John F. Nash, Jr.: introduction and postscript.

Holt, Charles A.

The task of finding a speaker seemed formidable in a year following James Heckman's address to the Southern Economic Association (SEA) only a month after receiving a Nobel prize. I began by asking myself who would be the one economist in the world that people would be most interested in hearing at the meetings. After some discussion with others, the answer became clear. Although Professor Nash's Princeton Ph.D. is in mathematics and he remains a mystery to most of us, he is, after all, the person whose last name is heard in class at least as often as that of Greenspan or Smith. So please forgive me if I refer to him as just Nash, out of habit and lack of personal contact for many years.

The unfolding of this mystery surprised many of us who were at the 2001 SEA meetings in Tampa, Florida. Professor Nash joined a dinner group heading for Ybor City. Over a beer, he was refreshingly candid about his work. Question: "The Nash bargaining solution is a startlingly original theorem because the conclusion, that bargaining will maximize the product of utility differences, seems to be so different from the nature of the axioms about the independence of irrelevant alternatives, or that people maximize expected utility." The answer was that he knew that expected utility had to be invariant to additive and (positive) multiplicative transformations. Thus, utility differences would take out additive constants, and multiplicative constants would factor out of products. With a chuckle, he admitted that the rest was just working back to find the assumptions that would force the only admissible outcome to be equivalent to the maximization of utility increments above threat point levels. This bargaining solutio n is still widely used today, especially in law and economics and the economics of the family, as indicated by Marjorie McElroy's presidential address the next day.

Many economists may not realize that John Nash was one of the first people to become involved in laboratory experiments. One of these experiments, conducted more than fifty years ago, was inspired by his second great accomplishment: the definition and existence proof for Nash equilibrium. This experiment was conducted at the RAND Corporation in Santa Monica, California, on the same day that the two mathematicians who designed it heard about the surprising theorem that had been proved by a young graduate student on the other coast (for details, see Sylvia Nasar's "unauthorized" biography, A Beautiful Mind). The experiment payoffs were for a two-person game with two strategies, which would today be called "cooperate" and "defect." Nash's thesis advisor noticed the payoffs written on a blackboard and made up the story of the "prisoner's dilemma." Nash later objected to the procedure in which the participants were paired together for many rounds, repeating the same game. Because Nash later ran his own experiments, I jumped at the opportunity to ask him what he thought of this methodology. His reply startled me: "Experimental economics is the ultimate truth. Anyone can write down a theory and just say it is true."

The lecture, on "Ideal Money," was followed by a question-and-answer period that revealed one of the many reasons for Professor Nash's breakthroughs. In "Ideal Money," he begins to think about monetary management with a fresh slate based on indices of producer goods prices. This talk was clearly not an attempt to refine someone else's ideas. This reminded me of his 26-page Princeton dissertation with the notation written in by hand. It had two references, one to von Neumann and Morgenstern's Theory of Games and Economic Behavior, and one to his own 1950 paper in the Proceedings of the National Academy of Sciences, "Equilibrium Points in N-person Games." In the question period after the talk, I asked him about how he thought of the definition of what we call the Nash equilibrium. In particular, I wanted to know if it were driven by the nature of the mathematical tools he was using or by an effort to generalize the work of Cournot more than a hundred years earlier. He replied that he did not recall, and that he had no paper trail to reconstruct the answer. Later by e-mail he did say that he was not aware of the work of Cournot at that time. Any of you who have ever struggled with hard problems and proofs while driving or taking a shower will recognize how a fresh perspective may just pop up if you can manage to break out of the standard, well-explored approaches. This is an advantage that Nash had as a mathematician who was taking a fresh look at bargaining and equilibrium problems.

For many of us, the discovery from Tampa was that this god-like legend in economics really exists as a person and as a scientist. For three days he hopped from session to session, asking thoughtful questions in a polite manner. At the reception in honor of Professor Breit's retirement, he inquired, "Who is Marshall Jevons?" and I answered, "There is Marshall, and over there is Jevons." Then he pulled out his camera and took several photos, after having been patient about being on the other end of the lens numerous times already. For those who are interested, some photos of this reception can be found at http://www.people.virginia.edu/~cah2k.

Many economists have tried to improve on Professor Nash's basic notion of equilibrium that was the basis for his 1994 Nobel prize in economics. Juicy adjectives have been used, heavy mathematical refinements have been developed, and additional experiments have been run. Nash's insight has provided a clear framework for this discussion, and it is a tribute to his accomplishment that his approach is still by far the most commonly used way to solve economic games. On a more fundamental level, it is reassuring to know that this equilibrium exists, even if we often are not able to solve for it and must be content with qualitative characterizations. And it is reassuring to know that John Nash exists as a person and continues to think creatively.