The movie has been rated high at around 9 on Douban, and is also really good, having seen it several times. John Nash's storied life story, his theory of Nash equilibrium, and his final end of life are all, of course, inevitable subjects of extended study after watching the movie.
In 1950, at the age of 22, Nash graduated with a 27-page doctoral dissertation on the topic of non-cooperative games (Non-cooperative Games) in which he proposed an important concept, which was later known as " Nash equilibrium " game theory (Game Theory). Subsequently, Nash stayed at Princeton University to teach, but is the career in the sky, the 30-year-old Nash suffered from severe schizophrenia, and two consecutive admitted to a mental hospital, the end of his academic career.In the late 80's, Nash miraculously came out of severe schizophrenia, and in 1994 won the Nobel Prize in Economics, he only returned to the familiar academic stage.
On May 23, 2015, John Nash died at the age of 86 in a car accident with his wife in New Jersey, USA.
Nash's most important legacy to the world is his "Nash Equilibrium" (Nash Equilibrium) theory. So what is the Nash Equilibrium theory, and how is it applied in real life?
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Case 1: "Prisoner's Dilemma"
This is the most classic example: two suspects (A and ?B) were caught by the police after committing a crime, and were interrogated in isolation; the police's policy is "leniency in confessing and strictness in resisting"; if both of them confessed, each would be sentenced to 8 years; if they confessed, each would be sentenced to 8 years; if they confessed, each would be sentenced to 8 years. If one confesses and the other doesn't, the one who confesses is released and the one who doesn't is sentenced to 10 years; if neither confesses, they are sentenced to one year each for lack of evidence.
In this example, the participants of the game are the suspects ?A and ?B, each of them has two strategies, namely, confess and do not confess, the possible four situations: A and ?B are confessed or are not confessed, A confesses ?B does not confess or ?B confesses A does not confess, is the result of the game. Obviously the best strategy is for both parties to confess, with the result that everyone gets only ?1 year. However, since the two men are in isolation and unable to conspire, their choice to confess is the best strategy. Because confession can expect the best solution: release, but, provided that the accomplice denies, obviously much better than their own denial of 10 years in prison; and if the other confessed and he denied, then he would have to sit in jail for ?10 years, too unprofitable! Even if both of them confessed at the same time, at most they would only be sentenced to 8 years, which is better than being sentenced to 10 years. It's better than being sentenced to 10 years.
The result? The strategy of both men choosing to confess and the resulting sentence of ?8 years? The outcome is called a "Nash equilibrium", or a non-cooperative equilibrium, because each party chooses only the strategy that is most advantageous to him or her, without regard to the collective interest or the interests of any other adversary.
According to Adam Smith's theory, in a market economy, everyone starts from a self-interested purpose, and eventually the whole society achieves an altruistic effect. The "Nash equilibrium" leads to a paradox: from the self-interested purpose? The Nash equilibrium leads to a paradox: starting from self-interested ends, the result is neither self-interested nor self-interested, as is the fate of the two prisoners. In this sense, the paradox of "Nash equilibrium" actually shakes the cornerstone of Western economics.
From the "Nash equilibrium", we can also realize a truth: cooperation is a favorable "profit?
What we also learn from Nash's Equilibrium is that cooperation is a favorable "self-interest strategy", but it must conform to the Golden Rule: do unto others as you would have them do unto you, but only if they do unto you in the same way.
Case 2: price war Take my translation industry as an example, suppose the two translation companies participating in the game are A and B, the market share of the two was balanced at one time, but B in the cost and price is more advantageous, so his market share is gradually expanding, so what should A do, is it to maintain or reduce prices?
From?A's point of view?
From?A's point of view? better than maintenance, price cuts can at least guarantee better than ?B; from ?B point of view, the effect is the same, price cuts are equally better than maintenance. In this round of the game, both A and B use price reduction as a strategy, so each has a loss? , and the whole also has a loss, and the overall gain is the worst. This is the Nash equilibrium that ultimately emerges from this game, where each part seeks to maximize its benefit, while the overall benefit is not optimal, or even the worst.
Case 3: Coalition
In real life, there is not only "non-cooperation", but cooperation is a phenomenon that can be found everywhere, such as small-scale coalition organizations in some industries.
If it is not a single game, but multiple and long-term game, people have the possibility of cooperation, the Prisoner's Dilemma is possible to break? , cooperation would be possible. Successive cooperation has the potential to be an equilibrium solution to the repeated Prisoner's Dilemma. Game theory research shows that in order for cooperation to become an equilibrium solution to repeated games, one side of the game (preferably the stronger side, let's call it an ally) must take the initiative to show the goodwill of cooperation to the opponents through credible commitment, try to make this goodwill clear, and form a reputation in the opponents of the game, and maintain this reputation attentively.
So, for an ally to call the shots and reach a cooperation that maximizes the collective good, it requires the utmost goodwill and real commitment. At the same time, if it is a long-term cooperation, other allies from the long-term interests of their own benefit to them to abide by the covenant, relying on the rules of the organization to constraints can not be relied upon, as long as there is a party to the backroom operation, increase production or reduce prices, that will inevitably lead to the other partners to make the corresponding action, resulting in the failure of the alliance.
Case 4: Freedom of trade and barriers ?
Any country in international trade is faced with the dilemma of trade freedom and trade protection. The problem of trade freedom and barriers is also a "Nash equilibrium" problem, if the two sides of trade to take the strategy of non-cooperative game, country A tries to import trade restrictions on country B, such as raising tariffs? If country A tries to impose import trade restrictions on country B, such as raising tariffs, country B will inevitably counterattack by raising tariffs as well, and no one will benefit as a result. In the language of game theory, the current Sino-US trade, (fight, fight) is the Nash equilibrium of this game, and the ultimate direction of this game. However, this result is clearly not the optimal choice, both sides choose "not to fight", the benefits will be significantly higher, which also constitutes the U.S. trade war "Prisoner's Dilemma".
China and the United States for their own interests and compete with each other and strive to achieve the equilibrium of the game, the equilibrium point is very likely not the optimal interest point of each country, but it must be the two countries in the trade conflict can be achieved in stages of the optimal point of the negotiation process, a country must be in full consideration of the interests of the other country on the basis of the scope of possibilities to maximize the benefits.
Of course, although game theory is crucial to the interpretation of behavior, game theory alone cannot thoroughly explain all the motivations for behavior, and cannot help explain all aspects of complex national behavioral choices. International trade is a comprehensive game of political economy between states.
"Trump looks crazy because acquiring a reputation for being wildly irrational is a particularly important strategy in repeated games. If Trump has such a reputation and he has already used this insanity to defeat many competitors in the past, it is plausible and feasible to convey the threat of trade conflict to China by projecting an impression of irrationality and belligerence, in which case his consistently insane demeanor also reminds potential competitors (China) that obeying me may be better for you. Trump's irrational game cannot simply be measured in absolute terms of economics' immediate profit and loss; he is engaged in a trade war. When the market competition escalates to "war", means that the economic problem has been transformed into a political problem, so to use political thinking to think about the logic of its behavior, he to "hurt the enemy a thousand self-loss of eight hundred" way to seek to re-adjust the power of both sides, trying to change the pattern of interests of China and the United States. He is trying to re-align the power of both sides by "hurting the enemy a thousand times and damaging eight hundred times" in an attempt to change the pattern of interests between China and the United States."
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Case 5? Good and Bad Nash Equilibria
The concept of Nash equilibrium is an analytical tool that does not contain value judgments. So there are both good and bad Nash equilibria.
Take China's people's commune period as an example, the government's goal is that peasants work hard and everyone has food to eat, but the result is that in a people's commune, peasants instead have no incentive to produce, which eventually leads to poverty. The process of the game naturally formed a Nash equilibrium - poverty. And after the reform and opening up, the government changed the policy, the farmers can have their own land, the production enthusiasm increased, the living standard also increased accordingly, which formed a new Nash equilibrium: production and living standard increased.
Therefore, the former formed a bad Nash equilibrium, the latter formed a good Nash equilibrium, from bad Nash equilibrium to good Nash equilibrium requires a series of institutional adjustments, the premise is that the two sides of the game respect each other's free will and choice.
Cooperation is based on voluntariness, and voluntariness is based on respecting everyone's heart, respecting everyone's interests, and establishing a set of rules of the game or policy in this way. "If property rights are clearly defined and the rule of law is perfect, everyone can see the long-term game, so there is a proverb in the West that honesty is the best business policy," said economist Zhang Weiying.
Nash has passed away, but the Nash equilibrium theory he left behind has helped us analyze many phenomena in real life. Beautiful mind, beautiful theory, although this can not simply achieve a beautiful world, but perhaps can bring some more beautiful equilibrium and cooperation.