Beautiful Mind

I just read Sylvia Nasar's absorbing, novel-like biography of the great mathematician John Nash (A Beautiful Mind: Simon and Schuster, 1998), who eventually won the Nobel for economics. I also finally viewed the 2001 movie based on it. The movie surprised everyone by sweeping the Academy Awards -- how can a movie about a a man of ideas be popular?

Well, as you may know, they did it by cheating: the movie isn't about Nash's ideas at all but about his battle with schizophrenia (among his heroes were Nietzsche and Newton, also men of ideas who went insane).

The one scene in the movie where the screenwriter tries to explain a Nash idea -- the Nash equilibrium, an idea from his dissertation for which he won the Nobel -- is so bad it virtually inverts the meaning of the idea involved. Apparently, there was no math or econ technical advisor on this production at all.

The scene takes place in a bar, where Nash says "If we all go for the blonde and block each other, not a single one of us is going to get her. So then we go for her friends, but they will all give us the cold shoulder because no on likes to be second choice. But what if none of us goes for the blonde? We won't get in each other's way and we won't insult the other girls. It's the only way to win. It's the only way we all get laid. ... Adam Smith said the best result comes from everyone in the group doing what's best for himself, right? Adam Smith was wrong! The message: Sometimes it is better to cooperate!"

Wow. How many things are wrong with that? They begin with the admittedly technical-sounding fact that Nash's idea only concerns non-cooperative games and makes no comment on cooperation.

Here's one thing that I think is fairly important. The writer is obviously thinking of Adam Smith's famous statement: "It is not from the benevolence of the butcher, the brewer or the baker, that we expect our dinner, but from their regard to their own self interest. We address ourselves [ie., in trading with them], not to their humanity but to their self-love, and never talk to them of our own necessities but of their advantages."

Smith is definitely not saying that self-interest somehow generally leads to doing what is in the interest of the other. He is talking about the butcher, the brewer, and the baker. In other words, he is taking about markets. He is not, for instance, talking about warfare, which is a situation where self-interest typically tends to be very detrimental to the other person. The Prisoners' Dilemma, which was first formalized by Nash's dissertation adviser Albert Tucker, is a situation in which uncoordinated self-interest is suboptimal both for the self and the other.

In the book, Nasar actually says that the connection to Smith here is positive. She contrasts Nash in this respect with the great founder of game theory, John von Neumann. Von Neumann, she claims, tended to think that in order to establish social order "players would have to form coalitions, make explicit agreements, and submit to some higher, centralized authority." To Nash, on the other hand, "individual rationality and self-interest, not common agreement on some collective good, seemed sufficient to create a tolerable order." Thus, she says, he gave "economics an updated, far more sophisticated version of Adam Smith's great metaphor of the Invisible Hand." (pp. 14-15)

Updating is very different from revising.

Human beings tend to find many of the basic ideas of economics deeply counterintuitive. This is very important, as it may mean that no democracy can have an economic policy that makes any sense. One of these troublesome basic ideas is that from the uncoodinated interactions of self-interested individuals social order can emerge. Nash's idea was a contribution to understanding this crucial fact.