Thursday, October 13, 2005

Tyler Cowen, wondering about the future of game theory, considers the following possibility:

5. The real world is in fact indeterminate or close to indeterminate. The indeterminacy and multiple equilibria of game theory are not a problem, but rather reflect how closely the theory mirrors reality. Yes you might prefer sharp, clear predictions, but tough tiddlywinks, you're not going to get them. Faithfulness to reality is more important than fulfilling abstract methodological strictures.

What does this mean for game theory? the case of #5 [we can] declare victory and go home.

So let's see. Cowen considers a scenario where game theory is useless for predicting the world and decides that in this case game theorists can "declare victory," on the grounds that they are attempting the impossible. I must say, his definition of "victory" sounds a lot like my definition of "defeat."

More broadly, it seems like game theory has so far failed to give any useful predictions. Or rather, it has given us lots and lots of predictions, but no a priori way of separating the useful from the useless. Virtually any outcome observed in the real world can be explained by game theoretic models.

To understand whether the real world is determinate or not, and to get concrete predictions out of complicated models for human behaviour, it makes sense to study nonlinear dynamics, not game theory. Once questions in nonlinear dynamics are completely understood, complicated or probabilistic models for human behavior will not present a problem.

I'll add another one to Cowen's possibilities.

6. All attempts to write down realistic models of human behaviour yield equations which are too difficult to solve or solving them involves undecidable or NP-Complete problems.

I hope game theoriests won't be declaring victory in this case.


At 9:34 PM, Blogger angela said...

This comment has been removed by a blog administrator.

At 8:59 PM, Blogger angela said...

ok, "alex", i take it back. nonlinear dynamics = très sexy. ever since you told me about it over the phone while i was laying in bed, i cant stop thinking about it.


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