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Testing game theory

from Lars Syll

The “prisoner’s dilemma” is a familiar concept to just about everyone who took Econ 101 …

GametheoryYet no one’s ever actually run the experiment on real prisoners before, until two University of Hamburg economists tried it out in a recent study comparing the behavior of inmates and students.

Surprisingly, for the classic version of the game, prisoners were far more cooperative than expected.

Menusch Khadjavi and Andreas Lange put the famous game to the test for the first time ever, putting a group of prisoners in Lower Saxony’s primary women’s prison, as well as students, through both simultaneous and sequential versions of the game …

They expected, building off of game theory and behavioral economic research that show humans are more cooperative than the purely rational model that economists traditionally use, that there would be a fair amount of first-mover cooperation, even in the simultaneous simulation where there’s no way to react to the other player’s decisions.

And even in the sequential game, where you get a higher payoff for betraying a cooperative first mover, a fair amount will still reciprocate.

As for the difference between student and prisoner behavior, you’d expect that a prison population might be more jaded and distrustful, and therefore more likely to defect.

The results went exactly the other way …

The paper … demonstrates that prisoners aren’t necessarily as calculating, self-interested, and untrusting as you might expect, and as behavioral economists have argued for years, as mathematically interesting as Nash equilibrium might be, they don’t line up with real behavior all that well.

Business Insider

Many mainstream economists — still — think that game theory is useful and can be applied to real-life and give important and interesting results. That, however, is a rather unsubstantiated view. What game theory does is, strictly seen, nothing more than investigating the logic of behaviour among non-existant robot-imitations of humans. Knowing how those ‘rational fools’ play games do not help us to decide and act when interacting with real people. Knowing some game theory may actually make us behave in a way that hurts both ourselves and others. Decision-making and social interaction are always embedded in socio-cultural contexts. Not taking account of that, game theory will remain an analytical cul-de-sac that never will be able to come up with useful and relevant explanations.

Over-emphasizing the reach of instrumental rationality and abstracting away from the influence of many known to be important factors, reduces the analysis to a pure thought experiment without any substantial connection to reality. Limiting theoretical economic analysis in this way – not incorporating both motivational and institutional factors when trying  to explain human behaviour – makes economics insensitive to social facts.

Game theorists extensively exploit ‘rational choice’ assumptions in their explanations. That is probably also the reason why game theory has not been able to accommodate well-known anomalies in its theoretical framework. That should hardly come as a surprise to anyone. Game theory with its axiomatic view on individuals’ tastes, beliefs, and preferences, cannot accommodate very much of real-life behaviour. It is hard to find really compelling arguments in favour of us continuing down its barren paths since individuals obviously do not comply with, or are guided by, game theory.

Apart from a few notable exceptions it is difficult to find really successful applications of game theory. Why? To a large extent simply because the boundary conditions of game theoretical models are false and baseless from a real-world perspective. And, perhaps even more importantly, since they are not even close to being good approximations of real-life, game theory is lacking predictive power. This should come as no surprise. As long as game theory sticks to its ‘rational choice’ foundations, there is not much to be hoped for.

Game theorists can, of course, marginally modify their tool-box and fiddle with the auxiliary assumptions to get whatever outcome they want. But as long as the ‘rational choice’ core assumptions are left intact, it seems a pointless effort of hampering with an already excessive deductive-axiomatic formalism. If you do believe in a real-world relevance of game theoretical ‘science fiction’ assumptions such as expected utility, ‘common knowledge,’ ‘backward induction,’ correct and consistent beliefs etc., etc., then adding things like ‘framing,’ ‘cognitive bias,’ and different kinds of heuristics, do not ‘solve’ any problem. If we want to construct a theory that can provide us with explanations of individual cognition, decisions, and social interaction, we have to look for something else.

Applications of game theory have on the whole resulted in massive predictive failures. People simply do not act according to the theory. They do not know or possess the assumed probabilities, utilities, beliefs or information to calculate the different (‘subgame,’ ‘tremblinghand perfect’) Nash equilibria. They may be reasonable and make use of their given cognitive faculties as well as they can, but they are obviously not those perfect and costless hyper-rational expected utility maximizing calculators game theory posits. And fortunately so. Being ‘reasonable’ make them avoid all those made-up ‘rationality’ traps that game theory would have put them in if they had tried to act as consistent players in a game theoretical sense.

  1. December 5, 2020 at 7:17 pm

    To be ‘rational’ in Aesopean terms and those of the early Greeks before the abstraction of definition –the coming of an new Prometheus according to Socrates– brought in what’s best regarded as the rationality of logic best described and developed back then by Aristotle.

    Rationality based upon using foresight to best plan to avoid the worst outcomes a future event might possibly bring differs from ‘logical’ rationality in that the former makes provision as best it can to get through that event. This is the message of the Grasshopper and the Ant fable. One does not ‘maximize’ satisfaction or pleasure. Rather one chooses to survive by providing for oneself, one’s family, and one’s community. Any economics or ‘game theory’ which emphasizes the former (and selfish behavior at all times) while ignoring the latter is destined to be inadequate.

    That’s because history shows that cooperative behavior is a primary means human beings have of providing for themselves within their communities. It does not matter what community we are talking about; or, for that matter, what species of social animal. The ‘outlaw’ is outlawed for non-cooperative behavior.

    Economics is, in my view, about our ability to provide for ourselves now and in a partly forsee-able future even when we cannot know precisely what the future is likely to be. The myth of individual self-sufficiency is only that: a myth. Ideologies which promote economic self-sufficiency are irrelevant to that reality and dangerous for our species.

    • December 6, 2020 at 12:54 pm

      I agree with Larry rather than Lars here. Genuine economics might even be referred to as “provisioning”. When I followed the story of Nash’s equilibrium on TV it seemed to me the maths guys were missing the point: the “rational” way to our personal equilibrium was to give way to other people seeking theirs, i.e. to to provide ourselves with conventions like giving way to more urgent road traffic (e.g. ambulances) and traffic from the driver’s side on roundabouts. There are of course irrational people who enjoy the thrills of waging war or endangering other traffic. Equilibrium for them is rationally provided by locking them up.

    • Yoshinori Shiozawa
      December 6, 2020 at 3:36 pm

      In my post below on December 6, 2020 at 3:07 pm I did not refer to evolutionary game theory. As this became fairly popular among game theorists, Lars Syll’s attack on game theory above is not sufficient, because many game theorists, those who work on evolutionary game theory in particular, will think that Syll is attacking old game theory (called classical game theory), but game theory has already developed to evolutionary one.

      Larry’s comment above (December 5, 2020 at 7:17 pm) gives a good hint to point out a defect of evolutionary game theory. Indeed, as Larry put it, “one chooses to survive by providing for oneself, one’s family, and one’s community.”

      Evolutionary theory is often understood by the principle of survival of the fittest. If this principle simply means that those who survived are the fittest, this principle is a mere tautology. If the fittest means that a species is maximizing something such as fitness or efficiency (as it is often assumed in evolutionary game theory), it contains a grave error because the species (or strategy) with the greatest fitness has a strong tendency to increase its population. A rapid increase of the population often damages the chance to survive, because it rapidly deteriorates the environment and risks to perish faster than the species with lesser “fitness”.

      Actual mankind may belong to this kind of the “fittest”.

  2. Yoshinori Shiozawa
    December 6, 2020 at 3:07 pm

    Syll > Apart from a few notable exceptions it is difficult to find really successful applications of game theory.

    It is a welcome change that Lars Syll becomes more cautious in stating his contentions.

    But, how about these propositions by Lars Syll in the above post?

    (1) the boundary conditions of game theoretical models are false and baseless from a real-world perspective.

    (2) they [game theoretical models] are not even close to being good approximations of real-life.

    Here are my comments: 

    Re (1): Is the term “boundary conditions” appropriate? What does it mean? “Assumed situation” would be better than boundary conditions. Even if it has a good meaning, is it right to ask whether the boundary conditions or assumed situation are true or false? He can ask whether they are suitable or often observable (opposition of inappropriate or rarely observable), but to ask if a situation is true or false violates a simple rule of modern logic.

    Re (2): As I have argued in my comment on January 13, 2018 at 1:24 am posted as a Reply to Lars Syll’s blog article “On the real-world irrelevance of game theory” January 12, 2018″, game theory is better understood as a part of mathematics. If it is mathematics, what should be blamed is not mathematics (game theory) itself but its bad usage or applications when the “applications of game theory resulted in predictive failure”. If we reflect deeply on this point, game theory cannot be tested, because it is not a testable theory with reference to social reality. It is the theory in which game theory is used that is testable. In the same way, the theme of Lars Syll’s article “Game theory–theory with little substantive content” on October 5, 2020 is committing a category mistake, because mathematics has no contents in the sense it stands for something in the real world.

    N.B. My comment on January 13, 2018 is cited again in my comment on Lars Syll’s blog article “On the real-world irrelevance of game theory January 12, 2018 linked above. I must beg pardon for my bad English.

    I am not opposed to Lars Syll’s offense against game theory or its applications in economics. I only hope that he sallies forth more accurate attacks on the defects of mainstream economics. There are many “intelligent” people among mainstream economists. Inaccurate attacks do not persuade them to draw off from their economics but reconfirm their beliefs that they are better than their critics. Inaccurate attacks do not work well on the young economists who are wondering whether to go. They will push those young economists away toward mainstream economics. Effective critique requires well thought judgement and expression.

  3. ghholtham
    December 7, 2020 at 5:05 pm

    Did the women in the Lower Saxony prison experiment know each other? Even a “rational” inmate will use any knowledge they have of the other players in forming a strategy. Game theory just explores the logic of choice in highly abstract situations. It might be useful in understanding a given real situation or it might not, depending, as Lars says on information sets, and cultural factors influencing motivations. The theory saved the British government billions when it was used to construct the auction system for 3G bandwith – because there it was reasonable to assume phone companies were out to maximise profits in a well-defined situation and had no qualms about doing so. Lars points out limitations of an abstract theory. Granted, but all theory deals in abstractions; it is misapplications of it that should concern us..

  4. Ken Zimmerman
    January 1, 2021 at 12:59 am

    I look at game theory from the other end. No doubt, the “boundary conditions of game theoretical models are false and baseless from a real-world perspective.” If one takes this real-world perspective as what is found ‘on the ground’ into which game theory is dropped. If one takes the culture assumed by game theory as the end goal of experimentations to change one’s entire society, then game theory is the cultural goal. Meant to change all norms and values in a society to match the assumptions of game theory. This was the explicit goal of Soviet planners during most of the ‘Cold War.’ And has been the goal of American government since the 1980s and American corporations since the 1960s (although limited until the 1990s to internal corporate culture). While the goal of turning Soviet citizens and American employees and consumers into self-interested, calculating ‘machines’ was the same in each instance, the ultimate goals for doing so are clearly different. For the USSR, the goal was to limit or destroy any efforts at organized opposition to the government. For American government and corporations, the goals were to control elections and focus Americans on expanding consumption. There was resistance to all these efforts. Some of it effective. But resistance collapsed and then resurged weaker after the Communist party lost power in the USSR. In the US, efforts have collapsed. Mostly from government and corporate incompetence. Along with some increasingly well-organized resistance. Particularly from academics and Americans 18-35. If you believe people cannot be turned into self-interested, calculating sociopaths, look around for yourself.

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