Home > Uncategorized > Why game theory fails to live up to its promise

Why game theory fails to live up to its promise

from Lars Syll

Why, it might be objected, should the goal of social science be mere causal explanations of particular events? Isn’t such an attitude more the province of the historian? Social science should instead be concentrating on systematic knowledge. The Prisoner’s Dilemma, this objection concludes, is a laudable example of exactly that – a piece of theory that sheds light over many different cases.

Greek retreat from game theory | LARS P. SYLLIn reply, we certainly agree that regularities or models that explain or that give heuristic value over many different cases are highly desirable. But ones that do neither are not – especially if they use up huge resources along the way. When looking at the details, the Prisoner’s Dilemma’s explanatory record so far is poor and its heuristic record mixed at best. The only way to get a reliable sense of what theoretical input would actually be useful is via detailed empirical investigations. What useful contribution – whether explanatory, heuristic or none at all – the Prisoner’s Dilemma makes to such investigations cannot be known until they are tried. Therefore resources would be better directed towards that rather than towards yet more theoretical development or laboratory experiments.

R. Northcott & A. Alexandrova

Game theory is, like mainstream economics in general, model-oriented. There are many reasons for this – the history of the discipline, having ideals coming from the natural sciences (especially physics), the search for universality (explaining as much as possible with as little as possible), rigour, precision, etc. Most mainstream economists and game theorists want to explain social phenomena, structures and patterns, based on the assumption that the agents are acting in an optimizing (rational) way to satisfy given, stable and well-defined goals.

Building their economic models, modern mainstream economists ground their models on a set of core assumptions describing the agents as ‘rational’ actors and a set of auxiliary assumptions. Based on these two sets of assumptions, they try to explain and predict both individual and social phenomena.

The model used is typically seen as a kind of thought experimental ‘as if’ benchmark device for enabling a rigorous mathematically tractable illustration of social interaction in an ideal-type model world, and to be able to compare that ‘ideal’ with reality. The ‘interpreted’ model is supposed to supply analytical and explanatory power, enabling us to detect and
understand mechanisms and tendencies in what happens around us in real economies.

But if the models are to be relevant, we also have to argue that their precision and rigour still holds when they are applied to real-world situations. They often do not. When addressing real economies, the idealizations and abstractions necessary for the deductivist machinery to work simply do not hold. If the real world is fuzzy, vague and indeterminate, then why should our models build upon a desire to describe it as precise and predictable?  Being told that the model is rigorous and amenable to ‘successive approximations’ to reality is of little avail, especially when the law-like (nomological) core assumptions are highly
questionable and extremely difficult to test.

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.

As noted by Northcott and Alexandrova, 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. Robert Locke
    October 3, 2020 at 8:35 am

    I note Neunmann and Morgenstern’s critique of the math used in neoclassical economics in their 1944 classic. And so we keep on refuting the refuters==that’s scientific progress.

  2. Yoshinori Shiozawa
    October 4, 2020 at 9:53 am

    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.

    A behavioral and cognitive theory that does not build on rationality of agents and equilibrium framework is already presented and is applied to analyze a system as big as world economy. See Chapter 1 and Chapter 2 of our book Microfoundations of Evolutionary Economics. It is a powerful value theory (theory of relative prices of industrial products) that can be extended to international value theory (see Section 2.6). It is now a unique economic theory that can analyze global value chains (GVCs), because four generations of mainstream trade theories (textbook Ricardian, HOS theory, New trade theory, and New new trade theory) cannot analyse trade of input goods. Needless to say, a GVC is a network of production across countries connected by input trade. A general theory of input trade is necessary in order to analyze GVCs.

    As I have argued in my comment on January 13, 2018 at 1:24 am as a comment to Lars Syll’s article On the real-world irrelevance of game theory, game theory can be used successfully in analyzing interactions between small number parties (two or three) but is not applicable to a large economy as big as national or global economies. Mainstream economics based on neoclassical and game theoretic economics are now in a defensive situation and is trying to hide its defects, or inability to analyse important issues as for example GVCs. Another important issue is unemployment under international trade situation. Four generations of trade theory assume away unemployment by assumption. So they cannot analyze unemployment and firm’s bankruptcy caused by liberalization of trade.

  3. Gerald Holtham
    October 4, 2020 at 5:11 pm

    Two short stories. An experiment was conducted, allegedly of telepathy. Students had to guess how a coin toss would come out. The toss was not fair and was rigged to come out 60 per cent heads. The students were paid for getting it right. The optimal strategy in that situation is to say heads every time – 60 per cent payoff. In fact the students realised the coin wasn’t fair but said heads 60 per cent of the time. They event-matched which is sub-optimal (unless they were indeed telepathic, which they were not). Why? Because they thought there must be more to it. They looked for a determinate rule which would predict the coin toss every time. If you form and reject theories with successive tosses, you will tend to event-match (theorem). The students were rational but they mistook the nature of the rigged game.
    I once had to play a game in teams. Being an economist I spotted that we had to get to a co-operative equilibrium for the best outcome. I got my team to adopt Axelrod’s tit for tat strategy: be nice until someone is nasty, punish them once then revert to being nice as soon as they are nice. It was a total failure. The best outcome was never reached and the teams screwed each other up. When I asked why the other team reacted as they did, they said: we couldn’t work out what you were up to but we assumed you had some super-sophisticated plan for advantage that we had to counter. Same problem: they were looking for something that wasn’t there and formed a different conception of the nature of the game.
    Human beings are seldom content to just play the odds. They tend to think there is more determinacy than there really is. It’s what I call the “seeing canals on Mars” syndrome. Game theory works when the parties share a consensus on the nature of the game. When used to design competitive auctions, to assign radio wavelengths for example, it has been very successful but applied to vaguer situations its predictive value is low, It is more used in war-gaming by the military than it is in economics – if that makes you feel better.

  4. Ikonoclast
    October 6, 2020 at 11:03 am

    Game theory also depends on where you draw game boundaries. Many years ago, I had a friend who liked to play the game Diplomacy. He roped me into a few social games. Before the game, and out of earshot of all other players, he suggested I support him for the whole game in a secret (conspiratorial) agreement to play to assist him to win. He suggested (a) the outright win was only possible for one and I would be likely to come second with the stratagem which would be fun too.

    I agreed as (a) the game was social (b) I was a learner so I was happy to have a chance to last longer to learn more. IIRC, the strategy succeeded for him. I garnered quite a bit of in-game anger from a few other players for always seeming to stab them in the back at a crucial moment when their position was fragile (doing this to assist my friend). I don’t recall where I came but my friend won and my main reward was a bit of unpopularity which lasted until everyone had had about two drinks at the after-game party. I thought the whole thing was quite funny and was quietly amused at how invested people became in the game.

    People can also play to spoil games or to try to make all persons lose if they can’t win. This same friend also told a tale of a person in a Diplomacy tournament (apparently they had these) who locked another person in a broom cupboard or such-like to make them miss turns and default out of a game. Not sure how that turned out. Illegal confinement! A very serious offense!

    The game of economics is technically (IMHO) a competitive-cooperative game with rules. The rules are much-gamed and flouted. People start the game with different endowments in every sense. Some play by the rules, some don’t, some vary, some pay the rule makers for rules favorable to them and so on ad infinitum. There are rule makers, rule takers and rule breakers. To imagine that economics could have fundamental laws (as in scientific laws) is absurd. Every rule change and rule circumvention changes the supposed fundamental laws of the system. The “fundamental laws” of a given political-financial system with a given rule set are really theorems of the axiom set. However, the axiom set keeps being changed and evaded. Counterfeiting, for example, evades the given axioms (rules) of money creation at a given point in time. Starting a trade war or real war because you don’t like an international competitor beating your country at the current game of economics and international trade (when both sides are probably cheating and gaming the international system anyway) changes the rules (axioms) of the game system. What is said in this paragraph is true of legal laws, regulations. money and finance system.

    The real economy is a different kettle of fish. In the real economy, we can predict upwards causation (in inanimate materials and energies) by scientific laws. We cannot predict individual human actors well nor emergent crowd behaviors well. We also cannot predict well all the effects of changing the rules of legal laws, regulations, money and finance well all the time. Some effects we can predict well some the time. In other words, downward causation from game rules (axioms) to emergent real system behavior can be impossible to predict.

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