 mathematical genius, he was also a public relations genius. the choice of the name “game theory” was brilliant as a marketing strategy. the word “game” has friendly and pleasant associations. it gives a good feeling to people. it reminds us of our childhood, chess and checkers, children’s games. associations are very light, not heavy, although 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 must say, are extreme compared to many of my colleagues. I think game theory is very interesting. I’ve spent much of my life thinking about it, but I don’t respect claims that it has direct applications.
“The choice of the name ‘game theory’ was brilliant as a marketing strategy. the word “game” has friendly and fun associations, even when you’re trying to deal with issues like nuclear deterrence.”
The analogy I sometimes give is one of logic. logic is a very interesting field in philosophy, or in mathematics. but I don’t think anyone is under the illusion that logic helps people to be better in life. a good judge does not need to know logic. may be useful (logic was useful in the development of computer science, for example), but it is not directly practical in the sense of helping you figure out how to behave better tomorrow, say in a debate with friends, or when analyzing data you get as a judge, citizen, or scientist.
So the prisoner’s dilemma situation couldn’t happen 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 opinion about formal models is that a model is a fable. game theory is about a collection of fables. Are fables useful or not? in a sense, you can say that they are useful, because good fables can give you a new view of the world and allow you to think about a situation differently. but fables are useless in the sense of giving you advice on what to do tomorrow, or how to reach an agreement between the west and iran. the same goes for game theory. A main difference between game theory and the literature is that game theory is written in a formal mathematical language. which has advantages and disadvantages. the advantages are that the formal language allows us to be more precise, allows us to get rid of associations that are not relevant, and allows us to better examine some arguments. the disadvantage of the formal language is the level of abstraction, which has two main disadvantages. First of all, it makes the theory very far from one less 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 lose a lot of information and most of the details, which in real life are very relevant.
Overall, I’d say game theorists made too many claims about its relevance. every game theory book begins with “game theory is highly relevant to everything you can imagine, and probably a lot you can’t imagine.” in my opinion, that’s just a marketing device.
why do it then?
first, because it’s interesting. And I’m not saying it’s not useful indirectly. I think that intellectual thinking – philosophy or logic or game theory – is very useful in the cultural sense. it’s part of the culture, it’s part of our perpetual attempt to better understand ourselves and the way we think. what I object to is the approach that says, in a practical situation, “OK, there are some very smart game theorists out there, let’s ask them what to do.” I have not seen, in my entire life, a single example where a game theorist could give advice, based on theory, that was more useful than that of the layman.
There is probably a confusion in the public between the personal skills of game theorists and the power of the theory itself. the game theorist community contains some brilliant people who also have “two legs on the ground”. this rare combination is very useful. people like that can have interesting and original ideas. not everyone: there are brilliant game theorists who I wouldn’t ask for any practical advice. but the advice of the other, even if it is good, should not be based on an authority.
Looking at the reverse, was there ever a situation where you were pleasantly surprised at what game theory had to offer?
none. not only none, but my point would be that game theory categorically cannot do it. maybe somewhere in a sherlock holmes or agatha christie story there was a situation where the detective was very clever and applied some logical trick that somehow caught the criminal, something like that. you know that in america there was a show on cbs, called numbers, spelled numer3rs, with the ‘e’ inverted. numb3rs wanted to make people curious about mathematics through detective stories. I found out because I had done experimental work with Amos Tversky and Dana Heller, on the game of hide and seek. in one of the episodes they refer to the role. Of course it was a joke, but the fact that my name appeared in such a program made me very happy. but outside of those programs, I categorically don’t see any cases where game theory could be useful.
so if people study it, should it be just for love of the subject?
That’s my position on 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’m more familiar with. the social sciences and humanities, in my opinion, should not have any pretense of being directly useful. we are part of the culture. we are useful as sculptures are. perhaps a sculpture to be put in central park in new york will prove to have a lot of influence on people. this is how our models are.
The case of computer science is interesting. For many years, Israeli computer scientists were criticized because computer science was too abstract in Israel, while elsewhere it was thought more in terms of practical applications. but i think people will now agree that the great success of the israeli hi-tech industry in the last 20 years is also a result of the abstract way computer science was taught in places like jerusalem in the 1990s seventy and eighty. That created the cultural environment on which the incredible success and flourishing of Israel’s high-tech industry since the 1990s is based. This is a case where abstraction indirectly led to something practical. Of course, I’m not against something practical eventually coming out of abstract studies, but that’s not the point. Of course, I can give you examples where game theorists, because they were smart, gave good advice, and probably some examples where game theorists gave bad advice.
by the way, I don’t know enough about it, but it is very interesting to investigate the role of game theorists in the development of US policy on nuclear deterrence. Thomas Schelling and John von Neumann and many other game theoretic lions were connected to this effort. Some people, including John Nash, have been working for a few months or years at Rand and thinking about strategic situations like that. From a historical point of view, I think it’s interesting to know if there was any real effect for game theorists in the 1950s. Now in Israel, again, given the situation with Iran, the question of whether game theory can telling us something is up in the air. I hope that the Israeli government does not consult game theorists regarding its difficult strategic decisions.
Some of these people you’re talking about appear in the books you’ve chosen, so let’s talk and start talking about them. what did you have in mind when you chose this list? Are these the classics of game theory?
The first one I chose was Game Theory and Economic Behavior by John von Neumann and Oskar Morgenstern. there was game theory before von neumann-morgenstern, and, as with any field, people now say “in 1921 so-and-so did so-and-so”. I am sure that at the end of the day, someone will find something relevant also in the Talmud or in the Greek writings. but von neumann-morgenstern was the first comprehensive and systematic attempt to put together many game-theoretic ideas. they established 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 that if someone else had written the first book, say a philosopher, game theory might have taken a completely different path. it is beautiful to see the implicit or explicit decisions about terms and language. these decisions determined the content and boundaries of the field. it’s very hard to break those boundaries afterwards.
the book has pretensions. I read from page one: “The purpose of this book is to present a discussion of some fundamental issues in economic theory that require a different treatment than you have hitherto encountered in the literature.” is an interesting sentence, what does it make us feel? first, that it is different, a different set of models than previous economic models, and that these are 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 in this top five, because it set the tone and because of its brilliant ideas.
Are you still using this book?
currently I use it less and less. after jstor, it became very easy to search articles and magazine articles, but books are hard to search. this is changing now. More and more books are available on the web. the more they can be searched, the more we will use them again. it’s a much-referenced book, though I’m sure most of the references are from people who didn’t open it.
I can’t say I use it on a daily basis, and if a student comes to me and says, “I want to learn game theory,” it won’t be the first book I’d recommend. that would be a more standard book, which teaches the concepts in a didactic way, summarizing what was happening in the last almost 70 years. but in the second wave, I would advise you to read the book, especially if you really want to get into the theory. people sometimes say: “book x is the bible of a field”. this is not. Actually, I don’t know of any game theory bibles, and it’s probably a good thing there aren’t any. because once there is a bible in the field, it is very difficult to make a change. a “bible” could be the beginning and end of a field.
let’s talk about your next book, games and decisions.
this book is written by two other brilliant people, r duncan luce and howard raiffa. the book was written in the mid-1950s, about 10 years after von neumann-morgenstern, and of course it is a book that was greatly influenced by von neumann-morgenstern. it is a less formal book. it is beautifully written. it’s a book that I always tell students about, “there are a lot of ideas in there that haven’t been developed yet.”
luce and raiffa were thinking about elements of what we would now probably call modern choice theory. Standard classical choice theory deals with rationality, ways of applying rationality to decision problems. his way of thinking is natural, which is what I like about this book (and much of game theory in general). it is really on the bridge between natural thought and formal thought. von neumann-morgenstern set the formal standards, and luce and raiffa stepped back. this can be seen in the book’s subtitle, Games and Decisions: An 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 criticizing the rationality approach.
by the way, von neumann-morgenstern was not just the beginning of game theory. there is also a very important chapter on the expected utility model. this is the basic model still used by almost everyone in economics regarding decision making under conditions of uncertainty. it is the basis not only of game theory, but of almost everything in economic theory that involves uncertainty. luce and raiffa criticized this theory and suggested some ideas and alternatives that continue 30 or 40 years later.
Let’s move on to your next book, a collection of articles by Robert Aumann, winner of the 2005 Nobel Prize in Economics and, like you, Israeli.
This collection is interesting for several reasons. first of all, bob aumann is a very special man. I do not agree 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 all about”. from time to time he expresses views, for example on politics, backed up with the authority of the great game theorist. I don’t like those statements. Despite this, I admire him for his academic work and his personality. First of all, there is a beauty in his writing. he is a master in the way he writes, writes what he writes, and in the way he uses formal models to talk about game theory. It’s probably very hard for someone off the field to appreciate him, but he has an aesthetic. Aumann’s style contrasts with the dominant style in today’s economics. it is with much, if I may use the word, nonsense, much excessive pretense of being useful. in many current articles on economic theory, models are not models, tests are not tests. the fight for generality is misleading since each model is but a small example.
aumann has the ability to use more sophisticated mathematical tools than almost all other game theorists. but he is not tempted. he always tries to think of examples. he is always fighting for the simplest model. Aumann is truly a master of using formal models.
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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 a rabbi in orthodox Jewish 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, Talmudic scholars were studying the question of what to do at the temple site during the entire 2,000 years that we were disconnected from Jerusalem. one of the beautiful things about talmudic thought is that it is based on the study of examples. the examples are very simple scenarios that demonstrate something profound. i think 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 chose it because when you think of the field, you also think of the people involved. Of course, Aumann’s story, the story of many other people, is an interesting one, 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 telecom spectrum auctions in 1994. the auction was described, in my opinion wrongly, by the popular press and some game theorists as the glorious success of the field of game theory, in terms of making it applicable. But in any case, the success contrasted with the misery of one of her important collaborators, John Nash.
Just in case, despite the movie starring russell crowe, someone doesn’t know the story, john nash suffered from paranoid schizophrenia and spent years wandering the campus of princeton university, where he had been a graduate student.
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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. You may not know that Aumann is a religious Jew, you may think he is a Chinese Buddhist, but nevertheless everything he wrote will have the same meaning. that is probably less true about philosophers or writers. that is both the power and the weakness of formal models. so this book does not help to better understand the field, but it has a human message. gives hope to people dealing with this terrible mental illness. Because of my involvement in the Nash story, I came to talk to a lot of people about it, and I feel like the Nash story gave them a lot of hope.
Just to be clear, you appear in the book a little bit because you fought for nash to be recognized on the field. I love the line from the book, your response when you don’t get nash elected to one of these societies: “ariel had a fit.”
I was marginally involved in the nash story in a couple of ways described in the book. one was making him a member of the econometric society. this was when i was at the london school of economics, in the mid to late 1980s. the other members of the nominating committee were famous and open-minded economists. however, i was beaten four to one against making john nash a partner. it’s just an honour. but his mental state influenced even that. a year later it was, of course, corrected.
there is a big contrast between the attitude towards nash then and now, when nash is invited to lecture around the world. your conferences and your recovery are important as they give hope to the great community of people who have sick relatives. it gives people the opportunity to discuss society’s attitude towards mental illness. so i chose a beautiful mind as an important human story behind the history of game theory.
and its contribution to the economy is absolutely central, isn’t it? you use nash equilibrium all the time.
yes, but not that nash was the first to use nash equilibrium. people were using the concept before nash. but he put it in a fancy frame and showed everything he showed. he made a crucial move, but he would be very careful not to say: “without nash, game theory would not develop”. Without diminishing its importance, I don’t think nash has 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 like the fifth book. the fifth book is a book that has not yet been written. that is the point. the fifth book is a gap, it is a space that must be filled. the book that, in my opinion, is waiting so long to be written is a book that will criticize game theory. not from a sociological point of view, not an analysis of the personality of people like aumann or shapley or schelling or whoever, but a purely intellectual analysis. there is a need for a book that counteracts the natural tendency of people to find in game theory solutions to problems about which, in my opinion, game theory says nothing. i tried to do something small in this direction, in a book – economic fables. but my book is nothing more than a call to such a book.
I think people reading this interview would really enjoy it. it’s pretty funny, about the bar scene in a beautiful mind, for example, and how that has nothing to do with any idea of nash. but also, her discussions of experiments, and how knowledge of game theory would actually make her situation worse if she played these games in real life.
yes, many of the ideas we talked about you will find in the book. but, again, I am 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 lost book.
You have spent 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?
I studied math, although I wasn’t really that interested in math per se. I had a naive feeling that behind the symbols there was something else, which is connected with life. It’s a bit like going to a zoo. you see animals, but you don’t think about animals, you think about life situations. you think, “oh! the situation between the elephants is something that I recognize in my personal life.” That may not be the best analogy, but that’s the kind of feeling I had as a student. It’s not that I wanted to be practical, I never had the illusion that what I was doing had any practical value, but I wanted to understand the argument better. human argumentation was always something that interested me. I wanted to be a lawyer. As a child I thought of a lawyer as someone who goes to court, argues for justice and defeats evil. my thought was that formal models could help in this regard, from an intellectual point of view. and that’s it. If you ask me now if I would repeat my life this way, I don’t think so. If I could repeat my life, I would probably follow my unfulfilled dream of being a lawyer.
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