The latest Nobel Prize award to Aumann and Schelling has generated a bit of discussion about the value or otherwise of game theory. Generally speaking, economists are enthusiastic about game theory and other social scientists less so. Although I admire the work of Aumann and (even more) Schelling, as economists go, I’m a game-theory sceptic, for a fundamental reason I’ll try to explain.
My main problem has to do with the idea of a strategy and role in equilibrium concepts such as the famous Nash equilibrium. A game outcome is a Nash equilibrium if no player can gain by varying their own strategy, assuming that other players stick to their equilibrium strategy.
The problem here is to say what a “strategy” is. In a game like chess or poker, this is easy: the rules say what each player can do and when they can do it. The same is true in some special kinds of economic situations, such as auctions. But most of the time, there is no book of rules, so the set of strategies has to be described as part of the model.
If we look back at the Nash equilibrium idea, and put ourselves in the position of one of the players, it can be seen that there’s really no difficulty with the definition of our own strategy. We can look at the outcomes that are available, given the other player’s strategy, and pick whichever one is best for us. The way in which we label our choices doesn’t matter.
The critical problem is in the phrase “given the other player’s strategy”. In the absence of a rulebook, we can only know this if we know how the other player is going to react to this move (and the same holds in reverse for the other player). There was a large literature on this issue of “conjectural variations” before the rise of game theory, but it was generally felt to have ended in failure.
Although it’s easy enough to make the point in specific instances that if we choose a different assumption about strategies we get a different equilibrium, economic theorists strongly resist the argument that this is a general problem and that economic interactions with a well-defined strategy space are the exceptions rather than the rule.
At least, that’s the case in relation to finite games. For infinitely-repeated games, the strategy space gets very large, and the (in)famous Folk Theorem says, roughly, that anything can happen. This is really just the same problem in a different form.
This doesn’t mean game theory can’t be a useful source of insight, something Schelling in particular has shown. But it’s unlikely, in most cases, to yield definite and reliable predictions.
fn1. Digging around, I see the claim that we have witnessed in recent years a revival of Conjectural Variations in Game Theory