Wednesday, December 05, 2007

A Tale of Two Views on John Nash





Gavin Kennedy

Here are two treatments of the same scene from ‘A Beautiful Mind’, one the conventional treatment by the scriptwriter and the other a criticism that sets the record straight – well, almost:

Russell Crowe and the Choice Supply Side Problem’ in EDUWONK (‘education, news. Commentary’) here:

Bar scene from A Beautiful Mind: What if no one goes for the blonde? We don’t get in each other’s way, and we don’t insult the other girls. That’s the only way we win. That’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? That’s what he said, right? Incomplete. Incomplete! The best result will come when everyone in the group doing what's best for himself -- and the group.*” (Credited to ‘Guest blogger ggw’)

Eduwonk to its credit carries a kink to a promising criticism of the above in Hawaii Reporter (here):

“John Nash Biographers Defame Adam Smith's Beautiful Mind” by Stuart K. Hayashi (president of the Reason Club of Honolulu and an undergraduate in Entrepreneurial Studies at Hawaii Pacific University).

Many are familiar with the 2002 Best Picture winner “A Beautiful Mind” -- the real-life story of mathematician John Nash, who won the Nobel Prize in economics for his contributions in “Game Theory,” and who fought paranoid delusions for much of his life. This picture was based upon the biography of the same name, written by Sylvia Nasar.

It’s commendable that Nasar and the film’s makers wish to educate the public about schizophrenia and the brave struggles Nash endured for his very existence. Yet, with just a few sentences of text and dialogue, respectively, they have also done the world a great disservice by misleading people into believing that Nash’s work in Game Theory has disproved the practicality of free-market economics.
If policy-makers and the general voting public come to accept this inaccurate assertion, the ramifications could include the passing of new, unnecessary laws that harm us all.

Nasar and the film claim that John Nash’s ideas have refuted the “Invisible Hand” theory that Adam Smith, the first true economist, publicly explained in 1776. They get away with this due to what is, at best, a complete misunderstanding of what Smith said.

The “Invisible Hand” theorem is that a free market will regulate itself better than any mercantilist or socialist law would, thanks to the incentives it provides. Smith gave a number of examples, two of which are particularly famous.

First, Smith noted that it’s good for the consumer when businesses selling similar products or services learn to compete with one another, because each firm will reduce its prices and improve its quality to attract more customers. If a baker charges lower prices for bread than all other bakers, then the others have to lower their own prices or people will stop buying from them. It’s the self-interest of all parties involved that create the best condition for the economy in general -- the “Invisible Hand” of profit motivates it.

Second, Smith stated that, when one can serve his own self-interest by cooperating with others, he will do so. If Bob the baker wants $5 more than his loaf of bread, and Steve the customer wants a loaf of bread more than his $5, the two make a trade -- Steve buys Bob’s bread. Each person gives up what he wanted less, and ends up with what he wanted more, so both sides win.

These parties may not necessarily like each other, but they cooperate to serve their own respective self-interest, and, as long as no one’s rights are violated, everyone is better off. “The Invisible Hand” works again.

Nasar, the filmmakers, and some anti-capitalist Game Theorists get away with saying Nash refuted Adam Smith by remembering the first example, taking it out of context, and then ignoring the second. According to “the Nash equilibrium,” an individual will look at his own self-interest to decide whether to compete or cooperate with others.

For instance, imagine there are two men in a forest, who could hunt for rabbits or deer. This is a “Game Theory” scenario. If they each hunt for a rabbit alone, they will eat a little. To catch a deer requires both of them to cooperate, so, if they both work together to catch a deer, they’ll both eat a lot and “win big.” But if one man gets the other to hunt for deer while he hunts for rabbit instead, the rabbit-eater will eat and “win,” while the deer-hunter will end up with nothing and “lose.” The best solution for both men, said Nash, is not to compete but to work together to catch a deer, serving everyone’s self-interest best.

Ludicrously, Nasar and the filmmakers insist this refutes Adam Smith because the parties cooperate rather than compete. But that’s a “straw man” argument, because Smith never said that people always have to compete; he just said that competition between firms in the same industry benefits consumers.

And Smith also pointed out that self-interest motivates different parties to cooperate, helping everyone in the community, such as in the example of people making mutually beneficial business transactions. No matter the spin that the Hollywood Left and some anti-capitalist Game Theorists try to put on this, the “Nash equilibrium” somewhat affirms Smith’s “Invisible Hand” theory, whether Nash himself realizes it or not.

Nash has never refuted the free market. Nor will any of his students.

Adam Smith himself made mistakes in economics, but he had a beautiful mind too, and Hollywood would do us a favor if it didn’t misrepresent it anymore.”

Regular readers should know what is right and what is wrong with Stuart K. Hayashi’s, otherwise excellent rebuttal of the scriptwriters of ‘Beautiful Mind’ and Sylvia Nasar’s biography (assuming it contains the original errors in that scene).

Everything is fine in the rebuttal except Stuart’s continual references to the ‘invisible hand theorem’ of Adam Smith. He didn’t have a ‘concept’, a ‘theory’, a ‘principle’ or a ‘theorem’ of an invisible hand.

What he had was a metaphor and he wasn’t referring to markets or decisions in markets (these were discussed in Books I and II of Wealth Of Nations. He used the famous metaphor in Book IV on an entirely different subject after he had clearly explained what drove merchants to prefer to avoid trading abroad, namely their risk aversion.

Sometime in the mid-20th century in academe the invisible hand was promoted from Adam Smith’s use of it into a ‘concept’, a ‘theory’, a ‘principle’ and a ‘theorem’ of markets, and the rest as they say is ‘history’. It became what its proponents wanted it to mean – the proselytizers after all were graduates of the schools that adopted it and they taught it to their students, neither their teachers nor their students bothering to read Wealth Of Nations.

The metaphor is redundant as an explanation of markets; it adds nothing to our understanding of how they work. It introduces a ‘disembodied invisible body part’ into what claims to be a science and which goes to great lengths in its mathematics to ‘prove’ it is, or looks like, a science. It’s as if scientists explained gravity by an ‘invisible being’ carrying the world on its shoulders (oops, they did several hundred years ago, but science grew up and learned better).

But, meanwhile congratulations to Stuart Hayashi for understanding what is wrong with the alleged views of John Nash as represented in ‘Beautiful Mind’.


Blogger Unknown said...

I don't think you have truly studied Nash equilibriums or graphs. When making Nash graphs there is section that shows certain equilibriums in a game, where each player is using the optimal strategy against the other's strategy and as such these strategies are in equilibrium and will not change unless the rules of the game change. The problem is that these equilibriums can have vastly different payoffs for each player. So, studying Nash equilibriums simple leads to the conclusion that the rules of the game must be regulated to avoid such payoff discrepancies and then each player can continue to play by Adam Smith's strategy. They are not an argument against competition, they are an argument for regulation.

2:03 pm  

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