A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature by Tom SiegfriedMillions have seen the movie and thousands have read the book but few have fully appreciated the mathematics developed by John Nashs beautiful mind. Today Nashs beautiful math has become a universal language for research in the social sciences and has infiltrated the realms of evolutionary biology, neuroscience, and even quantum physics. John Nash won the 1994 Nobel Prize in economics for pioneering research published in the 1950s on a new branch of mathematics known as game theory. At the time of Nashs early work, game theory was briefly popular among some mathematicians and Cold War analysts. But it remained obscure until the 1970s when evolutionary biologists began applying it to their work. In the 1980s economists began to embrace game theory. Since then it has found an ever expanding repertoire of applications among a wide range of scientific disciplines. Today neuroscientists peer into game players brains, anthropologists play games with people from primitive cultures, biologists use games to explain the evolution of human language, and mathematicians exploit games to better understand social networks. A common thread connecting much of this research is its relevance to the ancient quest for a science of human social behavior, or a Code of Nature, in the spirit of the fictional science of psychohistory described in the famous Foundation novels by the late Isaac Asimov. In A Beautiful Math, acclaimed science writer Tom Siegfried describes how game theory links the life sciences, social sciences, and physical sciences in a way that may bring Asimovs dream closer to reality.
Harsanyi and R. Selten in for their work on Game Theory , many were very surprised. The relation between making decisions in Economy and making decisions in Strategic Games was brought to light. Some research was done in the early s , but when John Nash made an astonishing discovery early in his career, this intriguing subject took on a different dimension. It was now clear to many that if game theory was applied to other areas, it could generate very important and productive results. Interestingly this movie was directed by Ron Howard whose son used to actively play in S cholastic Chess Tournaments. The movie shows the life of a mathematical genius struggling with a painful and harrowing journey of self-discovery once he was diagnosed with schizophrenia.
This article is the winner of the general public category of the Plus new writers award Suppose you are one of a number of boys hanging out at the school coffee bar. At the other side of the bar there is a group of beautiful girls, all but one of them brunette. The only blonde girl in the group is the one all the boys would first approach. Should you disregard what the other boys would do and try to talk to the blonde first? What if everyone goes for the blonde?
Game Theory: A Beautiful Mind. For me, Nash was then just a short and catchy adjective attached to two abstract concepts that are central to game theory: Nash Equilibrium and the Nash Bargaining Solution. I must have realized that the word Nash was connected to a person. And if I had asked myself who Nash was, I probably would have guessed he was an English intellectual who died at the beginning of the twentieth century. I heard from other students that a crazy genius would roam around the campus, sitting for hours in the cafeteria with a pile of computer printouts in front of him, reading newspapers he collected from abandoned tables. They said there was one student who had dared to approach him and speak with him, and that he had readily helped the student. It was hard for me to identify him; a lot of weird people roam the lawns at Princeton.
Thinking about the economics of Moneyball lead me to think about the film and book A Beautiful Mind , about John Nash. Nash won the Nobel Memorial Prize in Economics in for his contributions to game theory. Still, as most adaptations do, the film differs from the book in several important ways. The most annoying problem with the film adaptation, however, is in the one and only scene illuminating the application of game theory in the film, the bar scene , the solution the Nash character provides to the game is not a Nash equilibrium. First, to clear away some brush. In the context of the film, the bar scene is supposed to illustrate the equilibrium concept Nash developed, that is, a Nash equilibrium.
John F. Nash Jr. Nash did not invent game theory; the mathematician John von Neumann did the pioneering work to establish the field in the first half of the 20th century. But Dr. Nash extended the analysis beyond zero-sum, I-win-you-lose types of games to more complex situations in which all of the players could gain, or all could lose. The central concept is the Nash equilibrium, roughly defined as a stable state in which no player can gain advantage through a unilateral change of strategy assuming the others do not change what they are doing.