A Beautiful Mind, winner of this year’s Academy Award for Best Motion Picture, dramatizes the life of John Forbes Nash, who in 1994 was a co-winner of the Nobel Prize in economics. It was based in part on Sylvia Nasar’s 1998 biography of the same name. As the first major Hollywood movie that centers on an important figure in economic theory, it has caused a stir among many who are interested in such things, including, I suspect, readers of this magazine. As might be expected in a production intended for a mass audience, however, there’s actually very little having to do with economics in it. Too bad, then, that what economics it does contain is mostly either wrong or misleading.
In an early scene set circa 1950, John Nash and his buddies, all of them male graduate students in mathematics, are sitting in a Princeton bar when five women enter, one of them a strikingly beautiful blonde. The math whizzes sadly deduce that, according to Adam Smith, individual ambition would drive each of them to try to date the blonde, but only one would win while the rest would lose. Nash has an epiphany: no, the outcome of that competition would not be a single winner, but mutual frustration. Too many men for the one, too little attention to the four rebuffed women. Instead, he reasons, each man would choose a less-attractive date and thereby ensure the best achievable outcome for himself and for everyone else (except perhaps the blonde). And he does so, not because his narrow self-interest is guided by a Smithian invisible hand, but because his decision deliberately takes into account the collective good as well as his own. Ergo, he declares, “Adam Smith was wrong!”
Next we see an inspired Nash working intensely in his dorm room as the seasons pass, feverishly scribbling graphs and mathematical equations. When later his math adviser reads the product of this toil, he assures Nash that it represents a major breakthrough, adding offhandedly that it “flies in the face of 150 years of economic theory.”
(If you’re wondering why mathematicians would know so much economics–150 years’ worth, evidently–the best answer I could come up with is that Princeton in the 1950s, specifically the Institute for Advanced Studies, was the home of the authors of Theory of Games and Economic Behavior, John von Neumann and Oskar Morgenstern, the latter an economist and a former member of Ludwig von Mises’s famous seminar in Vienna. None of this was mentioned in the movie, so we’re left to assume that mathematicians just know this stuff.)
Now, let’s take each of these in turn: the epiphany, math, Adam Smith, and 150 years of economic theory.
The purpose of the bar scene is to convey the idea of a “Nash equilibrium,” which is a solution to a game of strategy. For theorists, a game consists of two or more players, a set of strategies that a player can choose from, and a set of payoffs that depend not only on the strategy he chooses but also on the strategies his opponents choose.
Suppose you and I are driving from opposite directions on the same road. If you choose to drive on your left-hand side of the road while I choose to drive on my right-hand side, we’ll crash head-on and the payoff presumably would be very bad, indeed. Therefore, neither of us would want to stick to his current strategy. Another pair of strategies, “if you your right, then me my left,” would also cause an accident. So to be safe, if I see you choose your left, I would want to choose my left. And, if you see that I’ve chosen my left, this would give you an additional incentive to stick to your strategy of driving on your left. The same would be true if you choose to drive on your right: it would incline me to drive on my right, which would give you even more reason to drive on your right. Therefore, the strategy choices of “if you your left, then me my left” would be mutually reinforcing, and so would “if you your right, then me my right.”
So each player’s choice of strategy depends on the strategy he thinks the other players will choose. Sometimes these choices reinforce one another, sometimes they don’t. When the strategies chosen are mutually reinforcing, as in the driving example, the game is said to have achieved a “Nash equilibrium.” A Nash equilibrium, then, is a solution to a game in which each player chooses his best strategy, given the strategy chosen by every other player. John Nash won the Nobel Prize for proving that, under certain assumptions, any well-defined game has a solution like this.
Unlike the bar-scene solution, though, a Nash equilibrium doesn’t require each player to altruistically seek the common good with his own. It does require that he take into account the impact of his strategies on others’ strategies, and theirs on his. But because some Nash equilibria are undesirable to all players, such as a nuclear-arms race, there is no presumption that they always promote the common good.
Oddly enough, the real problem with the bar scene is that it doesn’t portray a Nash equilibrium at all. It’s true that if all the men pursue the blonde, they block one another. What happens next? If each thinks the others are going after the blonde, then he has an incentive to approach one of the other women so that he can at least get a date. Nash’s supposed insight is that if each one thinks this way, they will all do it, get a date, and leave the blonde alone. The trouble with this outcome, however, is that if each thinks all the others are leaving the blonde alone, he will assume that he now has an uncontested path to the blonde and go after her. And if each one thinks this way, they will all go for her and once again block one another. They’re right back where they started! In this situation, any player will switch his strategy once he thinks the others have chosen theirs, so the strategies are not mutually reinforcing and the “solution” portrayed cannot be a Nash equilibrium.
Economics as Mathematics
The movie also tends to perpetuate a widespread belief that economics is all about mathematics. On the contrary, there’s plenty of good economic theory that doesn’t require mathematical expression or operations. A lot of mathematics in economics is just window dressing (and in several scenes in the movie it really is window dressing). Mathematics is useful for conveying certain economic ideas, such as general equilibrium or in game theory. Whether these ideas are particularly useful for understanding the real social world, or whether many useful economic ideas can be adequately expressed mathematically, is problematic. To give but one example, it’s hard to imagine how mathematics could effectively capture Israel Kirzner’s description of competition as a process of discovering opportunities generated by sheer ignorance.
Also, in actual rivalries the players are typically not aware of all the payoffs and strategies available, to others or even to themselves, and things keep changing in unforeseeable ways. Such considerations, which can be highly inconvenient for those seeking elegant mathematical solutions, are basic to real people as well as to sensible economists–like Adam Smith. Real people simply don’t make choices knowing all the payoffs and probabilities, and for them rationality is not the same thing as mathematical optimization. As Mises and Kirzner have shown us, real people don’t calculate equilibria; they discover opportunities.
Contrary to the movie, Adam Smith’s central message was not that competition produces winners and losers, but that in free markets individual self-interest alone can unintentionally achieve remarkably high levels of social cooperation. For many followers of Smith, the marvel of the market is precisely that no single actor has to know very much in order to cooperate in a mutually beneficial, and thus self-reinforcing, way with the rest of society. Paris gets fed largely through individual self-interest guided by profit and loss.
And Paris has a lot more people than any bar in Princeton. Even so, Nash’s players have to know a great deal more about their problem situation than Smith’s human actors do, and in this sense Smith’s “invisible hand” achieves far more with far less than Nash’s bargaining solution. Not to detract from Nash’s contribution, but Smith solved a much more important and complex problem: how is large-scale social coordination possible without central planning?
In less than five minutes, however, the movie manages to impugn Adam Smith and the 150 years or so of economics that followed him.
And About Those 150 Years . . .
Actually, Nash published his first bargaining thesis in 1951 and Smith’s The Wealth of Nations appeared in 1776, so we’re really talking about 175 years. (They say mathematicians sometimes have trouble doing arithmetic.)
Anyway, this was well after 1936, when another John, as in Maynard Keynes, almost single-handedly revolutionized economic theory. If there was any overturning of economics to be done, Keynes did it long before Nash and did it much more thoroughly. While Nash radically reconceived economic rivalry as a bargaining problem, he basically kept within the overall framework of individual optimization. Keynes rejected that optimization framework altogether. (What he substituted for it economists are still debating, but that’s another story.) One could say that it was unusual, perhaps even courageous, for a cutting-edge theorist, in the midst of the Keynesian macroeconomic revolution, to risk his reputation by working within the bounds of what most would have considered microeconomic territory. But while game theory in that era was certainly nontraditional, it wasn’t revolutionary in nearly the same sense as Keynesian macroeconomics was. Nash did go against the grain of traditional microeconomics; but then almost every other major theorist at the time did, too.
Nash v. Howard
I don’t mean to disparage the real John Nash’s professional achievements, but to criticize producer-director Ron Howard’s characterization of them. Nevertheless, there is truth in a scene toward the end of the film where an elderly Nash is told that his concepts have influenced areas as remote from pure mathematics as antitrust and bandwidth auctioning. While Nash’s bargaining solution is used in these areas more to suggest what conditions may be needed for an equilibrium to emerge than to directly calculate it, the concept has indeed been useful.
And despite its problems, I found myself liking the movie very much. Partly because of the compelling human story it tells (edited here and there I’ve learned), but also because it’s about one of us, an economist–well, sort of. Perhaps someday Hollywood will release a major film about an economist who really did change the course of history for the better (which rules out Keynes), and who also suffered, struggled, and triumphed. As I imagine it, an early scene would be set, circa 1920, in a lively little coffeehouse in Vienna.