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2007-9-27
I am not turned to be good enough if I have not done anything great in my work. ---Nash
A Beautiful Mind is a biography film .This film was awarded Oscar Awards in 2002 and nearly won almost all top awards of film in the world. Character archetype of the film---John F. Nash Jr., a Nobel Prize winner who was a talent of math and had a legendary life.
John F. Nash Jr. was born June 13th, 1928.His father was a teacher who knew how to enlighten children. Hence, Nash was nurtured with well education. He was introverted by nature and not good at communicated with others. Hence, he preferred to read or think alone.
At about 14, his excellent genius in mathematics was showed. He had deep and distinguishable understandings of some math problems. In 1948, when he was still under the age of 20, Nash entered Princeton University where he would study for a doctor's degree. His classmates said that Nash was not a well-behaved student but had excellent talents. He sometimes hid in some corner reading instead of attending class. Someone even said that Nash had not attended a whole class in a term. True, skipping class is not a good manner, this did not stop him from obtaining knowledge. Princeton University possessed a group of excellent masters of the USA, including Einstein, John von Neumann, V. A. Livshits and so on. In addition, the strong learning atmosphere influenced Nash everyday. He sometimes stayed in the library for a whole day, where he could study each branch of mathematics, including topology, mathematics, logics, game theory which he was very interested in. He spent almost a whole summer to think about problems in game theory.
Actually, game theory had a long history. There was a famous story of Tian Ji Horse Racing in China 2000 years ago during the Spring and Autumn period. In this story, the famous military strategist helped the General Tianji to win in the horse racing by using a simple game theory. But this was not systematic and was just the beginning of game theory. The real game theory is created by Von Neumann who had made a systematic analysis of game theory and initiated this subject. However, Von Neumann's theory was so abstract that only few mathematicians could understand his method which made the development of game theory be restricted to some extent. This was not changed until Nash created the Non-Cooperative Games and represented the beginning of a new era of game theory.
Non-Cooperative Games was initiated by Nash in 1950 when he stayed in the library studying game theory. But he had to stop study of game theory temporarily for preparation of the final exams. A Beautiful Mind told such a story: after being librated from the library, Nash had chances to free him from game theory. One day, he went to a bar with his classmates. At this time, three common beauties and an unequalled beauty entered. Being encouraged by his friends, Nash went to strike a conversation with the unequalled beauty. But he was heartlessly refused. Common person may dismiss with a laugh or fly into a rage from shame. However, Nash is a genius who is good at discover and thinking about questions. Suddenly, he found that it maybe wrong to strike a conversation with the unequalled beauty of the four girls firstly. In fact, unequalled beauties all had many pursuers who restricted each other. Hence, no one succeeded finally.
Then, is it necessary to abandon the unequalled beauty and to pursue the three common beauties? No. because the common beauties would think that the guys did not have goodwill, he came just because of being refused. Then she would just be a substitute. Hence, she would also refuse the guy heartlessly. Non of the guys succeeded finally. What Nash thought about was distinguished, i.e. we should go to chat with the three common beauties instead of the unequalled beauty. In this way, it would seem that she was neglected. If someone took an action at this time, there would be more possibility to success. What a talent he was. Thank to this occasional chance, Nash was suddenly enlightened.
He came back to dormitory without stop to summarize his thoughts and formed a clear scheme. Subsequently, he finished his doctoral dissertation Non-Cooperative Games with his research results which was published on monthly bulletins of science institutes in USA and threatened a big storm immediately.
If you are not clear yet, here is an example. We can often hear price wars of various appliances, such as colour TV, refrigerators, air conditioners, microwave ovens, etc. Manufacturers and traders all make great effort to reduce the price so as to win more clients. Then, the consumers buy what they want at the lowest cost. It is of course favourable for the customers. However, the result of price war is destructive for the manufacturers. In price war, everyone tries to reduce the price which makes the appliances be sold at the cost and even lower than the cost. Finally, there will be no profit for the manufacturers, even that some will suffer loss. This can be explained by using "Nash Equilibrium".
Then, what is the best for a colour TV manufacturer during sales? That is, all other manufacturers keep a relatively higher price, while himself applies a normal one. The consumers will of course select the product at a lower price instead of that at a higher one. But this will not occur in Nash Equilibrium. There are two choices for the manufacturer during price setting: he can either choose a higher price which will reward him with a higher profit. But this is feasible in condition that the competitors also set a high price. At the same time, he also can choose a lower price. Because his will win part of the consumers no matter the price is high or low. Hence, it is favourable to select a lower price in condition of not knowing information about the competitors. This makes the manufacturers lower the price one by one and leaves little profit and even non. This pattern is called "Nash Equilibrium" or "Non-Cooperative equilibrium". Here, "Non-Cooperative" means that the manufacturers do not know each other and have no "coordination" during strategy selecting. They just consider themselves without other competitors. They are just absolute competitors.
Then, the readers will consider why not join together to make a higher price strategy? In fact, they are willing to do this in soul. There are industry associations which play a role of connecting each competitor in the industry. If all manufacturers set a high price, it will lead to monopoly and both the consumers and economic efficiency will be harmed. This is unacceptable for all countries and is also the reason why governments of all countries are making a great effort in anti-monopoly war.
Nash's Non-Cooperative Games challenges the principle of Adam Smith basically. According to the theory of Adam Smith, in market economy, everyone cares his own benefit and realizes the aim of gain profit all together finally. But a paradox is put forward in Nash Equilibrium. The colour TV manufactures compete to reduce price just because of self-regarding. Then, what about the result? It benefits non. So, Nash Equilibrium is a shock to western economics. It leads the economists to a new thinking direction.
Only cooperation in condition that both parties are equal and voluntary can create the largest benefit. What prevails in fact is that there are too many competitors who do not communicate intimately with each other. Hence, Non-Cooperation is more than cooperation. "Nash Equilibrium" makes great modification for Cooperative Games of Von Neumann which could be regarded as a revolution of western economics.
Unfortunately, Nash suffered serious schizophrenia when he was at the peak of career nearly 30 which forced him to rest at home and wandered like a ghost in campus of Princeton University. However, he is fortunate at the same time. The God presented him a good wife who took care of him during the decades of years with strong will. Finally, her endeavour was awarded the miracle that Nash recovered.In 1994, Nash won the Nobel Prize in Economic at the age of 66.
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Organizer:
Beijing Municipal Association for Science & Technology
Undertaker: Beijing Science & Technology
Consulting Center,
Information Center of Beijing Municipal Association for
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