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Mind Games

Mises Daily: Monday, January 14, 2002 by

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Russell Crowe is sure to win Best Actor for his portrayal of Nobel Prize-winning economist and mathematician John Nash in "A Beautiful Mind." The movie itself may win Best Picture.

In real life, Nash was a brilliant young man, a young man who could solve mathematical conundrums, break codes, and intuit the laws of economics. But then, seemingly at the peak of his career, he succumbed to paranoid schizophrenia.

After a series of involuntary commitments to mental hospitals, he was eventually released, as he puts it in his autobiography, "when I had been long enough hospitalized that I would finally renounce my delusional hypotheses and revert to thinking of myself as a human of more conventional circumstances."

While free, Nash expressed regret. With madness, he said, came greatness.

One aspect of this is that rationality of thought imposes a limit on a person's concept of his relation to the cosmos. For example, a non-Zoroastrian could think of Zarathustra as simply a madman who led millions of naive followers to adopt a cult of ritual fire worship. But without his "madness" Zarathustra would necessarily have been only another of the millions or billions of human individuals who have lived and then been forgotten.

Nash is wrong. I can certainly say that, in the area of economics (my discipline), Nash has made no contribution since he succumbed to mental illness. And, from what I can tell about mathematics, since succumbing to mental illness, he has made only marginal contributions in that area. Indeed, if Nash were a recording artist, he might be characterized as a "one-hit wonder." (This is if you only look at his one "hit" in economics, and do not consider his "hits" in mathematics.)

What is Nash's one "hit?" It is a proof that in any (finite) game, there exists an equilibrium in which no player can improve his or her outcome given the other players' strategies. Nowadays, we call this outcome a "Nash Equilibrium."

The Real John NashFor example, let's say you're the United States, and you're playing the game of "international trade." (Nash developed his contribution to Game Theory in the context of international trade.) You decide to raise tariffs, or devalue your currency, or adopt other such policies in order to improve your balance of trade. If we assume the other countries of the world are stupid, so that they do not retaliate against your policy, then you will achieve your objective.

But if we assume the other countries of the world are rational, and that they retaliate in kind, then you will not achieve your objective. Instead, you (the United States) and the other countries of the world will all suffer. Therefore, as long as you (the United States) are not yourself stupid, you will not adopt anti-free-trade policies in the first place.

Ludwig von Mises did not couch his commitment to free trade, sound money, free markets, and the like, as "strategies" within a "game." But in hindsight, it is clear that his principled commitments, and his detailed explanations, were designed to make these rules of the game inviolate, so that those with parochial interests would not try to "game the rules," such as by hobbling free enterprise through intervention, regulation, inflation, devaluation, or otherwise.

In the movie, Nash claims that his contribution "overturned" 150 years of economics (that is, economics since Adam Smith, wrongly understood). Such was Nash's arrogance. First, his contribution was merely an existence proof. While a brilliant insight that gave others encouragement and direction for subsequent work, it did not "overturn" anything. It extended mainstream economic analysis to new areas where its formal theory had previously prevented it from going.

Whereas before, economic analysis was considered to refer to "atomized" individuals, Game Theory opened the possibility that economic analysis could explain the behavior of individuals in various forms of relationships with others ("noncooperative games"), including games that involved rivalries (i.e., the possibility of winners and losers).

In a noncooperative game, there is a sequence of decisions, as first one player "moves" and then another. The "non" in noncooperative means that future moves are not constrained by prior agreements among the players involved (except that they at least tacitly agree to the rules of the game). The players are free, in their future moves, to make whatever moves are allowed by the rules of the game.

Nash's proof is that, for any set of strategies on the part of the players involved, there is at least one outcome that is best for each of those involved. Any deviation from this outcome would diminish the outcome of the player who deviates. Accordingly, this outcome is described as an equilibrium.

Game playing, in practice, often involves learning the strategies of the other players involved, so you can determine what is best for you to do. Learning the strategies of other players usually involves more than abstract principles, but requires specific knowledge of things such as the culture of the players involved.

We might even say that Nash's contribution has been subsequently "overturned," since one of the things we now know--and which Mises understood--is that strategies are not data, but are themselves choices. In particular, in international trade, if the world opinion clearly communicates that it will not tolerate "beggar thy neighbor" trade policies from any country, then countries that get themselves into trouble will realize that they have to address their own "internal" problems, instead of vainly pursing protectionist policies when they find themselves in trouble.

Another way that Nash's contribution has been subsequently "overturned" is the recognition that players in noncooperative games can often "break out" of their game in order to achieve a result that is better, or at least not worse, for each of the players involved.

For example, if men want to be promiscuous, this typically poses certain risks for women, so a legally binding marriage contract can be entered into that protects the woman. More generally, contracts (both implicit and explicit), legal presumption, and positive law can address the problems of certain games in which the Nash Equilibrium is inferior (from the standpoint of the players involved) to an outcome involving cooperation.

Getting back to the movie, a delicious part of the movie was the "game" played by Nash and his wife. Although partially emasculated by director Ron Howard's sugar-coating of the story, Nash's wife put her husband into a box: either choose to think rationally or be put away. (The movie intimates that Nash's wife did not sign the commitment papers, but she did, three times.)

Well, if you're as smart as John Nash, given the "tough love" strategy adopted by Alicia Nash, you will choose to think rationally, and--even as sick as he became--as a consequence of that choice, achieve a measure of productivity and happiness.

The movie also intimates that Nash partially recovered through his own willpower, unaided by medication. If you watch the movie carefully, you will see that, while it highlights a decision to go off his medicine (which such people often decide) and retrogression into delusional thinking, it also includes a brief comment that he subsequently went back onto his medicine, after which there was an arrest of his degeneration.

Mises was correct to observe that "the great creative genius who perpetuates himself in immortal works and deeds does not when working distinguish the pain from the pleasure. For such men creation is at once the greatest joy and the bitterest torment, an inner necessity." It is also true that intellectual promise can degenerate into arrogance, narcissism, and paranoia, such that genius becomes drivel.

With his beautiful mind, the young John Nash did some really fantastic work. But then something happened. Perhaps unleashing the potential for creativity that is within the human mind has a maddening effect. But, it is just as possible that Nash grew frustrated in no longer being able to be so creative, and then sought greatness in delusion.

Fortunately for him, a woman chose to remember the man she married and promised to love, and a great university took pity on him. Those who helped Nash in his time of need chose not to play the game but rather to make a choice, something that his own game theory cannot account for.


Clifford F. Thies is a professor of economics and finance at Shenandoah University, in Winchester, VA. Send him MAIL. See also his Mises.org Articles Archive.