Pure game theory — an irrelevant tautology

31 Oct, 2017 at 18:13 | Posted in Economics | 13 Comments

Applied game theory is a theory of real-world facts, where we use game theoretical definitions, axioms, theorems and (try to) test if real-world phenomena ‘satisfy’ the axioms and the inferences made from them. When confronted with the real world we can (hopefully) judge if game theory really tells us if things are as postulated by theory.

like-all-of-mathematics-game-theory-is-a-tautology-whose-conclusions-are-true-because-they-are-quote-1But there is also an influential group of game theoreticians that think that game theory is nothing but pure theory, an axiomatic-mathematical scientific theory that presents a set of axioms that people have to ‘satisfy’ by definition to count as ‘rational.’ Instead of confronting the theory with real-world phenomena it becomes a simple matter of definition if real-world phenomena are to count as signs of ‘rationality.’

This makes for ‘rigorous’ and ‘precise’ conclusions — but never about the real world. Pure game theory does not give us any information at all about the real world. It gives us absolutely irrefutable knowledge — but only since the knowledge is purely definitional.

Mathematical theorems are tautologies. They cannot be false because they do not say anything substantive. They merely spell out the implications of how things have been​ defined. The basic propositions of game theory have precisely the same character.

Ken Binmore

Pure game theorists, like Ken Binmore, give us analytical truths — truths by definition. That is great — from a mathematical and formal logical point of view. In science, however, it is rather uninteresting and totally uninformative! Even if pure game theory gives us ‘logical’ truths, that is not what we are looking for as scientists. We are interested in finding truths that give us new information and knowledge of the world in which we live.

Scientific theories are theories that ‘refer’ to the real-world, where axioms and definitions do not take us very far. To be of interest for an economist or social scientist that wants to understand, explain, or predict real-world phenomena, the pure theory has to be ‘interpreted’ — it has to be ‘applied’ theory. A ‘pure’ game theory that does not go beyond proving theorems and conditional ‘if-then’ statements — and do not make assertions and put forward hypotheses about real-world individuals and institutions — is of little consequence for anyone wanting to use theories to better understand, explain or predict real-world phenomena.

Pure game theory has no empirical content whatsoever. And it certainly has no relevance whatsoever to a scientific endeavour of expanding real-world knowledge.


  1. Further reading, on this subject: http://anthro.vancouver.wsu.edu/media/PDF/Hagen_and_Hammerstein_2006_Critique_of_evolutionary_games.pdf

  2. Dismissing all logical reasoning as nothing interesting and no more than a tautology is polemical but mistaken. Analysis has an essential role in developing knowledge. Yes, we must confront the world as it is and interact with the reality of actual phenomena, but when we do so we will find inevitably that the most interesting truths of mechanisms and cause and effect are not subject to direct observation. We seek to discover systems in the world, but must rely in part on our imaginative ability to gain insight into how those systems work by clever guesses and the conviction that the real world is a logical place and the working of systems we find there are not magical, but rather bound by logical necessity.
    It is certainly true that pure theoretical analysis is a priori and makes no statements about what is, only about what is possible. That a geometry is not itself a map does not rob geometry of either usefulness or interest.
    I object to efforts to test theory as if we could “test if real-world phenomena ‘satisfy’ the axioms and the inferences” of analytic theory. Analytic theories are not models of the world, little nomological machines isomorphic with the world. That is backwards: empirical investigation tests the world to find the world’s logic. And, empirical investigation requires operational models quite different in character from pure analysis, operational models that feature methods of objective measurement.
    Discovering the logic of the world may well provide useful feedback for analytic theory, showing the inadequacy of a convenient assumption or the incompleteness of an accounting for the necessary and sufficient conditions.
    Where game theory is concerned, the insight that, say, institutions, by prescribing roles and rules structure human behavior into a virtual reality is not a bad heuristic. The complexity of such behavior and structures in real cases must be daunting. But, the retreat from empiricism on account of such social complexity can not be defended as science.

  3. Bruce, defending bad theories with arguments of heuristics and pedagogy, is not enough. If game theory is going to have a fair chance of being relevant for real-world analysis it has to get out of its ‘Model Platonistic’ frame with its empirically empty thought-experimental model building strategy. A theory that is aprioristically true by definition is of no avail for understanding any real-world systems. A pure game theory that equates human behaviour with narrowly defined optimizing ‘rationality’ and ‘preferences’ is of course very ‘flexible’, but it only comes at the devastatingly high price of making the theory substantively empty and non-testable since any whatsoever ‘evidence’ (e.g. philanthropy, fairness, reputation, reciprocity, or any other motivation not based on ‘self-interest’) may be accommodated. Better then to face facts: pure game theory has over and over been shown to have little explanatory or predictive power when confronted with the real world. The right way to move forward cannot be to keep the core assumptions and hence burn all bridges to the real world. Is game theory to be relevant for economists and social scientists, it has to earnestly take account of all the — experimental and theoretical — evidence we’ve been collecting for decades now. The core of game theory is sick. It has to be replaced.

    • Dear Lars, it´ts a name for this type of mumbo-jumbo economics,”Voodo-Economics, and you can sadly get “Nobel Awarded” for this sort of non scietnific nonscence!! Hälsa Fabian i helgen 🙂 ! Jan

      • Ps. How nice it would be in the World, if those type of people was isolated in some rooms ,at loonly places in some forgotten Universites, there they could play with numbers and ideas,how much and what ever they wan´t . Alcatraz is abandond as fare as know ,i think theres of lot spare rooms available ,i think?Lot of space for those sort types and with nice sea-outlook all around .

        • I think we can create virtual reality technology so real, they will choose voluntarily to implement their models and live in the VR according to their philosophies. The promise of technology is that they can have their VRs and live as they wish according to models they prefer, and I can live in mine without ever having to know about them …

          • Indeed 🙂 !

  4. Lars, I came across Ken in connection with his work on auction design, as an application of game theory. It seems to me that he does understand what pure game theory is and is not, and how to apply it. His work, it seemed to me, had a significant global impact and he certainly made a lot of money out of his applied game theory. So I think you are misrepresenting him. I think your target should be game theory as understood by mainstream economists, not the real deal, which might be a part of getting us out of the mess we are in.

    • Dave, I have never doubted that Ken knows the difference between pure and applied game theory. The reason I mentioned him is that he defends the first variety, which I have difficulties as an economist to do if what I want is to increase our real-world knowledge. Auctions are examples that many defenders of mainstream theory put forward where the theory has shown itself to be ‘useful.’ Maybe so, but I would argue that is mostly because auctions are one of few economic examples where we get near the necessary closure conditions for the applicability of the theory. BUT — an economy — or a society — is not an auction.

      • They are remaking society so that it is more like an auction, by closing off sections of markets and applying their rationality to make lots of money there, then slowly spreading the auction conditions to everything, every single relation in society, that they can. They want us to be like them and will compel us to obey their norms of rational behavior … How much will you bid for a mother’s love? Hurry, if you don’t act now that love will be gone forever …

        • Indeed 🙂 !

      • Lars, my own take on this is that for any empirical subject no pure theory can ever be entirely reliable, but it can be illuminating. It seems to me that even a half-baked game theory can be useful, as long as one recognizes its limitations. As a mathematician I would argue that pure game theory is ‘a good thing’ in that it helps rid the half-baked variety of errors and ambiguities.

        There is a kind of dogmatic or simplistic game theory that cites pure game theory without seeming to engage with it seriously. I regard this as half-baked or perhaps over-baked. Whichever, it is dangerously wrong.

        Thus I see the problem as dogma and over-simplification, not game theory as such. I sometimes wonder if those who insist on the dogma are seriously deluded, or simply wish to delude others, so that they may profit from the confusion.

  5. I wonder, if ever we entered a world dominated by cyborgs, whether the rules governing their behaviour would somehow naturally evolve from a pure game theoretic paradigm, given that cyborgs are presumably the ultimate rational entity.

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