Universal American (Universal Pictures, USA) 2001年produced the film "A Beautiful Mind" (A Beautiful Mind) is known to everyone. The movie in one stroke the 59th won five Golden Globe Awards, and won the 2002 session of the 74th Academy Awards four awards. The film itself and the people behind the screen prototype, deeply shocked the world people's hearts.
"Beautiful Mind" art reproduces the mathematical genius, the 1994 Nobel Laureate in Economics one suffering from paranoia schizophrenia for more than 30 years and miraculously return to normal John Nash (John Nash) legendary life experiences.
In general of the documentary film, the actor always image than real life prototype of moving to more charisma. However, the incredible is that both face the reality of Nash demeanor than actor Oscar winner Russell Crowe (Crowe Russell) Lueshengyichou.
It is precisely this ancient Greek gods such as had generally handsome潇洒it strange wizard's mathematics and economics double genius - Nash, in game theory in the early days of the enormous contribution has been changing our lives.
However, the "Beautiful Mind" but truthfully reflect the Xibei Cross Nash's life: Nash in the field of mathematics, from the very early start on merit, in 1958 he was the U.S. "Fortune" (Fortune) magazine as a new generation of talent The most outstanding mathematicians in the figures. In Nash Chunfengdeyi, the industry will reach its peak when suddenly the fate suffered a serious blow to the merciless, from the sky into hell: 30-year-old Nash suffering from a severe schizophrenia. The genius of his life as troubled by schizophrenia, and in private life, not misconduct. Nash youth with a large 5-year-old girl he exchanges, the two have a natural child, Nash before the onset of schizophrenia and she has maintained a Ruojiruoli the ambiguous relations. His parents found that four years after the matter, Nash shortly after his father died, and I do not know whether this combat-related. After the death of his father, Steve Nash and the Massachusetts Institute of Technology (MIT) a beautiful young female students love Lixi Ya (Alicia) marriage, after more than 40 years Huannanyugong the love and affection, we can witness this is his personal life in the most perfect, the most fortunate Time.
Li Xiya in love going equipped pregnant, pending delivery of the same year, Nash's mental state is deteriorating. His increasingly erratic behaviour, is a truly mental frenzy. He entangled trouble, because in a male toilet was "not appropriate" exposed his body was arrested.
Driven to despair, love Lixi Ya in 1962, and Nash divorce. But her of his love and loyalty has not disappeared. 1970, Nash's mother died and his sister can not afford him, in Nash Guku no one to depend, to living on the street, kind-hearted love Li Xiya to pick him up with their own living. She not only in the interest on his personal and unique to women carefully sensitive care of his emotional life. She considerate he is unwilling to go to the hospital closed for the wishes of Bajia moved to the outside world away from the hustle and bustle of Princeton, with the hope that the quiet academic atmosphere contribute to the emotional stability of Nash.
Yanzheng Zheng Li Xiya not love watching the natural differences intrinsic genius of it is so depressed. Li Xiya as his wife's love with love to rescue her husband, even though the well-being of people in love when the Qingqingwowo at this time has gone. Nash was the wife of such an unshakable love and a firm conviction by the infection, the same determination to fight the disease in the end. His wife in love with the help of Li Xiya love, in his own genius and frenzy, Nash caught a fever on the high intellectual level.
This changed everything. After many years of hard work, Nash finally out of haze, rational has brought him peace of mind. Nash was in 1994 in the modern game by virtue of his outstanding contribution to the theory, the scientific community received the highest honor - the Nobel Prize.
People watching the movie, can not help but wonder, genius Nash in the game on the major contribution to what is » Why Hollywood for such a legendary master of game theory to such filming of the documentary film? » Why is the film that shocked the world in the hearts of hundreds of millions of viewers »
Many people may be of interest to game theory is the "Beautiful Mind" for this is handed down to the trigger.
As everyone knows, modern game theory from the Hungarian mathematician Von Neumann (John von Neumann) in the 1920s founded, in 1944 he and economist Oscar Morgenstern (Oskar Morgenstern) jointly published the masterpiece "Bo Game theory and economic behavior, "Game Theory marks the modern system of initial shape.
For non-cooperation, competition-type game, Neumann resolved by the only two zero-sum game, such as two people playing table tennis, won the party will lose the other two were the sum of zero profit. Can here and how to find a theory of the "solutions" or "balance", that is, both sides are involved in the most "reasonable" or the specific optimal strategy » How kind of strategy is "reasonable" »
On the application of traditional decision-making in the "minimum biggest" criteria, namely the game each side of the assumption that all the other strategy of their fundamental purpose is to make the most of defeat, and thus optimize their response, Neumann from the mathematical That, through a linear operator, for each two-person zero-sum game, can find a "minimum of the greatest." Popular with the words, the most famous theorem by the smallest of the basic idea is to "hold the best hope, so prepared for the worst."
Although the two-person game, and the solution is of great significance, but as a theory, it applied to the practice range is extremely limited. Game two, and the major limitations: First, in various social activities, often have multiple participants rather than only two parties, two parties involved in the interaction is not necessarily the result of some profit lost on some people, the whole group May be greater than zero or less than zero net profit.
1949, 21-year-old Nash wrote a famous paper "more balanced point of the game," Nash Equilibrium proposed the concept and method. This is the modern non-cooperative game theory in one of the most important ideological, but also laid a 44 after he received the Nobel Prize foundation.
Nash had in 1950 with the idea to him at the time of the meeting over the world, Feng Neumann (one of the founders of game theory, the genius mathematician), was categorically denied, in the meantime he has also been Einstein's Cold-shouldered. However, in science at Princeton University, relaxed environment, his paper still be published and caused a sensation.
For more participation of non-zero and Game issues, Nash, no one knows how to solve, or how to find a solution similar to the minimum as the biggest "balance." And find solutions, the following of course can not be carried out, let alone guide the practice. Nash on the game theory of the enormous contribution, is in his genius and to put forward the "Nash Equilibrium" The basic concept for the more common problems found broad understanding of the game.
1950 and 1951, Nash's two non-cooperative game theory on the important papers, completely changed the people of competition and market views. He proved that the non-cooperative game and balanced solution, and prove the existence of a balanced solution, that is, the famous Nash Equilibrium. Thus reveals the game with a balanced relationship between the economic balance. Nash laid the modern study of non-cooperative game theory the cornerstone of the subsequent game theory this research are basically along the main line of the start.
Nash's friend, Professor of Economics at Princeton University, Dixit said: "If every time someone wrote Nash Equilibrium, or start with the words, Nash will get a piece of money, so he is now May be a Monopoly! "
Neumann in the "Game Theory and Economic Behavior," a book also established a cooperative game theory of the basic model, but for which a two-way consultations, that is, participants how to "bargain", did not give a definite The solution.
Nash in this area have made outstanding contributions to the same, he not only raised the issue of bargaining axiomatic method, in theory make use of this method is a good forecast of further Nash programme: Game will be cooperative in the consultation into A wide range of non-cooperative game - a step towards the ultimate aim of the consultations is to maximize their own interests.
In addition, the testing of experimental game theory study, Nash is also a pioneer. He has started bargaining and the formation of the experiment, and has sharply pointed out that in other Shiyan Zhe the Prisoner's Dilemma experiment, repeated for a repeat of the participants in fact single-step strategy will be transformed into a large multi-step strategy问题. This thinking prompted the first time in the game theory of conspiracy to repeat the possibility of this discovery in the economic and political fields has played an important role.
"Beautiful Mind" in such circumstances: in 1994 the U.S. government to the business part of the electromagnetic spectrum auction large. This multi-round auction by many experts carefully designed game theory, the purpose is designed to maximize government revenue and traders utilization. This design achieved great success. Government access to over 10 billion U.S. dollars of income, the frequency spectrum have found a satisfactory end.
The corresponding is that the New Zealand a similar auction were failures. Because they do not have a game theory to design the auction rules. The results, the Government received only 15 percent of projected income, which was also unable to auction the frequencies best use. For example, because no one competition, a college students spent only one U.S. dollars on the purchase of a television licence.
It is precisely because the game theory of modern economic life is such a major impact and influence, in 1994 the Swedish Academy announced the scientists in the world the highest honor of the Nobel Economics Prize awarded to Nash, including the three math , And in recognition of their non-cooperative game theory analysis of the ground-breaking.
Perhaps, as Russell Crowe in time to receive the "Beautiful Mind" evaluation, Nash and his game theory to us, "can help us open mind, give us faith, in real life there will be a miracle to happen."
