Home > Uncategorized > Why game theory will be nothing but a footnote in the history of social science

Why game theory will be nothing but a footnote in the history of social science

from Lars Syll

Nash equilibrium has since it was introduced back in the 50’s come to be the standard solution concept used by game theorists. The justification for its use has mainly built on dubious and contentious assumptions like ‘common knowledge’ and individuals exclusively identified as instrumentally rational. And as if that wasn’t enough, one actually, to ‘save’ the Holy Equilibrium Grail, has had to further make the ridiculously unreal assumption that those individuals have ‘consistently aligned beliefs’ — effectively treating different individuals as incarnations of the microfoundationalist ‘representative agent.’

In the beginning — in the 50’s and 60’s — hopes were high that game theory would enhance our possibilities of understanding/explaining the behaviour of interacting actors in non-parametric settings. And this is where we ended up! A sad story, indeed, showing the limits of methodological individualism and instrumental rationality.

Why not give up on the Nash concept altogether? Why not give up the vain dream of trying to understand social interaction by reducing it to something that can be analyzed within a grotesquely unreal model of instrumentally interacting identical robot imitations? 

We believe that a variety of contributory factors can be identified …

gaIt is possible that the strange philosophical moorings of neoclassical economics and game theory have played a part. They are strange in at least two respects. The first is a kind of amnesia or lobotomy which the discipline seems to have suffered regarding most things philosophical during the postwar period … The second is the utilitarian historical roots of modern economics … Thirdly, the sociology of the discipline may provide further clues … All academics have fought their corner in battles over resources and they always use the special qualities of their discipline as ammunition in one way or another. Thus one might explain in functionalist terms the mystifying attachments of economics and game theory to Nash.

Half a century ago there was​ widespread hopes game theory would provide a unified theory of all social science. Today it has become obvious those hopes did not materialize. This ought to come as no surprise. Reductionist and atomistic models of social interaction — such as the ones neoclassical mainstream economics is founded on — can never deliver good building blocks for a realist and relevant social science.

  1. Alejandro Nadal
    October 6, 2017 at 6:31 pm

    Hi Lars, great post, right on target.
    The comment: Nash equilibrium when applied to an Arrow-Debreu model (which was built originally to use Nash’s application of Kakutani’s fixed point theorem) is a static construct where individuals calculate all sorts of things but nothing actually happens in the “market”. So, in addition to all of the highly unrealistic assumptions involved, in fact the model’s contribution to understanding explicit market dynamic processes is zero. Nash equilibrium is the result of individual agents’ calculations, but not of actual market processes. What’s your view on this?

    • October 6, 2017 at 10:28 pm

      Hi Alejandro,
      Thanks. Guess your right. Game theorists following in Nash’s footsteps often just assume that people reach a Nash equilibrium without adequately explaining why and how they get there. And the nowadays so popular repeated games ‘convergence’ via learning, seems to me to be a ‘cul de sac,’ since for every mechanism they come up with there are always games for which they do not apply even approximately. And when it comes to n-person market games, the CKR and CAB assumptions doesn’t actually help much in effectively finding/choosing a Nash equilibrium even if it would exist. So, as you write, the contribution of the model “to understanding explicit market dynamic processes” may very well be considered next to zero!. And I guess that goes for most applications of Brouwer-Kakutani style fixed-point theorems in economics at large!

      • October 9, 2017 at 10:41 am

        Hi Lars

        Wondering why you haven’t responded to or even acknowledged my comments below on the roundabout model of Nash equilibrium and the IOU interpretation of money, I’ve re-read your post and now think you are missing the point of equilibria in economics.

        We are discussing games, which are all about deception. The Nash game is to get everybody else to play by the rules so they make mistakes when confronted by behaviour not governed by the rules. The roundabout example is forcing one’s way into the traffic by intimidating cars already on the roundabout with fear of a collision. In economics the game is to pretend bank-money is valuable when it is not; in politics the game is to change the meaning of words so that supporting party rather than population is seen as patriotic. If anyone questions the truth of any Humean social science doctrine the game is to pretend there is no such thing as truth.

  2. Alan
    October 6, 2017 at 7:17 pm

    …widespread hopes game theory would provide a unified theory of all social science

    I think it got traction because the game theory crowd attracted institutional support and money as the MIC and the elites liked that sort of thinking. Mainstream economics thereby got to play disciplinary imperialism and drown out critics within economics and other social sciences. There were certainly other social science disciplines where there were never such “widespread hopes” for game theory because that sort of thinking was fundamentally at odds with core disciplinary commitments.

    Here’s an entertaining video clip in which Nash himself talks about the limitations of game theory.

  3. rjw
    October 6, 2017 at 7:20 pm

    I agree very much that the bubble in (rational choice) GT in the 90s was hopelessly oversold. I had that feeling at the time as an undergraduate, and invested very little time in it as a result. But I think you commit the sin of taking the thesis too far. The very simplest models in game theory (prisoner’s dilemma, assurance game, that kind of thing) are actually very useful little mental models that help one to understand the structure of some types of social interactions quite well. It is a bit like a Keynesian cross diagram. Yes, it is a bare bones representation, but capturing quite an important mechanism in a way that even the dimmest can grasp.

    The point is, diminishing returns set in phenomenally quickly with game theory. Most of what is useful can be picked up with a very introductory book. That was the point a lot of people missed, and it is on this point I agree with your ” footnote” judgement.

    But your last sentence also suggests that analysis at the level of individual agents (atomistic models) is inherently flawed, and that methodological individualism, even as a research strategy, is quite wrong. Perhaps I misinterpret your position, but if that is your view, I have to disagree. Starting with the question of why individuals behave as they do, and conceptualizing this as the outcome of a set of beliefs, constraints and preferences is hardly unreasonable as a starting point. It does not preclude taking a broader view of aggregates, or how people interact, for example when one looks at issues such as (group) belief formation.

    In this regard, I would find myself in agreement with Jon Elster, and much of his writing on methodological issues in social science. I think the teleological and functionalism inherent in (for example) much Marxist social theory is a far worse sin. And while I am a convinced heterodox economist, I still despair when I read stuff on heterodox sites which treat capital, or capitalism, as equivalent to thinking sentient beings (for example). Such writers could do with a little bit more atomistic thinking, not less. Similarly, there is plenty of good stuff in the “neoclassical” literature (say, models of asymmetric information).

    Bottom line, I think methodological dogmas cut both ways, which is why I tend to consider myself a pluralist, in broad terms. There is good and bad work in pretty much any school of economic thought one wishes to name that has little to do with their underlying methodological differences. The core problem with many orthodox (or neoclassical) economists, is precisely their methodological dogma. But at the same time there are plenty of people in the blogosphere who dismiss “neoclassical” economics out of hand, wholesale, despite having a very thin grounding in economics, largely (I suspect) because they reason backwards. Neoclassical economics = neoliberalism, and because they dont like the one, they dismiss the other out of hand. (I am certainly not, of course, accusing you of that, just to be clear.)

  4. October 6, 2017 at 8:19 pm

    Or, more briefly, every paradigm has three stages:
    First the innovators, brilliantly launch the new paradigm.
    Next the imitators copy the new ideas hoping to participate in the early adoption of the innovative development.
    Third the idiots show up. They never understand the essential innovation or the limitations of its adoption.
    These three “I’s” play out and then the search begins for another innovation.

  5. robert locke
    October 6, 2017 at 8:54 pm

    There is a certain irony in that John von Neumann and Oskar Morgenstern pointed out seventy years after Walras’ “achievement.” in the foreword to Theory of Games and Economic Behavior (1944): ‘The concepts of economics are fuzzy but even in those parts of economics where the descriptive problem has been handled more satisfactorily, mathematical tools have seldom been used appropriately. Mathematical economics has not achieved very much.’ (p. 8), which I note in my 24 September posting on Economic as Science, and your statement :”Half a century ago there was​ widespread hopes game theory would provide a unified theory of all social science. Today it has become obvious those hopes did not materialize…” Neumann and Morgenstern thought in 1944, as did so many others, that they had set mathematical economics on the path to achieve much.

  6. Norman L. Roth
    October 6, 2017 at 9:43 pm

    Oct. 06, 2017

    I quite agree with the verdict that GAME THEORY ran into diminishing returns quite early on following V. Neumann and Morgenstern’s boast that it explained Human “Economic Behavior” implicit in the 1944 title. BUT, curiously enough, when I was writing TELOS & TECHNOS, The Teleology of Economic Activity & the Origins of Markets, I did not dismiss John V. Neumann’s other thoughts about economic processes. To whit, his definition of a “free good”.:Page 161 of the 197 page edition. It turned out to be a good fit with other concepts developed in T &T, such as Nr,The Natural Participation Rate & T, Technological Time: .And the case against “robust” immigration policies when the Natural Participation rate is low. {Read the book, s’ils vous plaites !}

    I also like the sentiments expressed in rjw’s fourth paragraph a lot. But I emphasize that my usage of the Teleological-drive in human affairs has nothing in common with the Marxist version of the concept: Which is little more than automatic {imposed ?} linear determinism on steroids.. My usage of the .idea is much more related to that of Thorstein Veblen, Henri Bergson, or Joseph Schumpeter. I also like rjw’s poke in the ribs of those who dismiss virtually the entire body of economic thought & ALL economists, when their .”grounding in economics is so thin” that they don’t even know, let alone understand, the difference between “neoclassical” & “neoliberal”. Let’s have your name ‘rjw’. You’ve got nothing to hide. And you’re certainly on the right path: Despite a bit of ambiguity about what you mean by buzz-words like “heterodox economist”.

    Please GOOGLE: {1} Norman L. Roth {2} Norman L. Roth, Economist

  7. October 7, 2017 at 10:16 pm

    In “The Use and Misuse of Game Theory” (Scientific American, 1962), Anatol Rapoport long ago pointed out that one of the most important contributions of game theory was to reveal its own limitations. Apparently economists were not interesting in acknowledging those limitations.

  8. October 8, 2017 at 1:23 pm

    The unstated assumption in game theory is the teleological one of aiming to “win”. But the theory is purely mathematical, and it seems to me one can change the aim to dynamic equilibrium in the sense of not interfering with anyone else, which ( I suggested recently) is what happens to drivers when they give way at a roundabout. That ties in well with the convention that money is not a reward for work but an IOU to remind us that we owe others work: like the Copernican revolution, a simple inverse of what has long been assumed. What is the problem with this? Is it too simple for you clever guys?

  9. Norman L. Roth
    October 8, 2017 at 3:42 pm

    Oct. 08, 2017,

    John V. Neumann {and Oskar Morgenstern} were reported to have said about Paul Samuelson {& his acolytes at M.I.T} that “Samuelson has some very murky ideas about equilibrium”, .Indeed, he did ! But Mr. Taylor’s ideas about “money” and “teleology” seem equally “murky”.
    M. Taylor, Please read my comments of Oct. 06, above, as a guide for introductive thinking into the meaning of “Teleology”. It’s not all that “simple”.. even for “clever guys”. Nor is it just like “theology” with the ‘h’ omitted. .As for GAME THEORY ,being “purely mathematical”
    for all its limitations to economics, it WAS intended to have some ‘common sense’ applications to other areas of human interaction. Where it is far from useless. Why not compare it to the great classic ART of WAR by Sun Tzu, circa 2,500 years ago. He was one of the great thinkers of Human antiquity. And if you want some clarifying ideas about the history of {paper } money, you might read about China’s experience with it. THEY were the introducers of paper money. And the first to use, and manipulate its issuance for purposes of state. Please accept my suggestions in the spirit of didactic intervention.

    Yours respectfully, Norman L. Roth.

  10. Norman L. Roth
    October 8, 2017 at 7:40 pm

    Oct. 06, 2017

    Correction to first sentence of Oct. 08,:42 P.M.

    In the quotation, ‘equilibrium’ should be corrected to ‘stability’., That was V. Neumann’s original word. Equilibrium and ‘stability’ are not the same thing. Samuelson’s shallow imitation of a concept he cribbed holus-bolus from Physical Chemistry, should have finished off his reputation then & there. Especially his extreme leap into applying Le Chatelier’s ‘law’ to his version of ‘mathematical economics’ . Philip Mirowski had a satirical field-day about this in MORE HEAT THAN LIGHT.{1989} But again, It would be rash to dismiss the ENTIRE body of Samuelson’s working career. He had his moments. Indeed,he was following in Irving Fisher’s footsteps when Fisher’s version of the Quantity Theory of Money turned out to be a ‘borrowing’ from Boyle’s Law of Gases. Fisher, reportedly even built a working hydraulic model of the Quantity theory: Which may still be moldering away in some neglected storage room of the SMITHSONIAN. Incidently, Keynes loathed the Quantity Theory of Money.

    Thank-you one and all for your patience.

    Respectfully, Norman L. Roth

  11. October 8, 2017 at 11:00 pm

    From my dictionary: “Teleology: interpretation of things in terms of purpose”. One aims to achieve a purpose.

    From Wikipedia, re the model strategy of giving way at a roundabout: “In game theory, the Nash equilibrium, named after American mathematician John Forbes Nash Jr., is a solution concept of a non-cooperative game involving two or more players in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy.[1] If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitutes a Nash equilibrium. The Nash equilibrium is one of the foundational concepts in game theory. The reality of the Nash equilibrium of a game can be tested using experimental economics methods”.

    From W. re dynamic equilibrium: “Whereas in a static equilibrium all quantities have unchanging values, in a dynamic equilibrium various quantities may all be growing at the same rate, leaving their ratios unchanging.” As I’ve understood it, stability is a “fuzzy”, probabilistic version of these, understood in contrast to divergent or oscillatory behaviour permitted or driven by positive feedback.

    • October 8, 2017 at 11:10 pm

      PS. This went as I was about to revise the the first line. Another dictionary reading of ‘teleology’ is “the doctrine of the final causes of things”. I had been about to appreciate Norman’s joke about theology without an ‘h’!

  12. Norman L. Roth
    October 8, 2017 at 11:57 pm

    Oct. 08, 2017
    You’ve got it right in terms of how I used the concept, M. Taylor, In your first line. at that !
    Read the quotations in TELOS & TECHNOS just before the introduction. .especially by Eugen Von Bohm -Bawerk.

    Teleology as “final causes of things” does seem to be related to things “Theological. ” Or maybe even to “eschatological” .As in your second definition. But it’s a tricky concept that has been wrestled with by thinkers, east & west for the last 3000 years. Marx wasn’t much of an authority on the subject. See the second paragraph of my Oct. 06 letter,9:43 p.m. As you {plural} can plainly see, I’m far less dismissive of things theological than I am of most secular ruminations.
    I think Von Neumann had something in mind quite specific about his definition of “stability”
    It certainly didn’t resemble Samuelson’s ideas about it. Maybe V. Neumann’s .definition of “stability” can be researched by some one more mathematically proficient than I am. How about M. Lars Syll. Or yourself ?
    I.ve heard that Nash Equilibrium stuff has its acolytes in Schools of Business. But maybe there’s somebody out there who can enlighten us on the “reasons why”.
    Thank you for your input, M. Taylor. Have a good {Canadian} Thanksgiving. When do you celebrate it in the U.K. ?

    Respectfully, Norman L. Roth

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