As you can imagine, there has been quite a bit of buzz of late in the economics community about “A Beautiful Mind,” the Hollywood portrayal of the life of John Nash. Nash, a mathematician of remarkable intellect, shared the 1994 Nobel Memorial Prize in Economics with two other quantoids, John C. Harsanyi and Reinhard Selten, who extended his original concept.
I heard from colleagues around the world who wanted to chat or e-chat about it, some of whom had interacted with Nash at some point in their careers. Some wanted to nit-pick the details of his life, and criticize key omissions from the movie. Others don’t like it when someone from another discipline wins our big prize, figuring it takes away one of their opportunities. (By the way, Nash would have probably won the Fields Medal, the mathematics equivalent of a Nobel, had it not been for the fact that one of his most complex discoveries, having to do with the solution to a particular group of multidimensional differential equations, was simultaneously found by Italian mathematician Ernio de Georgi; Nash is not your garden variety of genius, and this is definitely not the stuff of dinner table conversation).
Most, including me, were simply pleased to have a movie made about the life of an academic who touched our field of study. After all, economists are not the most interesting lot. If they were to make a movie about me, they could get scenes of me talking on the phone, speaking at a Rotary Club, pouring over output or other associated programs, sitting in a meeting, staring at a computer screen and . . . well, that’s about it! We won’t even get into casting.
The occasion does call for a brief description of Nash’s idea, which was somewhat misstated in the movie. In fact, if you tried to do exactly as the movie suggested, you could lose a lot of money¾or worse (and we wouldn’t want that to happen).
Specifically, the movie suggests that you should pursue your own self-interest and the interest of the group (in our case, the economy). You can probably think of hundreds of examples in your life (economic and otherwise) where that is quite impossible. What actually came to be known as “Nash equilibrium” was the notion that as you pursue your own self-interest, you need to do so with an awareness of and reaction to the fact that those around you are doing exactly the same thing. We can’t blindly pursue our self-interest and be oblivious to our surroundings. Thus, what we pursue is not our wildest dreams, but rather the most we can achieve in the world in which we live. (In the example in the movie (which was correct), nobody got the girl everybody wanted, but everybody got a girl.)
This basic concept is quite simple, although it gets buried in some really convoluted mathematical jargon related to manifolds and algebraic variables. Adam Smith was not wrong (as implied by the movie), just incomplete. We still pursue our individual self-interest; and nobody else’s; we just do it within the context of the group (the later scholars who share the Nobel Prize with Nash extended the concept still further to encompass dynamic situations and incomplete information).
The fact that Nash expanded the analysis of markets rather than destroying it in no way diminishes the brilliance of the idea. The sound byte may not be as great, but Nash’s real concept fundamentally shapes our understanding and our behavior. Those who make money in the stock market do so by making decisions which account for the actions of other investors. Those who succeed in business do so by anticipating the reactions of competitors. Beyond economics, athletes win contests not just with ability, but also with a sense of the patterns of their opponents. Indeed, species survive by their ability to adapt and respond to changes in their environment. Much of our knowledge of how things hang together is owing to the mathematical scribblings of John Nash, and his accomplishments were made in the face of incredible odds. It is appropriate that he should be celebrated.