Danny Finkelstein in the Times says game theory is often too complicated to solve real world problems. He's right, if you try to use it to get precise solutions. But it has another use. It reminds us that there are (at least) three paradigms in economics and it matters enormously that we know which paradigm is relevant for which problem*.
One paradigm is parametric maximization: we maximize expected utility subject to given parameters.
This, though, isn't universally applicable, as the two envelopes problem teaches us.
Imagine I give you and a colleague an envelope each. I tell both of you that one envelope contains twice as much money as the other. I then ask you if you want to swap, paying me a small sum if you do.
Conventional maximization suggests you should swap. You figure: "I have a 50% chance of a 100% return and a 50% chance of a 50% loss. That's an expected value of plus 25%."
If both of you think like this, you'll both pay me to swap. But having swapped, the same reasoning applies again. So you'll both swap again. Each time, I get richer and you two get poorer.
The error you're making here is that parametric maximization doesn't apply. Your colleague is not a given parameter but a strategic thinker just like you. Once you see this you see that the game theory paradigm applies and so cease to be an egocentric framer. You figure "if he wants to swap envelopes, why should I do so?" You thus reject the trade and the logic that impoverishes you.
This is no mere thought experiment. One of the best-attested anomalies in finance is IPO under-performance; newly-floated stocks tend to do badly (pdf) in subsequent months. I suspect that one reason investors fall into this trap is that they apply the wrong paradigm. They think they are in the domain of parametric maximization and try to maximize expected returns for given prices but in fact they should apply the game-theory paradigm, and ask: if well-informed owners of the firm want to sell, why should I buy?
This isn't the only way in which getting the paradigm wrong can be costly. Governments or managers who set targets which are subsequently gamed make the same error. They think they are in the domain of parametric maximization when in fact they are in the game-theory domain: they forget that subordinates are not mere pawns to be moved, but strategic agents. (The Lucas critique makes a similar point about macroeconomic policy.)
However, there's a third paradigm - entrepreneurship. Introductory textbooks tell us that bosses try to maximize profits subject to given costs and technology. The entrepreneur, however, doesn't take these as given but rather tries to discover new technologies or newer cheaper suppliers. As Schumpeter said, he does things that "lie outside of the routine tasks which everybody understands." There's a thin line between the entrepreneur and the criminal because both try to break established rules.
Again, the failure to see which paradigm applies can be expensive. And not just in business but in politics too. The 1929-31 collapsed because it tried to impose austerity to keep the UK on the Gold Standard. When the subsequent coalition government took us off that standard, Sidney Webb, a Cabinet minister in the Labour government said: "nobody told us we could do that." This suggests the Labour government had been stuck in the parametric paradigm, when it should have applied the entrepreneurial one. Sometimes, constraints are only illusory.
Some of you might think the Labour party now is making the same error - of regarding public opinion and mediamacro as given parameters rather than trying to change them.
Maybe. But in business and in politics, entrepreneurship often fails. The parametric paradigm is often the right one. And sometimes - often - we just can't know whether it is or not.
* I'm talking here about fully rational maximisation: let's leave behavioural economics aside for now.