We can use the following game matrix to represent this game:
In this game, "attack" is Sima Yi's "dominant strategy". There are two Nash equilibria in this game, namely: (Sima Yi "attacks" and Zhuge Liang "defends the city"); Sima Yi "attacked the city" and Zhuge Liang "abandoned the city". But Sima Yi didn't know what he and the other party had paid under different action strategies, but Zhuge Liang did. Their understanding of the game structure is asymmetric: Zhuge Liang has more knowledge than Sima Yi. Of course, this asymmetry of knowledge is entirely "made" by Zhuge Liang.
How did Sima Yi reason? Sima Yi's reasoning is "induction". Sima Yi said: "Liang Yisheng is cautious and never takes risks. If the gate is opened today, there will be an ambush. If our soldiers move forward, they will fall into the plan. " In Sima Yi's view, Zhuge Liang was cautious all his life. Since Zhuge Liang has never taken risks in his life, he certainly won't take them this time. Zhuge Liang has an ambush. Sima Yi made a choice between "encirclement" and "retreat".
Here, Sima Yi made a wrong strategic choice. Nevertheless, it cannot be said that Sima Yi is irrational. Sima Yi made a wrong strategic choice because of incomplete information. In the game between Kong Ming and Sima Yi, Kong Ming created the illusion of an empty city in order to make Sima Yi feel that the "besieged city" was likely to fail. In terms of probability theory, Zhuge Liang's approach is to increase the subjective probability of Sima Yi's attack failure. At this time, in Sima Yi's view, "siege" is more likely to fail, and the expected utility of "retreat" is greater than "siege". That is, Sima Yi believes that the expected utility of "siege" is lower than "retreat". Only in this way can Zhuge Liang make Sima Yi withdraw.
I know this is a prisoner's dilemma.
That is, AB, two prisoners were arrested and put in two different cells.
If both of them don't confess, each person will only be sentenced to three years, and if both of them confess, each person will be sentenced to five years.
If one confesses and one does not confess, the one who confesses will be sentenced to one year, and the one who does not confess will be sentenced to ten years.
The best result, of course, is that neither of them will confess, but because of information asymmetry.
For A, if B doesn't confess, it's better for him to confess, and if B confesses, it's better for him to confess.
Then confession is his dominant strategy, and he will choose confession.
Similarly, analysis B will also choose to confess.
The end result is that both of them are recruiting people and in order to achieve the best choice of not confessing.
This is the prisoner's dilemma
General economics books will talk about it.
The end of prisoners
"Prisoner's Dilemma" is one of the most classic examples in game theory. Its model is like this:
Two suspects (A and B) were arrested by the police after committing the crime and were interrogated in isolation; The policy of the police is "be lenient in confession and strict in resistance". If both of them confess, they will be sentenced to eight years each; One person confesses, the other person does not confess, and is released and sentenced to 10 year; If you don't confess, the evidence is insufficient 1 year.
In this example, the participants in the game are two suspects, A and B. Each of them has two strategies, namely confession and non-confession, and the number of years in prison is their reward. The four possible situations: A and B are frank or not, A is frank and B is not frank, or B is frank and A is not frank, all of which are the results of the game. Both A and B are Nash equilibria of this game. This is because, assuming that A chooses to confess, B had better choose to confess, because B confessed to 8 years and denied to 10 years; Suppose A chooses to deny, and B had better choose to confess, because B will not be sentenced for confessing, but will be sentenced to 1 year for denying. In other words, whether A confesses or denies, B's best choice is to confess. Conversely, similarly, whether B confesses or denies, A's best choice is to confess. As a result, both of them chose to confess and were sentenced to eight years in prison. In this combination (confession, confession), neither A nor B can increase their income through unilateral change actions, so no one has the motivation to dissociate this combination, so this combination is Nash equilibrium.
The prisoner's dilemma reflects the contradiction between individual rationality and collective rationality. If both A and B choose to deny it, they will each be sentenced to 1 year, which is obviously much better than if both of them choose to confess and each will be sentenced to 8 years. Of course, A and B can form an "offensive and defensive alliance" before being caught by the police, but this may not be useful, because it does not constitute a Nash equilibrium, and no one has the enthusiasm to abide by this agreement.
The pirates shared the money.
There is a model of "pirates sharing gold" in economics, which means that five pirates rob 100 gold coins, and they put forward their own plans in the order of drawing lots: first, 1 puts forward the distribution plan, then five people vote, and more than half agree that the plan is passed, otherwise he will be thrown into the sea to feed sharks, and so on.
Assuming that "every pirate is extremely intelligent and rational", then "what kind of distribution scheme can the first pirate propose to maximize his own income?"
The reasoning process is as follows:
Push from the back to the front. If all the robbers from/kloc-0 to 3 feed sharks, only No.4 and No.5 are left, and No.5 will definitely vote against it and let No.4 feed sharks and take all the gold coins. Therefore, No.4 can only rely on supporting No.3 to save his life.
Knowing this, No.3 will put forward the distribution scheme of "100,0,0", and will leave all the gold coins to No.4 and No.5, because he knows that No.4 has got nothing, but he will still vote for it. With his own vote, his scheme will be passed.
However, if No.2 infers the plan of No.3, it will put forward the plan of "98,0, 1, 1", that is, give up No.3 and give No.4 and No.5 a gold coin each. Since the plan is more favorable to No.4 and No.5 than No.3, they support him and don't want him to be out and assigned by No.3 ... So No.2 took 98 gold coins.
Similarly, the scheme of No.2 will be understood by 1, and a scheme of (97,0, 1, 2,0) or (97,0, 1, 0,2) will be proposed, that is, No.2 will be abandoned and No.3 will be given a gold coin. At the same time, because of/kloc, This is undoubtedly the scheme that 1 can get the greatest benefit! The answer is: 1 robber gave robber No.3 1 gold coin, and gave it to robber No.4 or No.5, and he got 97 pieces himself. The allocation scheme can be written as (97,0, 1, 2,0) or (97,0, 1, 0,2).
"Pirate sharing gold" is actually a highly simplified and abstract model, which embodies the idea of the game. In the mode of "pirates sharing money", the key for any distributor to pass his scheme is to consider clearly what the distribution scheme of "challenger" is in advance, so as to get the maximum benefit at the lowest cost, thus attracting the most dissatisfied people in the distribution scheme of "challenger". Senior leaders in enterprises often abandon the second person when they engage in insider control, and get on well with accountants and cashiers, because the little people in the company are easy to be bought off.
1 It seems most likely to feed sharks, but he firmly grasped the first-Mover advantage, which not only eliminated the death threat, but also benefited the most. Isn't this the first-Mover advantage of developed countries in the process of globalization? No.5 looks the safest, has no death threat, and can even take advantage of fishermen, but because it depends on other people's faces, it can only be divided into a small part.
However, if the model arbitrarily changes a hypothetical condition, the final result will be different. The real world is far more complicated than the model.
First of all, in reality, everyone is definitely not "absolutely rational". Returning to the model of "pirates sharing gold", as long as one of No.3, No.4 and No.5 deviates from the assumption of absolute cleverness, pirates 1 may be thrown into the sea no matter how they share it. So 1 should first consider whether the intelligence and rationality of his pirate brothers are reliable, otherwise it will be the first to suffer.
If someone prefers to watch their partner being thrown into the sea to feed sharks. If so, wouldn't 1' s smug scheme be digging its own grave!
So there is a saying that "the heart and abdomen are separated". Because information asymmetry, lies and false promises are of great use, conspiracy will grow like weeds and take advantage of it. If No.2 throws smoke bombs at No.3, No.4 and No.5, it claims that it will definitely add another gold coin to any distribution scheme proposed by 1. So, what will be the result?
Usually in reality, everyone has their own standards of fairness, so they often whisper, "Who moved my cheese?" It can be expected that once the scheme proposed by 1 doesn't conform to its imagination, someone will make a scene ... When everyone makes a scene, can 1 walk out with 97 gold coins unscathed and calm? Most likely, the pirates will demand that the rules be revised and then redistributed. Think of Hitler's Germany before World War II!
And what if you change from a game to a repeated game? For example, let's make it clear that the next time we get 100 gold coins, Pirate II will be divided first ... and then Pirate III ... This is a bit like the presidential election in the United States, and we will take turns to be responsible. To put it bluntly, it is actually a democratic form of stolen goods sharing system.
The most terrible thing is that four other people formed a grand alliance against the number 1 and made a new rule: four people shared the gold coins equally and threw the number 1 into the sea ... This is Ah Q's revolutionary ideal: hold high the banner of egalitarianism and throw the rich into the abyss of death. ...
The system regulates behavior, and reason overcomes ignorance!
Suppose it becomes 10 person 100 gold coin, and more than 50% of the votes are passed, otherwise he will be thrown into the sea to feed sharks, and so on. 50% is the key to the problem, pirates can vote for themselves. So if there are two people left, no matter what scheme is passed, it is 100, 0.
Step up, when there are three people, the third from the bottom knows that if there are two people, then it will unite with the first person and give him a gold coin.
"Take a step forward. Now a more fierce pirate P3 has been added. P 1 knows-P3 knows he knows-if P3's scheme is rejected, the game will only be continued by P 1 and P2, and P 1 won't get a gold coin. So P3 knows that as long as P 1 is given a gold coin, P 1 will agree to his plan (of course, if P 1 is not given a gold coin, P 1 will get nothing anyway, and would rather vote P3 to feed the fish). So P3' s best strategy is: P 1 get 1, P2 gets nothing, P3 gets 99.
The situation at P4 is similar. He only needs two votes. Giving P2 a gold coin will make him vote for this scheme, because P2 will get nothing in the next P3 scheme. P5 used the same reasoning method, except that he had to convince his two companions, so he gave P 1 and P3 who got nothing in P4 plan one gold coin each, and kept 98 for himself.
By analogy, the final best scheme of P 10 is: he gets 96 pieces by himself and gives P2, P4, P6 and P8 a gold coin which is nothing in P9 scheme.
As a result, the final result of "pirate sharing gold" is that P 1, P2, P3, P4, P5, P6, P7, P8, P9, P 1, 0, 1, 0, respectively.
In the "pirate sharing", the key for any distributor to get his plan passed is to consider clearly what the challenger's distribution plan is in advance, so as to get the maximum benefit at the least cost, thus attracting the most dissatisfied people in the challenger's distribution plan.
It's really unbelievable. P 10 seems to be the most likely to feed sharks, but he firmly grasped the first-Mover advantage, which not only eliminated the death threat, but also gained the maximum benefit. P 1 seems to be the safest, without death threat, and can even take advantage of fishermen. However, because it depends on other people's faces, it can't even get a small piece of cake, so it can only help.
theory of game
Game theory is a theory that two or more people use each other's strategies to change their own confrontation strategies in an equal game to achieve the goal of winning. Game theory is a theory to study interactive decision-making. The game can analyze the advantages and disadvantages of yourself and your opponent, so as to establish your own advantages in the game. Therefore, there are many game theories that can help players analyze the situation, so as to adopt corresponding strategies and finally achieve the goal of winning. The types of games are divided into cooperative games, non-cooperative games, complete information games, incomplete information games, static games, dynamic games and so on.
Classification of games
Games are divided into static games and dynamic games. Static game means that in the game, two players choose at the same time or two people don't choose at the same time, but the latter player doesn't know what specific action the former player takes. For both sides, it is easy to form chaotic behavior reorganization. Because of strict and meticulous rules, anyone will lose after many times of equilibrium because of time problems, financial problems, psychological problems, etc. Most of them participate in static games and dynamic games. Dynamic game means that in the game, two participants have the order of action, and the latter actor can observe the action chosen by the former actor. In the dynamic game, the participant who takes the first action is called the decision maker, which is identified according to the selection criteria of the initial sample, and then the behavior characteristics of the sample are classified to determine the background information characteristics of the decision maker every time. It is solved by the behavior probability constant that people are very concerned about, which obviously shows the size and probability distribution of the advantage. The dynamic-static game itself is a country, there will be equilibrium, and the final result of the game is that the country is rational.
According to whether participants can form a binding collective action agreement, games can be divided into cooperative games and non-cooperative games. Nash and other game theory experts study more non-cooperative games.
The so-called cooperative game means that participants reach an agreement or alliance with other participants from their own interests, and the result is beneficial to both sides; Non-cooperative game means that participants can't reach a binding agreement when choosing actions. The economic activities of people's division of labor and exchange are cooperative games, while the prisoner's dilemma and the tragedy of public resources are non-cooperative games.
Games are divided into static games and dynamic games.
Static game means that the participants take actions at the same time, or even if the actions of the participants are orderly, the people who act later don't know what actions the people who act first have taken.
Dynamic game means that the actions of participants are orderly, and the latter actor can know the actions of the first actor.
Judging from the degree of knowledge possession, games can be divided into complete information games and incomplete information games. Information is an important content of game theory. Complete information game means that participants have a "complete understanding" of the strategic space and payment of all participants under the strategy combination, otherwise it is an incomplete information game. Strictly speaking, the game of complete information refers to the strategic space of both sides of the game and the payment under the combination of strategies, and it is a game of "public knowledge" of all participants in the game. For incomplete information games, what participants do is to maximize their expected payment or expected utility.
It is a game that gives priority to predicting the game before winning. -"Game Culture Feast"
The language of game philosophy can also reflect the following four game classifications:
Complete information static game, complete information dynamic game, incomplete information static game, incomplete information dynamic game.
Among them, strategic game should belong to complete information static game, while complete information dynamic game includes expansion game and repeated game. Static game with incomplete information is a reinterpretation of mixed strategy based on Bayesian equilibrium theory, while dynamic game with incomplete information is a signal game with perfect Bayesian equilibrium as its core concept.
Be flexible
Shimi hung the book in the corner. Shi Mi of Sui Dynasty was sent to the court of Yang Di as a bodyguard when she was a teenager. He is naturally flexible. When he was on duty, he looked around and was discovered by Emperor Yang Di. He thought the boy was dishonest, so he was excused from his job. Shi Biao is not depressed. After returning home, he studied hard and determined to be a learned man. Once, Shimi rode an ox to meet his friends. On the way, he hung Hanshu on the loudspeaker and took the time to study. This incident was passed down as a much-told story.
Dong Zhongshu didn't peek into the garden for three years. Dong Zhongshu devoted himself to research and worked tirelessly. Although there is a garden behind the study, he concentrated on reading and studying, and did not go into the garden to enjoy it for three years. Dong Zhongshu devoted himself to research and became a famous thinker in the Western Han Dynasty.
Youning sat down. Guan Ning and Hua Xin were old friends in the Han Dynasty. One day, two people were reading at the same table, and some dignitaries passed by by by car. Guan Ning was undisturbed, studying as usual, and Hua Xin went out to see it, envious. Guan Ning saw that Hua Xin and his friends were not really like-minded, so he cut the table and sat down. Guan Ning finally made a career!
Kuang Heng stole the light. In the Western Han Dynasty, there was a particularly learned man named Kuang Heng. When Kuang Heng was a child, his family was poor. In order to study, he chiseled through the wall of his neighbor's illiterate home and stole a candle to read, which finally touched his neighbor's illiteracy. With everyone's help, Kuang Heng Jr. learned something. During the Han and Yuan Dynasties, he served as a doctor, and was recommended by Shi Gao, a general of Fu and Che Qi, and moved to be a doctor.
Che Yin capsule fireflies read at night. Che Yin was born in Nanping (now Hubei Public Security Bureau) in Jin Dynasty. He comes from a poor family, but he studies very hard. "The poor don't often produce oil, but Xia Yue practices holding dozens of fireflies to shoot books, day and night." The story of Zhao reading has been circulated in history as a beautiful conversation, inspiring later scholars.
Chen Ping endured humiliation and studied hard. Chen Ping was famous in the Western Han Dynasty. When he was young, his family was poor and he lived alone with his brother. In order to maintain his father's orders, he was brilliant, childless and studied behind closed doors, but he could not get his sister-in-law's permission. In order to eliminate the contradiction between brother and sister, he endured humiliation again and again. With the intensification of his sister-in-law, he finally ran away from home and wanted to travel around the world. After being rescued by his brother, he no longer cared about the past. Finally, an old man came here to teach for free. After he finished his studies, he assisted Liu Bang and achieved great success.
Lu Yu abandoned Buddhism and joined the literature. Lu Yu, a famous scholar in the Tang Dynasty, was an orphan since he was a child and was raised by a Zen master. Although Lu Yu is in a temple, he doesn't want to read Buddhist scriptures all day, but he likes reading poetry books. Lu Yu insisted on going down the mountain to study, which was opposed by the Zen master. In order to give Lu Yu a difficult problem, the Zen master better educated him and made him learn to make tea. In the process of learning tea art, Lu Yu met a kind old woman. She not only learned complicated tea-making skills, but also learned a lot about reading and being a man. When Lu Yu finally brought the Zen master a steaming cup of Kuding tea, the Zen master finally agreed to his request and went down the mountain to study. Later, Lu Yu wrote the widely circulated Tea Classic, which promoted the tea culture of the motherland!
Juvenile Bao Zheng learns to solve crimes. Bao Qingtian and Bao Zheng, smart and studious since childhood, especially like to solve crimes by reasoning. His father was in close contact with the magistrate, and Bao Zheng learned a lot about solving crimes since childhood. Especially in the case of burning a temple to kill a monk, Bao Zheng peeled silk according to the clues on the spot, screened out the suspects, and pretended to be the king of Yan, trying to clarify the truth and help the magistrate catch the murderer and kill the people. He worked hard to learn the knowledge of law and punishment, which laid a deep knowledge foundation for solving crimes and vindicating the people like a god when he grew up.
Wan Sitong studied hard behind closed doors. Wan Sitong, a famous scholar and historian in the early Qing Dynasty, participated in the compilation of Twenty-four History, an important historical book of China. But Wan Sitong was also a naughty boy when he was young. Wan Sitong was criticized by the guests because he was naughty and lost face in front of them. In a rage, Wan Sitong overturned the guest's desk and was put into the library by his father. Wan Sitong went from being angry and disgusted with reading to thinking behind closed doors. Inspired by the Book of Tea, he began to study hard. In a blink of an eye, more than a year has passed. Wan Sitong has read many books in the library. His father forgave his son, and Wan Sitong understood his father's kindness. After long-term efforts, Wan Sitong finally became a well-known scholar who was familiar with history books, and participated in the compilation of Ming History in Twenty-four History.
Tang Bohu devoted himself to painting. Tang Bohu was a famous painter and writer in Ming Dynasty. When he was young, he showed superhuman talent in painting. As a disciple of the great painter Shen Zhou, Tang Bohu naturally studied harder, quickly mastered the painting skills, and was highly praised by Shen Zhou. Unexpectedly, due to Shen Zhou's praise, Tang Bohu, who has always been modest, gradually became complacent. Shen Zhou see in the eye, in mind. During a meal, Shen Zhou asked Tang Bohu to open the window. Tang Bohu found that his window was actually a painting by Teacher Shen Zhou. Tang Bohu felt very ashamed and devoted himself to painting.
Qu Yuan studied hard in the cave. When Qu Yuan was a child, he hid in a cave and secretly read the Book of Songs, regardless of the opposition of his elders. For three years, he familiarized himself with 305 Poems of the Book of Songs, and gained rich nutrition from these folk songs, eventually becoming a great poet.
Fan Zhongyan broke horseshoe crabs and rowed porridge. Fan Zhongyan grew up in a poor family. In order to study, he scrimped and saved. Finally, his thirst for knowledge moved the temple elders, who sent him to Du Nan College to study. Fan Zhongyan still insists on simple living habits and does not accept gifts from rich children to sharpen his will. After studying hard, he finally became a great writer.
Sima guang's police pillow is inspirational. Sima Guang is a child who loves to play and sleep, so he has been punished by his husband and laughed at by his peers. Under his inculcation, he is determined to get rid of the bad habit of sleeping. In order to get up early, he drank a full stomach of water before going to bed, but he didn't wake up in the morning, but peed in bed. So smart Sima Guang made a police pillow out of logs. As soon as I turn over in the morning, my head slides on the bed board.
Xuanzang studied Buddhism hard. Xuanzang was a monk in the Tang Dynasty. In order to obtain the original Buddhist scriptures, Xuanzang left Chang 'an in August of the third year of Zhenguan, trudged to Wan Li and finally arrived in India. It lasted 17 years, and he wrote The Tale of the Western Regions of Datang, which made great contributions to Buddhism, human progress and world civilization.
Yue Fei studied art. Yue Fei, a national hero, was born in troubled times and grew up in a poor family. With the support of his neighbors, he learned martial arts from Zhou Tong, a famous Shaanxi teacher. During this period, he witnessed the broken mountains and rivers, displaced people, sprouted the ambition of learning to serve the country and overcame complacency. Under the careful instruction of the famous teacher Zhou Tong, he eventually became a Yue family thief, and led Wang Gui, Tang Xian and other partners to join the patriotic torrent of resisting gold and saving the country.
Li Guizhen learned to draw tigers. Li Guizhen, a famous tiger painter in the Five Dynasties, liked painting since he was a child, especially tigers. However, because he has never seen a real tiger, he always paints it as a sick cat. So he decided to go deep into the forest to see the real tiger. With the help of Uncle Orion, he finally saw the real tiger. Through a lot of sketching and copying, his tiger painting skills have advanced by leaps and bounds, and the tigers in his works are vivid and confusing. Since then, he has traveled many famous mountains and rivers for most of his life, met many birds and animals, and finally became a generation of painting masters.
reform and opening-up
China has made great achievements in reform and opening up. Through this great reform and opening up, three great turning points have been realized: the first great turning point is the transformation from a highly centralized planned economic system to a socialist market economic system full of vitality and vitality; The second great turning point is from a closed and semi-closed society to an all-round open society; The third great turning point is the social transformation of people's life from food and clothing to a basic well-off society. Without reform and opening up, it is impossible to realize the three major changes. Therefore, the reform and opening up proposed by the Third Plenary Session of the Eleventh Central Committee is a key choice for the fate of contemporary China.
Reform and opening up is the only way to develop Socialism with Chinese characteristics and realize the great rejuvenation of the Chinese nation. It is pointed out that only reform and opening up can develop China, socialism and Marxism. I said these two paragraphs, highly summarized why the reform, why the reform is the only way, why is the destiny choice of contemporary China. Without reform and opening up, it is impossible to develop China, socialism and Marxism. Therefore, we should deeply understand this highly theoretical generalization put forward by the Third Plenary Session of the Eleventh Central Committee.
Look at the problem from a developmental perspective
Innovative ideas