The film "Beautiful Mind" produced by Global Company in 2001, which is based on the same name biography, and the artistic genius has reproduced mathematics. One of the Nobel's economics award winners. It has a miraculous recovery of existence schizophrenia. Little John Forbes? Nash Legend of life. This film, which won the 2002 Golden Ball and Oscar, along with the prototype behind the screen, deeply shocked the people's minds. To bring Nash awards, he has a great contribution to the development of game theory and his roughness, and it has also caused great response and attention.
What is a game theory? The ancient language has a cloud, the world is chess. Everyone in life is like a player, and every behavior is like a child who is invisible. The savvy chess players try to figure out with each other, honest, people fight, and make a lot of exciting, changing multiple ends Chess game. Game Theory is to study the number of middle-generalized, logical part of the players, and systematically become scientific. In other words, it is to study how individuals have the most reasonable strategy in an intricate interaction. In fact, game theory is being derived from ancient game or game such as chess, poker. Mathematics will abstract specific problems, and the system has studied the law and changes by establishing a self-complete logical framework. This is not an easy thing, with the easiest two people play as an example, I want to know this in this medium. If you assume that both sides have accurately remember that each step of themselves and the most "rationality" When the player, the god, in order to win the game, you have to consider the idea of B., and it has to consider the idea of A., so I have to think that B is thinking about his thoughts. I thought of he was thinking about the idea ...
In the face of how many times, how to analyze the problem, how to find the best solution to the abstract mathematics issues that are reality, thus providing the possibility of guiding practice in theory? The modern game theory is created by Hungary's large mathematician von. Novan began to create in 1944, in 1944, he and economist Oscar, MorganSten, and launched the "game theory and economic behavior", marking the modern system. The initial formation of game theory. For non-cooperative, pure competitive games, Jobman solves only two zero and games - like two people play chess, or play table tennis, one person wins, another person must lose, net Profit is zero. The abstract game problem here is that the participant collection (two), strategy set (all chess), and profit collection (winning), can you find a theoretical "solution" Or "balance", that is, the most "reasonable" and optimal specific strategy for participating in both parties? How is it "reasonable"? The "Minimum and Max" criterion in the application of traditional decisions, that is, each party of the game assumes all the fundamental purposes of the other party to make themselves to lose, and according to this optimization, Neuman has proven from mathematics Through a certain linear operation, a "minimum and biggest solution" can be found for each two-person zero and game. Through a certain linear operation, the competition two sides randomly uses the various steps in a set of optimal policies in the form of probability distribution, and can ultimately achieve the greatest and comparable to each other. Of course, its implied meaning is that this optimal policy does not depend on the operation of the opponent in the game. In a popular saying, the basic "rational" thought of this famous minimum and biggest aortrower is "Hold the best hope, do the worst plan".
Although the solvement of two people and games is significant, as a theory, it is extremely limited. Players who don't add games, you can say that in addition to military competition, it is almost difficult to use. The main limitations of the two people and the game are two. In various social activities, many participants are often involved rather than only two; the other is that the results of participating in the interactions are not necessarily profitable, and some people have lost. The entire group may have a net profit greater than zero or less than zero. For the latter, let's look at a most classic interest in history: "Prisoner Dilemma". The police said that the police arrested two stolen prisoners, and they cherished their failure, and they would like to confess their suspects. The police isolate two prisoners, respectively, and the exchange policies are as follows: frankly from wide, resistant to strict! If you are recruited, the other person doesn't make you, then you will release you, and another person sentenced for 20 years; if you don't recruited, another person recruited, then you have to be sentenced to 20 years, another person is released. If the two people are recruited, the police evidence is enough, and the two are sentenced to 10 years. As for the two people, they don't have to recruit, don't use the police to explain, two people have to judge, but because of evidence, it is a lot to be a lot, such as 1 year. The police finally said, there was a policeman on there, and the same policy was in the same way. The criminals played in the heart, if the other party tricks, I trick 10 years, no trick is 20 years, it is a citure; if the other party does not recruit, I am a trick is not guilty, don't trick, it is 1 year, or a recruitment. So, trick! The two "savvy" thieves have been tried, and they were sentenced to 10 years. Smart readers, in fact, if the two thieves do not recruit, will be sentenced to one year, is it better for them? In this prisoner dilemma, participants are still two (two thefts), but this is no longer a zero and a game, and people are damaged is not equal to my revenue. Two thieves may be sentenced to 20 years, or have been only sentenced to 2 years.
For multiplayer participation, non-zero and game issues, before Nash, no one knows how to solve it, or how to find "balance" similar to the minimum solitude. I can't find a solution, the following research is of course unable, and I can't talk about guidance. Nash's great contribution to the game theory is that he gently proposed the basic concept of "Nash Balance", which found aware of the more general extensive game issues. Nash's basic idea is that all participants in this unconventional strategy is the best countermeasures for other participants, no one can improve their revenue by altering its strategy. Take the previous prisoners as an example. If the thief believes that the thief is convincing, then his best strategy is to confess, and if the thief believes believes that the thief is confession, then his best strategy is still confession. This is a nash balance, it is "self-determination". In the prisoner's dilemma, there is only one nash balance. However, if conditions change, in many other specific problems, Nash balance may more than one. Nash is unique to use mathematics skills, proves that the following Nash Qi Qi: For any N-person participation, non-cooperative game (zero and non-zero), if each participant has only limited strategy, then there must be at least one Nash Balanced decoction. Like many of the most outstanding thoughts, this concept solves the problem of hanging without knowing the unclear way. It seems simple, it seems that it is something that "I can think of" I can think of ", but then, in addition to Nash, a generation of masters did not think. The proposal of Nash is proposed, and the development of game theory has produced revolutionary impact. The concept of Nash is the cornerstone and center of modern game theory (although this point is still controversial in a small number of game theory). Nash's friend, Professor of Princeton University, Dickste, said, "If someone talks or writes the Nash equilibrium, Nash can get a dollar, then he will be a rich man now! "The game theory mentioned above is trying to solve non-cooperative problems, that is, between participants, in addition to the decision results, without other forms of information exchange. Through the prisoner's dilemma, if the participants can negotiate with each other, the strategic decisions they have made will be very different (of course, the two people compete together). It is true that in the various life behaviors, in addition to competitive relationships between people, there is also a cooperative relationship, often two relationships, and reasonable cooperation can bring common interests to both sides. This is the category of cooperative game theory research. Noumman established the basic model of cooperative game theory in "Game Theory and Economic Behavior", but no one can be given to the two-way negotiation issues (ie, how to "bargain") Determined solution. Nash has also made an excellent contribution in this area. He not only proposed a pro-bargaining axioms, directly benefiting labor economy and international trade, but also in theory, in theory, the good predictability of this solution further proposes Nash Plan: Cooperation The gaming in the game is a step in a broader non-cooperative game - the purpose of negotiation is ultimately to maximize your own interests. In addition, Nash is also a pioneer in the behavioral experiment of test game theory. He has launched an experiment, and has pointed out that in the prisoner's dilemma of other experiments, repeatedly letting the participant repetition experiments actually transform the single step strategy into a big multi-step strategy. problem. The next idea suggests that the possibility of silence between the reproduction of the play in the economic and political fields of the economy and political fields.
These may seem slightly boring theories, with logic reasoning as tools for rigorous and orderly mathematics of competition and cooperation behaviors in people's daily lives, and when mathematicians are tirelessly rising into science, then counter-acting It is difficult for its far-reaching impact. Today, the modern game theory of Nash is the continuous development of many experts, not only has their own theoretical systems, but also widely used in economics, political, military, and even biology. In the field of biology, game theory is used to study the competition between race genetics and evolutionary biology, and the competition between individual genes, and in turn promotes the ideological development of game theory. In the field of politics, military, game theory is used to analyze the election strategy, the war, the legislative agenda arrangement, etc. In the field of economics, game theory is more integrated into the mainstream of the entire discipline, and the economic textbooks and magazines have no income game theory. Economists have put the game theory of research strategy interact as the most appropriate analysis tool analysis Class economics, such as public economy, international trade, natural resource economy, industrial management, etc., and so on. As mentioned in the direct benefits of the game theory, it is mentioned in the book, such as the "Beautiful Mind" book, 1994 US government auctioned most of the electromagnetic spectrum for the merchant. This multi-round auction is carefully designed by a batch of game themeasures to maximize government gains and the principles of utilization rates, and achieve great success. The Government has achieved more than $ 10 billion, and the spectra of each frequency found satisfactory destination. Compared with this is that a auction that New Zealand has not had a game theory design. The government only got 15% of the expected revenue, and the frequency of being auction has not been used. For example, because of no competition, a college student has only spent $ 1 for $ 1, I bought a TV station license! It is because the game theory has such a major impact and impact on modern economics. In 1994, the Swedish Royal College announced the sixth mathematicians of the highest honor of the world of scientists in the year to include Nash. Commending their pioneering analysis of non-cooperative game theory. The world has finally recognized Nash's genius because of game theory. This year, he is a 66-year-old man. Compared to it in scientific and dazzling outstanding contributions, he wrote a long-lasting talent, full of hardships and pain, interleaving, and crazy legendary life. Feeling and admire. Nash was born in 1928 an electronics engineer family, and the child's era is lonely, on the one hand, the extraordinary mathematics can be displayed. At the age of 17, he entered this card Nairi Mellon University. During this period, he went to an international economics course, which triggered the interest of economic propositions, and later published on the problem of cooperative game bargaining issues were stems from some ideas at this time. At the age of 20, Nasa was taken to Bachelor of Mathematics and a master's degree in Carnegie, and accepted a graduate from Princeton University, becoming a graduate student here. He is interested in many mathematics, such as topology, on behalf of math, geometry, game theory and logic. When preparing a doctoral thesis, he is determined to have an innocent a new topic. In the end, the bargaining problem that has been thought-in, guiding him to establish the basic principles of non-cooperative game theory. In 1949, 21-year-old Nash wrote a famous papers "Equilibrium Point of Multi-person Game", which proposed Nash equilibrium concept, one of the most important ideas in modern non-cooperative game theory, and laid the foundation. After 44 years, he won the foundation of the Nobel Prize. In 1950, Nash has taken his thoughts to meet the Nobman who is full of world, but has been denied, but in Princeton University is relaxed in the scientific environment, his papers still get public and causing a sensation. In the same year, he obtained a Ph.D. in mathematics with the "non-cooperative game" in the paper.
With some Nash of the pure mathematician, after graduation, during the work of the Land Research Institute and Princeton University, it demonstrated a reversible isometric embedded ministry, and introduced a new method to prove that the difficult highway is equivalent to the sequestration, strong powerful The proof of existence, uniqueness, and continuity theorem of partial microscopy is promoted. For pure mathematicians, mathematics is the spiritual art gymnastics, the evaluation of a study, the standard is that the math depth and whether the new idea, new method, or a problem solved for long-term hanging . From this perspective, Nash's results, as well as more tough mathematics research hours during the MIT in MIT, more than his Nash equilibrium to convince mathematics. Indeed, 1958 Nasin was rated as the most outstanding figure in the new generation of genius mathemologists by the US "Wealth" magazine. However, there is an unexpected wind, people have a good fortune, just in the spring of Nash, when the cause will reach the peak, suddenly he suffer from the ruthlessness of the fate, from the cloud falls under hell. Nash suffered schizophrenia in his year. He is not a perfect person. In 1952, Nash is a big girl who is 5 years old. It has a private child with it. There is still a reason to keep it if it is still a relationship with her. In 1956, his parents found a rhyme of his son, and soon his father died, I don't know if it is related to this, and I don't know if Nash is. In 1957, he and the young beautiful female student of Massachusetts Institute of Technology, I got married, and more than forty years of affection and love and affiliated love and affection, this may be the most perfect and fortunate moment in his personal life. In 1958, I Lisia has pregnant, and has not yet delivered delivery, Nash's mental state begins to deteriorate. His behavior is getting more and more quirky, step by step to the mind is mad.
Nash is the most terrible kind of illusion schizophrenia, all of all mental illnesses. The patient is filling the mind with the unrealistic crazy thought of time, and will have a magic, miss, and talk to people you think. Nash will say to the air, there is information from another planet with other planets that can be cracked; will suddenly quit the position in MA, only to ran to Europe, to give up American nationality, or Alsia I went to drag him; at home, he continued to threaten his wife Alcia. Under the helplessness, Eliia divorced in 1962 and Nash. But she did not disappear with his loyalty love. 70 years Nash's mother died, and his sister could not bear him, just in Nash lone, he had to fall into the streets, and kind Eliya took him to live with himself. She not only cares about him, but also cares about his mood with a unique care of women. She thought he refused to go to the hospital to closing the wish, and moved home to Princeton, who hoped, hoping that the quiet and familiar academic atmosphere helped to stabilize Nash's emotions.
This is a grateful game. Nash, this research rational strategy mathematics genius, suddenly lost rational thinking of proudness, is not coming back and forth between awake and crazy, is it always going to the abyss or go back home? In that unmanned world, he has never given up to the love of mathematics. We cannot know all the pains that Nash suffer, but the huge conflicts between the will figure out the will and effort are how long is a long mental disaster. Fortunately, in this game, there is a loyal participant. When he muttered himself, when he didn't understand, when he was like a ghost, it was always a green campus. A pair of warm eyes and arms are courageous to accompany him. The strongest two things in the world, will and love, combine together, create an optimal strategy, that is, - miracle. Yes, the world witnessed the comedy ending of this game, in the 1990s after Nashi Schizophrenia, his spirit gradually returned to normal. In 1994, Dr. Nash did not mention the pain brought to him in the autobiography written by the Nobel Prize. At the end, he wrote. It is not normal. So I still have hope, perhaps through the current research or new idea, I can make a little valuable thing. "Read here, can't sigh, sigh this Game theory of the gifted genius, sighing his tenacious will, and the persistent heart without reservation! Perhaps these is also the source of Eliia love? The world is like a new game. The brilliance of the previous generation has become history, and the future is in the hands of the later people, depending on each of his (her). What kind of game will we be a game?
