The limits of game theory

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Lars Pålsson Syll
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The limits of game theory

If you read Binmore’s Essays on the foundations of game theory (1990) you will find a section where he says that, unfortunately, we get into a kind of impasse. We get this infinite regress linked to the common knowledge problem. For example, I drive frequently from Aix to Marseille. You have the autoroute and parallel to it is the route nationale. Say there is, one day, congestion on the autoroute and nobody on the nationale. I think: “Tomorrow I will take the nationale. But, wait a minute, these other drivers are intelligent too, so they will take the nationale tomorrow, I would do better to stay over here. But, wait a minute, these drivers are pretty intelligent so they can make that step too…” It is actually not logically possible to reason to the solution of these kinds of problems that people are supposed to be solving in game theory.

You can surely define an equilibrium, and say that if we were there nobody would want to move. But then you get to the problem of how we get to this equilibrium—the exact same problem that we have with general equilibrium …

For certain specific, local problems, game theory is a very nice way of thinking about how people might try to solve them, but as soon as you are dealing with a general problem like an economy or a market, I think it is difficult to believe that there is full strategic interaction going on. It is just asking too much of people. Game theory imposes a huge amount of abstract reasoning on the part of people …

That is why I think game theory, as an approach to large scale interaction, is probably not the right way to go.

Alan Kirman

Back in 1991, when yours truly earned his first PhD​ with a dissertation on decision-making and rationality in social choice theory and game theory, I concluded that “repeatedly it seems as though mathematical tractability and elegance — rather than realism and relevance — have been the most applied guidelines for the behavioural assumptions being made. On a political and social level, ​it is doubtful if the methodological individualism, ahistoricity and formalism those guidelines imply are especially valid for explaining real-world decision-making.”

This, of course, was like swearing in church. My mainstream colleagues were — to say the least — not exactly überjoyed.

Half a century ago there were widespread hopes game theory would provide a unified theory of social science. Today it has become obvious those hopes did not materialize. This ought to come as no surprise. Reductionist and atomistic models of social interaction — such as those mainstream economics and game theory are founded on — will never deliver sustainable building blocks for a realist and relevant social science. That is also — as yours truly argues in this article — the reason why game theory never will be anything but a footnote in the history of social science.

Heavy use of formalism and mathematics easily foster the view that a theory is scientific. But although game theory may produce ‘absolute truths’ in imaginary model worlds, in the real world the game theoretic models are nothing but fables. Fables much reminiscent of the models used in logic, but also like them, delivering very little of value for social sciences trying to explain and understand real-life phenomena. The games that game theory portrays are model constructs, models without significant predictive capacity simply because they do not describe an always much more complex and uncertain reality …

Although some economists consider it useful to apply game theory and use game theoretical definitions, axioms, and theorems and (try to) test if real-world phenomena ‘satisfy’ the axioms and the inferences made from them, we have argued that that view is without warrant. When confronted with the real world we can (hopefully) judge if game theory really tells us if things are as postulated. The final court of appeal for models is the real world, and as long as no convincing justification is put forward for how the inferential bridging de facto is made, model building is little more than hand-waving that give us rather little warrant for making inductive inferences from the model world to the real world.

The real challenge in social science is to accept uncertainty and still try to explain why different kinds of transactions and social interactions take place. Simply conjuring problems away by assuming patently unreal things and treating uncertainty as if it was possible to reduce to stochastic risk, is like playing tennis with the net down. That is not the kind of game that scientists working on constructing a relevant and realist science want to play.