Home > Uncategorized > Game theorists — people carried away by fictions

Game theorists — people carried away by fictions

from Lars Syll

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.

Daniel Hausmann once famously criticized Paul Samuelson’s overlapping generations models for having been “carried away by fictions.” As far as I can see, the same goes for game theorists and their models.

  1. July 7, 2019 at 4:57 pm

    I was arguing this the other day because of Nash’s equilibrium model. It seems to me that it is being used in strategic or tactical voting in Canada where we still have a FPTP — First Past the Post — system of party representation. The idea is to figure out from past voting patterns and current polling how one should vote in the next election in order to ensure that one party or leader is NOT successful. Many have buyer’s remorse about Trudeau because he broke his 1800 promises to end FPTP and bought a pipeline to ship bitumen while purporting to be an advocate for climate. But Andrew Scheer seems to be in bed with Trump supporter, Doug Ford, (also the brother of the now deceased crack smoking former mayor of Toronto), who is now the populist premier of the biggest province, Ontario, with the lowest polling satisfaction of any premier ever. Even lower it is alleged than the so-called socialist one, Bob Rae, who wound up being the Liberal leader before Trudeau.

    • July 8, 2019 at 8:44 am

      Ken’s discussion at http://www.nuff.ox.ac.uk/users/klemperer/biggestsept.pdf could be adapted. There’s a lot more to than ‘to figure out from past voting patterns and current polling how one should vote in the next election ‘.

      • September 17, 2019 at 3:00 pm

        Yes. Particularly this bit of its conclusion::

        “We learnt the need to widen our horizons to a whole range of legal and commercial issues. One cannot afford to defer to special experts in these fields, because they are frequently insensitive to the gaming opportunities that various measures may create for the bidders in a major auction. One must be ready to read the small print and to generate user-friendly examples of what might go wrong”.

      • Ken Zimmerman
        September 18, 2019 at 11:31 am

        Dave,

        “One cannot afford to defer to special experts in these fields, because they are frequently insensitive to the gaming opportunities that various measures may create for the bidders in a major auction”

        This is a judgment that requires not only contemplation but also a lot of background and experience with the issues of any particular auction. For example, when the UK setup an auction market for electric power in the 1990s it was a friend at Sandia Laboratory and I who pointed out to British regulators how the auction could be and was being gamed by some independent power companies by choosing to operate their plants (in terms of capacity) in certain ways before and during the auction. We would not have noticed this situation but for out special and detailed “expertise” in such auctions. No rule applies in all situations.

  2. Ikonoclast
    July 8, 2019 at 1:52 am

    The way I see it, the world is not governed by logic (a human invention) but by power. We can see this at the physical, biological and human social levels. The only genuine power is real power; that is to say that power measurable by physics. Power = work / time. This is to take a quite literal, physicalist view of such matters but not a reductionist view after further and necessary complex systems analysis. Biological entities and societies develop emergent ways to harness and apply power; specifically to harness exergy or “energy available for useful work”.

    We can always draw a line back from social power, including power conferred by property and capital in our system, to real physical power. There is the power to re-order things and people (structure, infrastructure, social structure) by capital, property and energy expenditure and also the power to unleash destruction and violence on property, people and environment. Violence is (in one sense only) the power which backs up, not the overall order per se of any society, but the given hierarchy of that order.

    Violence is one half of the equation and in a sense the most dependent half. The other half has already been hinted at above. The other power is to create and re-order. This is generative power; power which creates order. At the biological level, generative power is a very powerful force. So long as there are adequate energy sources from outside the system (mainly insolation from the sun but also energy from inside the earth) and so long as the bio-system is not catastrophically poisoned or destabilized, biological generative power, including human creativity as an aspect of this, will continue to generate complexity, albeit there are ultimate limits to complexity in a finite biosphere.

    In this purview, we can see that violence and conventional war are dependent and limited. Generation as biological reproduction and as social reproduction must occur before violence and conventional war can occur. Before anything is born, before anything is built, it cannot be attacked or destroyed. Before anything living can destroy or kill it too must be born and have resources (and often nurture and training) lavished upon it.

    In another context, I have written: “That which is not used for welfare is used for warfare.” One could perhaps propound this as part of a game theory or meta-game theory (what one needs to do to change the rules of the game). If one could starve the warfare state by promoting the welfare state, then this would be a desirable outcome. A proportion of welfare will be wasted, that is certain. But the proportion used usefully has a positive generative effect. Equally certain is the fact that ALL warfare expenditure is wasted (except possibly in those rare cases of just, defensive war) and it has a further multiplier destruction effect. This argument might look laughable until we ponder what neoliberalism has actually done over the last 40 years. It has successfully shrunk the welfare state and we have seen the warfare state and security state (defense, criminal justice, police, surveillance, security and prison budgets) concomitantly grown. That which is not used for welfare is used for warfare against citizens of other nations and against citizens of your own nation.

    To return to the issue of logic. Logic only becomes operational through personal and social power. This holds whether the logic is true or false (internally or with reference to experience). Both truths and falsehoods can become become operational through social power. Perhaps one thing we tend to forget on this site is this. Being scientifically or logically correct is worthless without the capacity (power) to have the logic implemented. Where science and logic grant instrumental power, for sure people are interested in that, but who gets to wield it? The question of political power, and the neoliberal stranglehold on it, still confronts us. Being right, empirically or morally, and yet powerless is no use at all.

    • July 8, 2019 at 8:51 am

      ‘One could perhaps propound this as part of a game theory or meta-game theory (what one needs to do to change the rules of the game).’ Yes. It seems to me that, as with other areas of mathematics, the problem is not game theory as such but too simplistic interpretations of it.

      With hindsight I think the analysis at http://www.paecon.net/PAEReview/issue81/Salter81.pdf might have been improved by looking at broader issues, but if so the solution was more and better game theory, not less.

      (Although I do accept that any theory is dangerous if it can’t actually be understood by practitioners!)

    • September 18, 2019 at 8:23 am

      If we knew who Ikonoclast was we could perhaps see better how far he is playing games. I counter his negativity with the argument that physical power has to be directed to the achievement of specific ends, and logic (which incidentally was a discovery rather than an invention) is the prior condition for directing it reliably to worthy ends.

      Yes, the question of who holds political ‘power’ in the neoliberal game still confronts us, but what it amounts to is persuading people they are powerless, and the answer to it is more like the Christian one, i.e. giving people the courage to believe that they are not: that they have inherited God’s power in diverse ways so need each other’s help, but need also a willingness to believe that “The stone which the builders rejected [here interest-free credit cards] can become the corner-stone”. The ‘money’ generated by this will be our own, not some gaming bankers, and in gratitude we will repay the credit others thereby afford us by doing our jobs.

  3. Yoshinori Shiozawa
    July 8, 2019 at 4:28 am

    Dear Lars is still trapped by the classical dichotomy between analytic and synthetic proposition theory. This theory is as old as Immanuel Kant and later developed by some Logical Positivists. It tells us sometimes something useful but often misses important points on our intellectual efforts to understand the world. We should remind that Kant and Logical Positivists are pholosophers before the notion of Bounded Rationality.

    Pure mathematical theory does not gives us any information about any concrete proposition whether it is true or not, but it gives us a method how to understand logical relations between propositions which may describe something about the real world. There is no better method than mathematics.

    Lars Syll >> Pure game theory does not give us any information at all about the real world.

    If Lars Syll argues within the classical dichotomy, he cannot explain why in some cases game theory could have provided and is still providing a powerful tool for analyzing and understanding some aspects of economic phenomena. Instead of inappropriate dichotomy between Pure and Applied game theory, it is better to contrast Small Games with Large Systems. When it is concerned with two-person or three-person game, game theory gives us a powerful tool.

    Indeed, thanks to game theory, we came to know much more concretely and clearly about (at least some aspects of) interactions between two (or at most three) persons than any philosophical reflections about them. However, game theory was almost useless in analyzing any large system like national economy or world economy. Except special aspects like industrial conflict between capital versus labor (this is a two-person game), game theory has nothing to say about economy, because it is a large system which most often comprises more than millions of people and thousands of firms. Game theory (except evolutionary game theory that is free from rational choices) are useless because strategic or opportunistic behaviors have no relevance in large systems. Large system has its own rules and institutions (like ownership, exchange and money) which generates and governs its working. Rationality (or optimal choice) has little to do with large systems like an economy.

    For more details see our new book “Microfoundations of Evolutionary Economics” from Springer (Ch. 1 and 2 in particular).

    • September 17, 2019 at 3:08 pm

      It seems to me logic is about eliminating untruth and game theory about making it invisible.

      • Ken Zimmerman
        September 18, 2019 at 11:41 am

        Dave, if you’re referring to the truth as defined by the rules of an identified logical framework, I agree. Otherwise, not.

  4. July 8, 2019 at 8:16 am

    It is the same issue all over: those “economists” are not interested in the economy or any similar reference system that their critics always refer to. They are interested in their models. These models are their object of scientific endeavour but not human decisions, society or other minor nuisances. Therefore, also, no degree or force of criticism will ever reach them because they just don’t care.

    • July 8, 2019 at 8:33 am

      Spookily, when I was first obliged to show an interest in economics, Kewn said much the same.

  5. July 8, 2019 at 8:42 am

    Flanagan’s comments seem to me excellent, and to apply to any application of mathematics and statistics, not just game theory. Ken states the essential point, but perhaps not so well. So what makes him a ‘pure’ game theorist? He is notable for http://www.nuff.ox.ac.uk/users/klemperer/biggestsept.pdf where he comes across as making an honest attempt to apply game theory within the constraints of the time. (I.e. ‘not upsetting the horses’.)
    So what would an applied game theorist look like, and how does Ken fall short of those standards?

  6. Ken Zimmerman
    July 15, 2019 at 1:42 pm

    Mathematics is like everything in human life, cultural and historical.

    That the ancient Greeks could not solve the paradox of Achilles and the tortoise is vastly instructive. Here is the problem about which the inventors of school geometry argued till they grew hoarse and developed writer’s cramp. Achilles runs a race with the tortoise. He runs ten times as fast as the tortoise. The tortoise has 100 yards’ head start. Now, says Zeno, Achilles runs 100 yards and reaches the place where the tortoise started. Meanwhile the tortoise has gone a tenth as far as Achilles and is therefore 10 yards ahead of Achilles. Achilles runs these 10 yards. Meanwhile the tortoise has run a tenth as far as Achilles and is therefore 1 yard in front of him. Achilles runs this 1 yard. Meanwhile the tortoise has run a tenth of a yard and is therefore a tenth of a yard in front of Achilles. Achilles runs this tenth of a yard. Meanwhile the tortoise goes a tenth of a tenth of a yard. He is now a hundredth of a yard in front of Achilles. When Achilles has caught up this hundredth of a yard, the tortoise is a thousandth of a yard in front. So, argued Zeno, Achilles is always getting nearer the tortoise, but can never quite catch him up. Of course, Zeno and his associates recognized that Achilles really did get past the tortoise. So why the odd story? That’s our concern today. Not the math Zeno and the others seemed to lack. Ours is an historical problem. Trying to make sense of this episode in ancient Greece. But the problem for Zeno and his friends was that the ancient Greeks had not invented a mathematics to answer the question of whether Achilles caught the tortoise. We today inherited the mathematics for answering the question. That mathematics is part of our culture because some culture(s) invented it and it was shared among many cultures.

    Productive intellectual activity of the cleverest people draws its strength from the common culture that all of us share. Beyond a certain point clever people can never transcend the limitations of the culture they come into. When clever people pride themselves on their own isolation, we may well wonder if they are very clever after all. Mathematics like all parts of culture is a shared creation. Whenever the culture of a people loses contact with the common life of humanity and becomes exclusively the plaything of a leisure class, it is becoming a priestcraft. And will end, as does all priestcraft, in superstition. Humans’ survival depends on the responsibility to its common cultural history and to its continuation. Failure to adhere to this task is as stupid as it is wicked. No culture, no society, particularly those so intricate and mechanized as ours, is safe in the hands of a few clever people. Even clever game theorists. Let’s not give in to the temptation to treat mathematics as magic or a transcendent truth. It’s a cultural object. Albeit a useful artifact. But not magical or transcendent in any way.

    Game theory originated in efforts to understand parlor games like poker and chess and was first fully formulated as a mathematical tool for describing economic behavior. But in principle, game theory encompasses any situation involving calculated interaction—from playing tennis to waging war. Game theory provides the mathematical means of computing the payoffs to be expected from various possible choices of strategies. So, game theory’s math specifies the formulas for making sound decisions in any competitive arena or cooperative undertaking. As such, it is “a tool for investigating the world,” as the economist Herbert Gintis points out. But it is much more than a mere tool. “Game theory is about how people cooperate as much as how they compete,” Gintis writes. “Game theory is about the emergence, transformation, diffusion and stabilization of forms of behavior.” The math of game theory is specific and limited, and very focused. In this sort of job, math can be a useful tool. So long as we specify clearly the terms of the problem with which the math deals. Such as competition, cooperation, behavior, payoff, etc.

  7. Yoshinori Shiozawa
    September 18, 2019 at 4:11 pm

    It is totally false that game theory is “a tool for investigating the world” such as “playing tennis to waging war”. Game theory works in an environment of which the set of strategies and payoffs are is strictly and exactly determined. In that case, some games can be treated as a part of mathematics but in other cases, the utility of game theory is only commercial puffery.

    It is quiti strange that Ken Zimmerman cites Herbert Gintis. He was once a leading radical economist but now a politically-liberal neoclassical economist. We may call him dissident but has no power and intention to re-build economics with a new paradigm. See his article at Evonomics
    https://evonomics.com/new-economics-with-tradtional-economics/

    • Ken ZImmerman
      September 19, 2019 at 1:46 pm

      “Game theory works in an environment of which the set of strategies and payoffs are is strictly and exactly determined. In that case, some games can be treated as a part of mathematics but in other cases, the utility of game theory is only commercial puffery.”

      Yoshinori, don’t disagree. Just a repeat of what I said. “The math of game theory is specific and limited, and very focused. In this sort of job, math can be a useful tool. So long as we specify clearly the terms of the problem with which the math deals. Such as competition, cooperation, behavior, payoff, etc.” But, that does not negate game theory as a tool. Perhaps not a very successful tool in the view of some, but a tool none the less. I don’t know Gintis’ current politics or academic standing. These quotes seemed to fit my needs.

      • Yoshinori Shiozawa
        September 19, 2019 at 2:32 pm

        Ken,
        please read Gintis’s article that I have cited above. If you read it, it is sufficient to know his political stance. It is not a long article.

      • Ken Zimmerman
        September 20, 2019 at 12:31 pm

        Yoshinori, I’ve read the Gintis article you suggest. The only “stance” I see in this article is Gintis is an economist. With the usual hang-ups of economists. This bothers me but I would not expect anything else from an economist. Even famous rebel economists (e.g., Galbraith (father and son)) are still economists. I don’t accept any of their assumptions without looking into how they were created. Having done this, I find most assumptions of economists rather limited and non-reflexive.

  8. Yoshinori Shiozawa
    September 20, 2019 at 5:27 pm

    Ken, I understand that you see all economists as an economist. It means that you don’t see any differences between economists, neoclassical or others.

    Herbert Gintis and Samuel Bowles had a research program in which they planned to construct an evolutionary social science which they claim to comprise sociology, political science and anthropology. They even worked with anthropologist Robert Boyd, although Boyd is a more biological anthropologist than being a cultural anthropologist.

    For me, Bowles and Gintis represent a bad example which sought to create a unified social science and failed. Ken’s research program is not new to me at all. In 1970’s we saw many social scientists who claimed “inter-disciplinary”, “trans-disciplinary” and more unified science. A typical example was Immanuel Wallerstein, who passed away recently. He had an immense scheme but for me he wanted to put all events into his predetermined scheme. His influence is still great and left some good impacts, for example in creating global (economic) history.

    What is asked now for Ken is whether he can go beyond these failed attempts to build an unified social science. By high probability, Ken can produce no significant results, because he is in his essence a romanticisit who dreams than tries building up

    • Ken Zimmerman
      September 21, 2019 at 3:29 pm

      Yoshinori, humans divide experience. They put experience into buckets. One of those buckets is economists. When someone tells me they are an economist, I accept the bucket assignment, at least until I feel a need to check its accuracy.

      I am aware of Bowles’ and Gintis’ work with Boyd, and others. I must agree on their interdisciplinary efforts as failures or worse. I don’t know much about Wallerstein’s world system theory, but what I do not is not impressive. It reminds me of Arnold Toynbee’s work. Not a good sign.

      As to dreaming vs. acting, contrary to your claims, I’ve little use for dreaming. But I must admit that my public activism is greatly reduced in the past several years due to many old injuries and new pains.

      • Yoshinori Shiozawa
        September 21, 2019 at 6:30 pm

        That is too bad. We should care for our health. Please cheer up.

      • Ken Zimmerman
        September 22, 2019 at 11:03 am

        Thanks. Twenty years a marine. What would you expect.

    • Yoshinori Shiozawa
      September 22, 2019 at 3:24 am

      Ken Zimmerman,

      One of my friends has published two books on study of management using anthropological idea together with other various disciplines including economics.

      https://www.springer.com/gp/book/9784431549154
      https://www.springer.com/gp/book/9789811371929

      If you contend the importance of anthropological point of view, how about writing a paper or a book which develops some aspect of contemporary economy based on anthropological insight. If you can provide an effective contribution to economics, the economics will change a little. In this way, we can find our starting point. Criticizing neoclassical economics alone does not produce any positive result except expelling young researchers from economic affairs.

      • Ken Zimmerman
        September 22, 2019 at 12:53 pm

        Yoshinori, I don’t write books, on anything. I decided long ago that the academic life was not for me. And I’m too involved in the efforts to make and change policy (government, corporate, etc.) to take off a year or two to write a book. Books and academics are certainly not irrelevant, but they seem to have less impact than face-to-face talks and directly advocating for policies. Also, the policy process is deeply political. Academics often have difficulty dealing with political situations, both in terms of competence and attitude.

        My areas of interest, infrastructure, government regulation, public goods, and citizen welfare didn’t find voices in Anthropology until the late 1980s. Although there were anthropologists who led the way in these areas who wrote and advocated before that period. For example, before 1995, anthropologists saw the study of infrastructure as unexciting and irrelevant. That began to change when the era of infrastructure as inert, nearly invisible and functional began to break down during the Reagan Administration. Anthropologists had wrongly concluded (a conclusion that has always puzzled me) that infrastructure as a domain of technical solutions and arrangements was independent of the political and the lived experience. Shows how dumb social scientists, including anthropologists can be. Nothing that humans invent, build, and re-build is beyond the political and lived experience. I knew anthropologists were incorrect because I’m also an historian. Social history and public history are deeply involved in considerations of infrastructure and have been for nearly 75 years.

        However, anthropologists’ exploration of infrastructure is not just via infrastructure failure. Anthropologists have explored how infrastructure is the foundation of aesthetical experiences of the built environment, hard wiring our sense of self and place in the world in the form of wires, pipelines and cement structures. As such, modernity itself is not just made of visions and assumptions, but is a specific material experience on which individuals, nations and societies ground identities, aspirations and expectations. Infrastructure provides fragile foundations for modernity and people’s sense of the self, however, often undergirding highly hierarchical and fragmented societies. The term infrastructure evokes ideals of inclusion, integration and a vision of an all-encompassing totality. As a result, “building infrastructure” has often been seen as an effective means to serve the “public good,” being both inclusive and necessary for a society to function-as-a-whole. However, as ethnographers and geographers have pointed out, building infrastructure is not a neutral endeavor. While continuing to embody visions of progress, pipelines, highways and electric lines serve vested interests, enforce regimes of control, and create geographies of misery and segregation.

        Reading infrastructure politically does not merely mean seeing pipelines and highways as consequences of politics. Conversely, considering infrastructure has also entailed rethinking the nature of the political. Building on Foucault (2008), researchers of techno-politics have examined how infrastructure and technical knowledge, often embedded in calculation, abstraction and generalization, have shaped government actions and political processes. Also, infrastructure has not only shaped ideas of the public good, but also informed people’s experiences and understandings of citizenship as a right to infrastructural provision and connectivity. In other words, while infrastructure might serve powerful interests and produce geographies of segregation, infrastructure also provokes claims and demands from below, showing how dissent and conflict can coexist within a shared appreciation of infrastructure as the necessary material foundation of society. Note here, this helps us understand why Trump shows little interest in re-building or creating new American infrastructure, except as for-profit private property. But I don’t believe even this will hinder infrastructure’s role in forcing the haves to hear and consider the voices of the have nots.

        The centrality of infrastructure as the nervous systems of contemporary life also reveals the contingency and unpredictability of collective existence. Infrastructure remains a term to describe that assemblage of people, objects, practices and institutions on which both the realization and distribution of patterns of connectivity, movement, flow and presence are dependent. Infrastructure as an ideal totality reveals precariousness and not completion. Assemblages make the world contingent not only on how humans relate to each other, but also on how the substances travelling through pipelines and wires gain agency to entangle human assemblages, often through the flaws and the shortcomings of infrastructural design and planning. With such a focus on contingency and materiality, the study of infrastructure has inspired anthropology’s and geography’s most recent imaginations of political alternatives. Studies have highlighted the material and spatial underpinnings of politics, framing it as a struggle over the control of both space and flows. The study of infrastructure has suggested that the achievement of just societies does not depend on relations alone, but on the nature of these relations between people and with their environment. Infrastructure, as a bundle of relations, can be an agent of oppression or liberty. Hence, what makes the difference is the extent to which grids of splintered connectivity and differentiated provision are transformed into platforms for a politics of redistribution and collective responsibility.

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