The two important papers in Nash, 1950 and 1951, thoroughly changed people's views on competition and market. He proved non-cooperative game and its balanced solution, and proved the existence of a balanced solution, that is, the famous Nash equilibrium. This reveals the intrinsic links of game balance and economic balance. Nash 's research laid the cornerstone of modern non-cooperative game theory, and later game theory is basically unfolded along this main line. However, Nash Talent Discovery has been denied by von Noman, before that, he was also subject to Einstein's cold. But the bones challenge the authority, despise the nature of the authority, so that Nash adheres to his own point of view, and finally a master. If it is not more than 30 years of serious mental illness, I am afraid he has already
Standing on the Nobel Prize in the Nobel Prize, and will never share this award with others.
Nash is a very talented mathematician. His main contribution is made from 1950 to 1951 in Princeton a doctoral degree. However, his genius found that the balance of non-cooperative games, ie "Nash Balance" is not smooth.
1948 Nashisa is a Ph.D. in Princeton University. He was less than 20 years old that year. At that time, Princeton was universal, and the master was like a cloud. Einstein, von Noyman, Leffhetz (Director of Mathematics), Albert Tuck, Allenzo Chic, Harold Kun, Nogman Stirund, Elf Fox ... is all here. Game theory is mainly created by von Noyman (1903-1957). He is a mathematician who born in Hungary. He not only created economic game theory, but also invented a computer. As early as the early 20th century, Semelo, Borel and Von Neuman have begun to study the accurate mathematical expression of the game. Until 1939, Von Noyman encountered an economist Oscar. Oskar Morgenstern and cooperation with its cooperation have enabled game theory to enter economics.
In 1944, he was published with Oscar Morgan Morgan's huge work "Game Theory and Economic Behavior", marking the initial formation of the game theory of modern system. Despite the research on gangs, research can be traced back to the 19th century or earlier. For example, 1838 Ancient Naño is a simple double-oligarchy game; 1883 Betlang and 1925 Achivichi studied two oligarchy production and price monopoly; 2000 years ago, China's famous military home Sun Wu's descendant Sun Wei Using the game theory method to help Tian Joji Mass wins, etc., the germination of the early game, which is characterized by sporadic, fragmentatic research, with great incident, very unsurified. Feng Nomanian and Morganns' concept, the concept and analysis method of the standard, expanded and cooperative game model proposed in the book "Game Theory and Economic Behavior", which laid the theoretical basis of this discipline. The cooperation game has reached the peak period in the 1950s. However, the limitations of the game theory of Nobiaman also exposed, because it is too abstract, making the application scope significantly, in a long time, people have little about game theory, just a few mathematicians Patent, so the influence is limited. It is at this time that the non-cooperative game - "Nash Balance" came into being, it marked the beginning of the new era of game theory! Nash is not a student who presses the class, he often absenters. According to his classmates, they couldn't remember when and when I was over, I will pass the whole ground, but Nash argued that at least I went to the algebraic topology of Stir Rod. Stir Rod is precisely the founder of this discipline, but there is no less than a few lessons, Nash determines that this course does not match his taste. So, it's been away. However, Nashpha is an extraordinary person who is in the hell, and he is widely involved in every branch of the math kingdom, such as topology, algebraic geometry, logic, game theory, etc., deeply. Nash often shows his different confidence and self-contained, full of aggressive academic ambitions. In 1950, Nash is busy with the tight exam, and his game theory research work is forced to break, and he feels that this is a lot of waste. I don't know this temporary "give up", so that the original vague, messy and innocent idea, under the sustained thinking of subconscious, gradually form a clear context, suddenly the inspiration! In October of this year, he sent a feeling of flowing, and his dream pen flowers. One of the most dazzling highlights is the concept of non-cooperative game equalization of "Nash Balance" in the future. Nash's main academic contributions are embodied in two papers in 1950 and 1951 (including a doctoral paper). In 1950, he wrote his research results as a long doctorate papers that "non-cooperative game", published in November 1950, and immediately caused a sensation in the US National Academy of Sciences. It is said that this is a few days after the brothers David Gaier. After a few days of von Noyman, he encountered Gair, telling him that he has already "the smallest and biggest principle" of Feng Noyan. MINIMAX SOLUTION is pushed to the field of non-cooperative game, and the method and equilibrium point of universalization are found. Gail heard very seriously, he finally realized that Nash's idea is more likely to reflect the situation of the realistic situation, and the math priority of rigorous and beautiful mathematics is extremely admired. Gail suggested that he immediately sorted out to prepare, so as not to be in advance of others. Nash's first priest, did not know the sinister of competition, never thought about it. The result is that Gair acts as his "broker", and the Director of the Department of Scrutical Medicine, Director Leffhetz personally submitted the document to the Academy of Science. There are not many articles written by Nash, but it is enough, because it is a boutique in the boutique. This is also worth thinking about. In China, a professor requested a number of articles on the "core publication". Possible Nash is not necessarily qualified according to this standard.
In 1996, Nobelis Economics Morris did not publish any articles when Oxford University Achworth economics, special talents must have special selection methods. Nash started to study on the game theory of pure mathematics when he was on college, and after entering Princeton University in 1948, it is like a fish. 20 years old has become a math of the world. Especially in the field of economic game theory, he made a contribution to the erasing, and is one of the greatest game themeasures after Feng Novan. The concept of the famous Nash equilibrium of Nash is played in the core role in the theory of non-cooperative game. Subsequent researchers' contribution to game theory is based on this concept. Due to the proposal and continuous improvement of Nash equilibrium, it has laid a solid theoretical basis for the game theory in the field of economics, management, sociology, political science, military science.
Two difficult situation in prisoners
Large theory
To understand Nash's contribution, we must first know what is a non-cooperative game problem. Now almost all game theory, there will be examples of "two difficult situation in prisoners", and the examples in each book are different.
After all, game theory is mathematics, and more exactly is a branch of operation of operation. It is not a matter of math language, and the foreign party seems to be just a lot of mathematical formulas. Fortunately, the game is concerned about the daily economic life, so you can't eat fireworks. In fact, this theory is the term borrowed from the competition, charming and decision-making issues, and actually have important practical significance. Master Game Theory looks like a chess bureau, often in the game. So, get started from the mortal little things in our daily lives, do an example in our side, and it is not boring. One day, a rich man was killed at home, the property was stolen. In the detection process of the case, the police arrested two criminal suspects, Skalfish and Nahis, and founded the property lost from their accommodation. However, they denied people who have killed people, arguing that the rich people were killed first, and then just took the sheep and steal some things. So the police will isolate the two, and close the interrogation in different rooms. Local prosecutors talk to everyone separately. The prosecutor said, "Because your stealing crime has conclusive evidence, you can judge you a year. However, I can make a transaction with you. If you frankly kill the crime, I only sentenced you for three months. Incident, but your colleague is to be sentenced to ten years. If you refuse to report, but you will be sentenced to ten years, he only sentenced three months of imprisonment. But if you are both Frankly, then, you have to be sentenced to 5 years. "What should Skalfi and Name? They are facing two difficulties - frank or reliable. Obviously the best strategy is that both parties have represented, and the result is that everyone is only sentenced for one year. However, because the two are in isolation, it cannot be supplied. Therefore, in accordance with Adam Smith, everyone is starting from the purpose of interest, and they choose the frank explanation is the best strategy. Because the context can be expected to get a short imprisonment - 3 months, but the premise is that the accomplices, it is obviously more than 10 years better than yourself. This strategy is a strategy of harmfulness. Not only that, but also more benefits. If the other party frankly and herself, he had to take a 10-year fastener. Too bad! Therefore, in this case, you should choose a frank explanation, even if the two are frank, only more than five years, it is better than being sentenced to 10 years. Therefore, the reasonable choice of the two is frank, and the strategy (reply) and ending (sentenced to 1 year) will not appear. This two people choose a confession strategy and therefore sentenced to 5 years of ending is called "Nash equilibrium", also known as uncomfortable balance. Because each party does not have "seek" (string) when selecting a policy, they just choose the most favorable strategy for themselves, regardless of social welfare or any other opponent's interests. That is, this strategy is composed of the best policy combination of all bodies (also known as the parties, participants). No one will take the initiative to change their strategy to make yourself greater. "The two difficulties of prisoners" have extensive and profound meaning. Personal rationality and collective rational conflicts, the final ending caused by all people pursue interest behaviors is a "Nash Balance", which is also unfavorable to everyone. Both of them first thought of themselves in confession and reputation strategy, so they would inevitably serve the length of death. The results of the shortest time imprisonment can only be obtained when they first think about each other, or in each other (string). "Nash Balance" first challenged the principle of Adam Smith. According to Smith, in the market economy, everyone has started from the purpose of interest, and the final society reaches the effect of interest. Let us relive the famous sayings in this economics in "Guo Fei": "By pursuing (individual) own interests, he often promotes social interests more effectively than it actually wants.
"From the" Nash Balance ", we will introduce a paradox of the principle of" invisible hand ": From the purpose of the interest, the result is unfavorable, which is unfavorable. It is not good. The fate of two prisoners is this. From this meaning Believe, the paradox proposed by Nash Balance actually shakes the cornerstone of Western economics. Therefore, from "Nash Balance", we can also realize a truth: cooperation is a favorable "self-contained strategy". But it must meet The following golden rhythm: According to you willing to come to others in the way others, but only they also act in the same way. That is, the Chinese said "I don't want to do not to people". But the premise is that people do not It is not to apply to me. Secondly, "Nash Balance" is a non-cooperative game equilibrium, which is common than cooperation in reality. So "Nash Balance" is von Noyman and Moististism The major development of cooperation game theory can even be said to be a revolution. From "Nash Balance", we can understand the economic, social, political, national defense, management and daily lives of the Siko. We will Examples of many examples similar to "two difficulties in prisoners" are exemplified. Such as price wars, military competitions, pollution, etc. The general game issues are constituted by three elements: That is, the Chinese people (Players), Participants, strategies, etc. Collection, Strategies collection and the choice of each pair of bians and win (payoffs). The so-called winning means that if a specific policy relationship is selected, each The utility of people. All game issues will encounter these three elements.
Price war betting:
Now we often encounter a variety of home appliances, color TV wars, refrigerator wars, air conditioning wars, microwave war ... The beneficiaries of these wars are the first to consumers. Whenever I see a price war of home appliances, the people will "not steal music." Here, we can explain the outcome of the manufacturer's price war is also a "Nash Balance", and the result of the price war is no money to earn. Because the profits of the game are just zero. The result of competition is stable, ie a "Nash Balance". This result may be advantageous to consumers, but is disastrous to manufacturers. Therefore, the price war means suicide for the manufacturer. From this case we can lead two questions, one is the result of competition price or "Nash equilibrium" may result in an efficient zero profit ending. Second, if you don't take price war, what is the result of Vivalry Game? Every business will consider adopting a normal price strategy or take high price strategy to form monopoly prices, and try to get monopoly profits. If the monopoly can be formed, the common profit between the game is the largest. This situation is what monopoly operations are often raised. Another extreme case is that the manufacturer uses normal prices, and both parties can get profits. From this point, we have led a basic standard: "Building your own strategy is based on the assumption of opponents will be based on its best interest." In fact, the balance of complete competition is "Nash Balance" or "non-cooperative game equilibrium". In this state, each vendor or consumer is decisive in accordance with all the prices of all others. In this balance, each company must maximize profits, consumers should maximize utility, resulting in zero profit, that is, the price is equal to marginal cost. In the case of complete competition, non-cooperative behavior leads to the economic efficiency of society expectations. If the manufacturer takes cooperation action and decides to turn to monopoly prices, the economic efficiency of society will be destroyed. This is why the WTO and governments should strengthen the meaning of anti-monopoly.
Pollution game:
If there is pollution in the market economy, the government does not control the environment. In order to pursue the maximum profit, it would never take the initiative to increase environmental equipment investment in the expense of the environment. According to the principle of visible hands, all companies will start from the purpose of self-contained, and adopt a strategy regardless of the environment, thereby enters the "Nash equilibrium" state. If a company starts from the purpose of interest, investment management pollution, while other companies still don't care about environmental pollution, then the production cost of this company will increase, the price is to improve, its products are not competitive, and even enterprises must be bankrupt. This is an illustration of a failure of "valid complete competition mechanism that is invisible." This is the case that the blind development of China township enterprises caused serious pollution in the mid-1990s. Only when the government strengthens pollution control, companies will take low pollution strategy portfolio. Enterprises In this case, the same profits are obtained with high pollution, but the environment will be better. Trade Freedom and Barriers:
This problem is especially important for China who has just joined WTO. Any country is facing two difficulties in maintaining trade freedom and implementing trade protectionism in international trade. Trade freedom and barrier issues are also a "Nash Balance". This balance is the strategy of the two parties to adopt a non-cooperative game. As a result, the two sides have been damaged by trade. X King tries to carry out imported trade restrictions on Y country, such as improving tariffs, then Y country will definitely counterattack, and improving tariffs, no one has not yet got up. Conversely, such as X and Y can reach a partnership, that is, from the principle of mutual benefit, both parties reduce tariff restrictions, and everyone has achieved the most benefits from trade freedom, and the total benefits of global trade have also increased. (Sun Jian)
