Game theory — a critical introduction

9 July, 2014 at 18:20 | Posted in Economics | 13 Comments

Back in 1991, when yours truly earned his first Ph.D. with a dissertation on decision making and rationality in social choice theory and game theory, I concluded that “repeatedly it seems as though mathematical tractability and elegance — rather than realism and relevance — have been the most applied guidelines for the behavioural assumptions being made. On a political and social level it is doubtful if the methodological individualism, ahistoricity and formalism they are advocating are especially valid.”

This, of course, was like swearing in church. My mainstream neoclassical colleagues were — to say the least — not exactly überjoyed.

For those of you who are not familiar with game theory, but eager to learn something relevant about it, I have three suggestions:

Start with the best introduction there is

carm

and then go on to read more on the objections that can be raised against game theory and its underlying assumptions on e.g. rationality, “backward induction” and “common knowledge” in

varoufakis

and then finish off with listening to what one of the world’s most renowned game theorists — Ariel Rubinstein — has to say on the — rather limited — applicability of game theory in this interview (emphasis added):

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.
rubinThe 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 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.

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.

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?

… 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.

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.

One of the proof methods that I was especially critical of in my dissertation was the use of “backward induction.” I have to confess I haven’t given it much thought outside the class room since then, but after having spent yesterday afternoon reading Ken Binmore’s Game Theory: A Very Short Introduction, I have to confess I’m slightly surprised that it — obviously — still holds such a strong position among game theorists. For those of you not familiar with it I recommend looking at the video below and afterwards take a minute or two and try to figure out how convinced you are about backward induction really helping us to understand what is after all the very idea of game theory — to analyze, understand, and explain strategic thinking …
 

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  1. Another good source is the Complete Idiots Guide to Game Theory. It is really clear and comprehensive.

  2. About 20 years ago, I was all set to start a PhD on game theoretics of nuclear deterrence!! Then, I got a job instead… I thought I was turning my back on a leading role at the UN (!)…only when I’d been around a bit did I get a sense of the limitations of its’ applicability…

  3. What are you talking about? Ken Binmore “Backward induction is a particularly doubtful rationality principle” .http://www.tark.org/proceedings/tark_mar13_94/p150-binmore.pdf

    • What am I talking about? Well continue to read chapter 3 of the book and you will see how Binmore gladly portrays both “common knowledge” and “backward induction” as “useful instruments” when discussing “subgame perfection” and “trembling hand” equilibrium. My critique is that even if these assumptions are “useful,” that is not enough to warrant using them. Assuming that people are green and come from Mars may be very useful when constructing economic models, but what has that got to do with understanding and explaining structures and causal relations in real economies?

      • Game theory has proved very successful in market settings (experiments), where it is principally applied in economics. But Binmore has been a leading critic of those who believe that economics contains a “selfishness axiom” (false) or that rationality implies backward induction (also false). “To defend backward induction, one needs not only that it is common knowledge among the players that they are all utility maximizers, but that they disregard any evidence to the contrary that they might receive when playing the game.” See Section 5 of http://else.econ.ucl.ac.uk/papers/uploaded/262.pdf .

  4. Well, as Heap and Varoufakis show, there is not much choice. Without backwards induction it’s impossible to deal precisely with certain rationality principles. In any case, in microeconomics, game theory has been useful and interesting. There is even some interesting stuff being with game theory and macroeconomics.

  5. […] Game theory — a critical introduction Lars P. Syll […]

  6. “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.”

    Uh… hang on a minute… logic will not help you in a debate? Is this guy serious? Sorry, I don’t buy that at all. Logic is extremely important in debates and people with a poor grasp of logic will tend to be poor debaters. This is a very odd statement.

    • I assume the author is talking about the kind of logic you would study in a course in mathematical logic or a philosophy course in symbolic logic. Unlike Leibniz’s dream, when we have a deciion to make or a dispute to setle, we don’t sit down and say “Let us calculate.”

  7. Hi Lars, do your books cover Adam Curtis’s BBC documentary series The Trap?

    http://www.correntewire.com/comment/228981#comment-228981

    Episode 1: “F**k You Buddy” (11 March 2007)

    –snip–
    In this episode, Curtis examines the rise of game theory during the Cold War and the way in which its mathematical models of human behaviour filtered into economic thought.

    The programme traces the development of game theory with particular reference to the work of John Nash (the mathematician portrayed in A Beautiful Mind), who believed that all humans were inherently suspicious and selfish creatures that strategised constantly. Using this as his first premise, Nash constructed logically consistent and mathematically verifiable models, for which he won the…Nobel Prize in Economics. He invented system games reflecting his beliefs about human behaviour, including one he called “Fuck Your Buddy” (later published as “So Long Sucker”), in which the only way to win was to betray your playing partner, and it is from this game that the episode’s title is taken. These games were internally coherent and worked correctly as long as the players obeyed the ground rules that they should behave selfishly and try to outwit their opponents,[citation needed] but when RAND’s analysts tried the games on their own secretaries, they instead chose not to betray each other but to cooperate every time. This did not, in the eyes of the analysts, discredit the models but instead proved that the secretaries were unfit subjects.
    –snip–

    Episode 2 “The Lonely Robot”

    –snip–
    Curtis’s narration concludes with the observation that the game theory/free market model is now undergoing interrogation by economists who suspect a more irrational model of behaviour is appropriate and useful. In fact, in formal experiments the only people who behaved exactly according to the mathematical models created by game theory are economists themselves, and psychopaths.
    –snip–

    etc.

    Quotes are from Wikipedia entry for The Trap but were included in longer discussion at Corrente. I’d highlight the ends of both quotes — subjects must be valid psychopaths for games to work, cooperators disqualified.

  8. Lars, game theory has been usefully used in analyzing the behavior of lion prides.One could interpret this as an indication of limited the theory’s usefulness really is. von Neumann didn’t think much of Nash’s bargaining work while simultaneously recognizing it was clever.

  9. There is much to find fault with in the video, not least that backward induction gives a super-dumb answer, but I think backward induction is something that one should think about before playing the game.

    More generally, I think the problem is not in the game theory itself as in the misconceptions that people have about the theory.

  10. […] Ariel Rubinstein, experto mundial en teoría de juegos […]


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