On the limited applicability of game theory

by
Lars Pålsson Syll
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from Lars Syll

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 known anomalies into the core claims of the theory. 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 (perhaps) few notable exceptions — like Schelling on segregation (1978) and Akerlof on ‘lemons’ (1970) — 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.

In real life, people – acting in a world where the assumption of an unchanging future does not hold — do not always know what kind of plays they are playing. And if they do, they often do not take it for given, but rather try to change it in different ways. And the way they play – the strategies they choose to follow — depends not only on the expected utilities but on what specifics these utilities are calculated. What these specifics are — food, water, luxury cars, money etc. – influence to what extent we let justice, fairness, equality, influence our choices. ‘Welfarism’ – the consequentialist view that all that really matters to people is the utility of the outcomes — is a highly questionable short-coming built into game theory, and certainly detracts from its usefulness in understanding real-life choices made outside the model world of game theory.

Games people play in societies are usually not like games of chess. In the confined context of parlour-games – like in the nowadays so often appealed to auction negotiations for ‘defending’ the usefulness of game theory — the rather thin rationality concept on which game theory is founded may be adequate. But far from being congratulatory, this ought to warn us of the really bleak applicability of game theory. Game theory, with its highly questionable assumptions on ‘rationality’, equilibrium solutions, information, and knowledge, simply makes it useless as an instrument for explaining real-world phenomena.

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,’ ‘trembling-hand perfect,’ or whatever 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.

The lack of successful empirical application of game theory shows there certainly are definitive limits of how far instrumental rationality can take us in trying to explain and understand individual behaviour in social contexts. The kind of preferences, knowledge, information and beliefs — and lack of contextual ‘thickness’ — that are assumed to be at hand in the axiomatic game-theoretical set-up do not give much space for delivering real and relevant insights of the kind of decision-making and action we encounter in our everyday lives.

Instead of making formal logical argumentation based on deductive-axiomatic models the message, we are arguably better served by social scientists who more than anything else try to contribute to solving real problems – and in that endeavour, other inference schemes may be much more relevant than formal logic.

Game theoretical models build on a theory that is abstract, unrealistic and presenting mostly non-testable hypotheses. One important rationale behind this kind of model building is the quest for rigour, and more precisely, logical rigour. Instead of basically trying to establish a connection between empirical data and assumptions, ‘truth’ has come to be reduced to, a question of fulfilling internal consistency demands between conclusion and premises, instead of showing a ‘congruence’ between model assumptions and reality. This has, of course, severely restricted the applicability of game theory and its models.

Game theory builds on ‘rational choice’ theory and so shares its short-comings. Especially the lack of bridging between theory and real-world phenomena is deeply problematic since it makes game-theoretical theory testing and explanation impossible.

The world in which we live is inherently uncertain and quantifiable probabilities are the exception rather than the rule. To every statement about it is attached a ‘weight of argument’ that makes it impossible to reduce our beliefs and expectations to a one-dimensional stochastic probability distribution. If “God does not play dice” as Einstein maintained, I would add “nor do people.” The world as we know it has limited scope for certainty and perfect knowledge. Its intrinsic and almost unlimited complexity and the interrelatedness of its organic parts prevent the possibility of treating it as constituted by ‘legal atoms’ with discretely distinct, separable and stable causal relations. Our knowledge accordingly has to be of a rather fallible kind.

To search for precision and rigour in such a world is self-defeating, at least if precision and rigour are supposed to assure external validity. The only way to defend such an endeavour is to take a blind eye to ontology and restrict oneself to prove things in closed model-worlds. Why we should care about these and not ask questions of relevance is hard to see. We have to at least justify our disregard for the gap between the nature of the real world and the theories and models of it.

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? Even if there always has to be a trade-off between theory-internal validity and external validity, we have to ask ourselves if our models are relevant.

‘Human logic’ has to supplant the classical, formal, logic of deductivism if we want to have anything of interest to say of the real world we inhabit. Logic is a marvellous tool in mathematics and axiomatic-deductivist systems, but a poor guide for action in real-world systems, in which concepts and entities are without clear boundaries and continually interact and overlap. In this world, I would say we are better served with a methodology that takes into account that the more we know, the more we know we do not know.