Warm Notes｜Game Theory of Wanwei Steel Elite Daily Class

Game theory is not "Thirty-six Strategies"

"Thirty-Six Strategies" is to a large extent a book of conspiracy. There are three problems with tricks: first, tricks carry huge risks. To succeed, you not only have to tightly block information, but also assume that your opponent is stupid; second, tricks cannot be used for a long time; there is another bigger problem. The problem is that they are all "zero-sum" games. In the real world, apart from war, there are few life-or-death situations like this.

If there are too many schemes, there will not be enough fools. Game theory studies games between "rational people". Game theory assumes that people are rational, which is reflected in three requirements: first, you must know what you want and have a clear order of what you want; second, your actions must be within certain rules. First, strive to get what you want; third, you know your opponent thinks so too, and your opponent also knows the rules. Sometimes people are hijacked by certain emotions. This situation is not the research content of game theory.

Game theory studies how a group of smart people choose the strategy that is most beneficial to them under certain rules. Traditionally, when it comes to games, we have studied how to choose a better strategy, but what I want to tell you is that if all parties are rational enough, then it is not the strategy that determines the situation, but the rules.

Game theory requires you to assume that what you can think of can be thought of by others, so what should you do? Any action you take must consider your opponent's reaction. There is no conspiracy here, it's all conspiracy.

Like other knowledges, I think a major benefit of game theory is that it can cultivate sentiment. Your temperament will be improved and you will be a more awake person. When the general onlookers sigh and sigh at the major events around them, you can observe the game pattern. Even if you don't have the chance to intervene, at least you know where the joints are, and at least you won't have unrealistic illusions. Game theory can also help you be more proactive. The spirit of game theory is never to sit on the sidelines, but to be a player! Dare to take proactive action to get what you want.

How to deal with "irrational" people

The premise of game theory is that both parties are rational. If one party is irrational, then there are two situations. If the other party does not know that he is irrational, then the irrational party will eventually suffer heavy losses and may die, but the rational party will also suffer losses. And if the rational party knows that the other party is irrational, then in order to avoid being harmed, he will choose to give in. Therefore, it is good for you to act irrational and let the other person know that you are irrational. Rational people may pretend to be irrational. This is why some people cry in public places as if they don't care.

War of Crows

Three basic concepts of game theory: "Pareto optimality", "overwhelming strategy" and "Nash equilibrium".

Player is called a player in a game, a player in a sports competition, and a participant in game theory. In fact, they all mean the same thing. Game Theory (Game Theory) talks about games. If you have a little spirit of participating in the game, you have the right to take actions that are most beneficial to you within the rules. You are proactive and you will treat your opponents equally - you are not a muddle-headed person who does things based on other people's settings all day long. People who don’t have the illusion that the whole world revolves around them. Game theory requires us to consider the other party every time we make a judgment—not considering how to treat the other party well, but considering what the other party will do, and then what you will do.

Pareto improvement means that this improvement can make at least one person's situation better without harming anyone's interests. If a situation is so good that there is no room for Pareto improvement, the situation is called "Pareto optimal".

"Dominant Strategy", this strategy overwhelms all other strategies. No matter what your opponent does, this strategy is the best for you.

Nash equilibrium means a situation in which no party is willing to unilaterally change its strategy in this strategy combination.

Mathematics is only an auxiliary tool for game theory, and the ideas of game theory are not reflected in mathematics. When studying game theory, it is better to have ideas but no mathematics than to have mathematics but no ideas.

Ideal young people like Pareto optimality, while rational young people look for Nash equilibrium.

Peace is the most important

Game theory studies are generally "non-cooperative games". The participants are not thinking about one place and working together to achieve great things. But what everyone thinks about is how to win. The starting point is non-cooperation, but the result is cooperation.

This is also the glorious tradition of economics. Starting from Adam Smith, people have known that even if everyone is selfish and works for their own interests, the whole society can achieve a high level of cooperation. Cooperation in game theory research is not about engaging in "ideological and moral education" to persuade people to do good, nor is it about letting a powerful force control people, but about seeking a mechanism that allows people to cooperate voluntarily. Good cooperation must be a Nash equilibrium.

If there are multiple Nash equilibria in a game, how should people make choices? The focal point is the most conspicuous one among many possible Nash equilibria, and people will automatically cooperate at this point. The role of focus is coordination. Some focus points are designed, and some focus points are historical path dependent. With focus thinking, we should take the initiative to propose a focus point when there is no focus point to promote cooperation. You can take advantage of it first. The greatest value of a focal point is its existence itself. Traditional culture and social customs actually serve as a focal point for coordination and cooperation. Please note that a key prerequisite for focus to be so useful is that there is no fundamental conflict of interest between the parties. We all want to make this collaboration happen, all we need to figure out is where. People who want to collaborate need focus. Any excuse can be a focus as long as you can find it. In fact, even if there is a certain conflict of interest, as long as the desire for cooperation outweighs the conflict, we can still use focus.

Don’t condone, but be tolerant

The most intuitive way to prevent betrayal is to turn a single game into a repeated game. Why are the meals at tourist attractions of inferior quality and high prices? Because it's a single game. If you don't come next time, he'll cheat as much as he can. And a chain store like McDonald's, even if it opens in a tourist attraction, will ensure quality because it is responsible for the reputation of the entire brand. Many businesses say we want to do this for a hundred years, and some stores engage in membership systems. These are repeated games. Repeated games work because defectors are punished. The most direct punishment is that I will betray you next time, so that you will not get the benefits of cooperation.

For a group of people to cooperate, they must meet at least one of the following two conditions: first, cooperation is good for themselves and people already want to cooperate; second, non-cooperation will be punished. Benefits and penalties are just hard conditions. Without a basic level of internal trust, cooperation is fragile.

In the 1980s, Robert Axelrod, a political scientist at the University of Michigan, organized a game competition. The content of the game is the prisoner's dilemma. You have to decide under what circumstances to cooperate and under what circumstances to betray. Scholars from various fields submitted different strategy algorithms, and everyone took turns playing the game to see who would gain more in the end. Unexpectedly, the winner was a very simple strategy, called "Tit for Tat" in English, generally translated as "Tit for Tat". This strategy is: (1) No matter who I play with, I will choose to cooperate in the first round; (2) After the first round, I will copy what my opponent did in the previous round. If you cooperated with me in the last round, I will cooperate with you in the next round. If you betray me, I will betray you in the next round.

Tit for tat, simple, crude and effective. But what you may not know is that tit-for-tat is actually a fragile strategy. This strategy is very error-unfriendly. Computer simulations are always accurate, but real-person games can make mistakes. In the real world, tit for tat is not the best strategy, it is not forgiving enough. Game theory experts propose an improved version of tit-for-tat: if the other party betrays me once, I will continue to cooperate; only if the other party betrays me twice in a row, I will retaliate. Research shows that this approach works better than tit-for-tat in games where things can go wrong.

In real life, others may make unintentional mistakes, and you may misjudge. The Chinese have a saying, "Take a step back and the sky will be brighter." Strong men usually don't like this saying, but in fact it makes sense - tolerance can avoid vulnerability. However, please note that the key word in this sentence is "one step". Taking one step back is tolerance, taking two steps back is connivance.

There is a saying that "Keep your friends close and your enemies closer! (Keep your friends close and your enemies closer)" After the Cuban Missile Crisis, the United States and the Soviet Union Guo Yi saw that this was really not going to work, and they must not get into a fight because of misunderstandings, so the two sides established a "hotline" to call and ask about anything first to eliminate misunderstandings.

The benefits of pretending to be a good person

If both parties clearly know that the other party is a rational person, there will be no cooperation in a limited number of repeated games. But there are some people in society who are willing to be good people, and they are willing to cooperate. So when you face a good person, do you cooperate or betray? Your rational choice is to cooperate.

The "KMRW theorem" says that in an incomplete information game, participants do not know whether the other party is a good person or a rational person. As long as the game is repeated enough times and cooperation can bring enough benefits, both parties will Be willing to maintain your reputation as a good person, cooperate as much as possible in the early stages, and only choose to betray in the end.

You can't tell the difference between a good person and a rational person in most situations. Zhang Weiying mentioned in the book "Games and Society" that the KMRW theorem can explain "a great wisdom is like a fool". "Wisdom" means that people should be selfish and all actions are for their own benefit. "Foolish" means one would rather suffer a loss than betray others. Choosing betrayal in every round may seem selfish, but in fact that is "Xiao Zhi". And if you would rather suffer some losses than choose to cooperate, you will build a good reputation and more people will cooperate with you. This is "great wisdom" in the long run.

A rational person has good reasons not to reveal that he is a rational person. You should pretend that you are a good person. So how far should you go to pretend to be a good person? In experiments with limited repetitions of the game, both parties usually reveal themselves as rational people and choose to betray until the penultimate game. Game theory experts will never advise you to be a truly good person. Good people often have wishful expectations about the world. Some good people think that they can influence others. He thinks that if I cooperate with others this time, even if I suffer a loss, others will cooperate with me next time out of embarrassment or to repay me. Game theory experts would say this idea is dangerous. In fact, if you are in a relatively dangerous social environment, then not only should you not be a good person, but you should also pretend to be a bad person.

But having said that, there is one major advantage of being a truly good person, and that is that you will feel good about yourself. In order to maintain this good feeling, you are willing to sacrifice financial benefits. An imaginary fraternity is formed between good people and good people. This is actually an illusion, but there is no way. The imaginary homosexual body is the most powerful social force. This feeling can sometimes be so strong that we think the material benefits are not worth it. This is actually rational! As long as you know what's most important to you. Game theory doesn't care about specific values, but game theory requires you to have a clear and stable ranking of what you want. You have to know what to sacrifice for what.

Common people compete, powerful people collude

This game pattern is that if the interests are great and there are few participants, these participants will join forces. As long as you get on this table, you can carve up the world steadily, so why fight to the death?

There is a saying circulating on the Internet that "people from the upper class praise others, people from the middle class compare themselves to others, and people from the lower class despise others." This sentence sounds ugly, but it has some truth. If the benefits of cooperation are great, there will be no competition, and if the cost of betrayal is low, there will be betrayal.

How to break this situation? One way is to expand market access, allow more participants to come in, and make coordination among merchants less easy. Another way is to rely on the power of the government to fight against monopoly, which is equivalent to all consumers uniting to deal with those giants.

There is a kind of dilemma called freedom, and there is a kind of liberation called prohibition

Game theory is the first principle of human rational behavior.

To solve the prisoner's dilemma, liberals may prefer to use spontaneous methods such as repeated games or coordination to achieve cooperation, but ordinary people have a more intuitive solution: let the government control it. The most advanced view is that you should treat the government as a player. And the government should also regard itself as a player. Since it is a player participating in the game, the government also needs game theory.

Strike first

The essence of dynamic games is not to take turns, but that you can change the rules of the game.

There is a classic game situation called "chicken" in English, which means "little chicken" and means to compare who is timid. On a straight road, two people, A and B, each drove a car towards each other and were about to collide with each other. The rule of the game is whoever turns the steering wheel first and pulls over is the coward and the chicken. Of course, both sides definitely don't want to die first, so turning the steering wheel is inevitable. The question is who turns first. Game theory experts don't work by being bold. Our suggestion is that you can take off the steering wheel of your car in front of your opponent. Your action clearly tells the other person that you will definitely not be able to turn the steering wheel, because your car no longer has a steering wheel and you can only go in a straight line. So now whether two cars will collide depends entirely on the other. As long as the other person doesn't want to die - and you know he definitely doesn't want to die - he can only turn the wheel so you win.

You are a game changer. Originally, the rules of the game were that both players could choose to be chickens or die, but you changed the rules so that only your opponent could choose to be chickens or die. You give up your options, but leave the only possibility of being a chick to the other person.

"it's

better to ask forgiveness than permission" - Rather than asking for permission beforehand, it's better to ask for forgiveness afterwards. If you are sure that there is nothing the other party can do if you do it, then you should do it directly.

Since no one wants to die, why not just surrender from the beginning? The answer is that if you upgrade first and then surrender, you are no longer a chicken. We have all proven our bravery, and both sides have promoted the escalation of the crisis. At this time, as long as there is a step, we can negotiate a solution and each side takes a step back. It is not a shame. Both sides have adhered to their principles and saved face. Both sides can claim that the other side will never dare to do so next time. In fact, I really don’t dare. The cliff strategy is very dangerous and can easily turn into a real disaster if it goes wrong.

In fact, if you let the other party make the first move, you are already wrong. The best way is to give the other party a deterrent so that he doesn't dare to take action at all. "Deterrence has three elements: strength, determination and letting the opponent know." First, I have the strength to destroy you; second, I have the determination to destroy you; third, you have to know that I have the strength and determination to destroy you. From the perspective of game theory, there is another particularly important point, that is, neither party wants to be destroyed - both parties must be fully rational.

If he is not upright, he will not obey orders

There are two basic concepts in dynamic games, one is called threat and the other is commitment. A threat is when I ask you not to do something—and I say that if you do it, I will punish you. The so-called promise means that I ask you to do something - if you do it, I will give you a reward. Threats and promises are essentially the same. I have said in advance that I will take a corresponding action based on your next action.

Thomas Schelling proposed a key concept called "credibility". Uncredible threats and promises are in vain and will only make people think you are unreliable. But credible threats and promises are very useful. Whether it is credible or not depends on the subsequent interest pattern. It is credible only if you have no choice after the fact, and it is in your interest at that time to fulfill your threats or promises, and the ex ante optimality is consistent with the ex post optimality. It is untrustworthy because of the inconsistency between "ex ante optimal" and "ex post optimal".

Credibility = No Choice

In order to make a credible threat or promise, you must actively tie your own hands. I roughly summed it up, there are three ways. The first way is to give others the power to punish you; the second way is to take the initiative to cancel your own options; and the third way is to build reputation. The best thing about reputation is that it allows you to make credible threats and promises at no cost to you. Damaging your reputation is the biggest punishment for breaking your trust.

The logic of late-mover advantage

First movers expose information and late movers exploit the information. If you're already ahead, don't take the risk. Laggards should be allowed to initiate uncertainty first. The laggard has no chance at all if he does not change his style of play. He must take risks if he wants to win - while the leader only needs to follow.

Large companies that dominate a market are often reluctant to be the first to do particularly radical innovations. We are doing well now, so why bother? Radical innovations are often initiated by small companies. In the face of radical small companies, if a large company feels that its new style of play may threaten itself, it is actually easy to deal with it. One way is to simply acquire this small company, and of course another way is to directly imitate the small company.

The latecomer advantage = the first mover’s information + the late mover’s right to take action.

Information is an opportunity for imitation, and power is an opportunity for innovation.

The first-mover advantage lies in occupation, while the late-mover advantage lies in information and the right to take action only at this time. If the first mover can occupy the market and the late mover can only be forced to innovate, then the correct approach for the first mover at this time is to imitate the late mover - but for various reasons, the first mover often cannot do this. Learning from previous experience can help you avoid detours. But if you want to win and surpass your predecessors, then you must have an overtaking maneuver that no one before you has.

The real "trick" is randomness

Von Neumann said that if you want to really confuse your opponent, you must mix lies with the truth.

Because there is no Nash equilibrium of pure strategy, game theory cannot tell you how to play to win this game. However, if you are going to take a lot of penalty kicks, game theory can give you a guide to help you win with a "system". Game theory requires you to use "mixed strategies." Your mix of probability choices should minimize the maximum reward your opponent can get. "Minimax theorem" is a basic theorem of game theory. It involves very complex mathematics, but the spirit is easy to understand - first, you have to mix your own games according to a certain probability. method; secondly, the law of your mixed play must be something that your opponent cannot take advantage of. When a hero does something, there must be absolutely no rules that can be exploited by the enemy.

Randomness is the real "trick". Mixed strategy is not a conspiracy but a conspiracy. With a mixed strategy, your opponent can't do anything even if you tell him how you made your decision. The conspiracy is not afraid of being discovered... In the final analysis, everyone is a slave of the Nash equilibrium.

Game designer

Most people follow the rules, a few people violate the rules, and some people make the rules. Designing a game is much more difficult than participating in it. This is the knowledge of managers.

In 1961, economist William Vickery proposed a bidding method that allowed bidders to bid with confidence, now known as the "Vickrey auction" ”, also called “Second-price sealed-bid auction”. This auction method is a hidden bid. Each bidder only bids once and puts it in an envelope so that no one can see it. The highest bidder wins the bid—but ends up paying not the price of his own bid, but the price of the second-place bid. This sounds a bit counter-intuitive, but because of this, bidders can confidently bid the highest price they can without worrying about suffering a loss because they do not understand the market! Vickery won the 1996 Nobel Prize in Economics for his research on auctions.

There is a certain number in the world

The starting point of game theory is freedom.

You must first be a free player who can independently choose game strategies before you can use game theory. But the outcome of game theory is usually unfreedom. As a rational person, your strategy is always one of the Nash equilibria - if there is only one Nash equilibrium, you have only one choice.

Just as biological evolution is the competition of genes and cultural evolution is the competition of "memes", the evolution of games is the competition of strategies. If using a strategy brings good rewards, people will imitate the strategy and the strategy will become popular.

The never-ending game

"Game" and "game" are the same word in English, both called game. Novices are prone to emotions, while veterans are rational. And being rational is not enough, you must choose the right strategy. If the opponents in the game are relatively weak, you can try various ways of playing and enjoy your capriciousness; as the difficulty of the game increases, you don't have many choices; to play on the highest difficulty level, there is often only one correct way to play. And if your opponent is a human player like you, then you may not win even if you do everything right.

When no one is aware of the game, you may be able to win even if you are poetic and picturesque; when a few people are aware of the game, whoever realizes the game wins; when everyone is aware of the game, then you can only Compare execution—or see who can realize the new game.

Maybe you have enough forward-looking thinking to predict future gaming situations, maybe you can draw inferences from one example and skillfully deal with various gaming situations, or, now you are at least a player who dares to play games.

Summary

"Nash equilibrium" is the most important idea in game theory, and it is also a sobering agent to get rid of delusions. The meaning of Nash equilibrium is that if all parties in the game are smart enough, everyone's final strategy choice must be such a situation: in this situation, everyone accepts their fate, and no one can unilaterally change their strategy to seek a strategy that is more beneficial to themselves. Good ending.

Nash equilibrium is the end point of strategic calculation.

If all parties have a strong willingness to cooperate and the game has more than one Nash equilibrium, then we need a "focus".

If cooperation benefits everyone, but defection has direct benefits to the defector, it is a "Prisoner's Dilemma."

To escape the Prisoner's Dilemma, if the game is repeatable, we should seek to punish defectors. "Tit for tat" is the most classic approach, but appropriate tolerance can promote cooperation.

Choosing to be a good person in a cruel world seems irrational on the surface - but as long as there are more games, even if it is only a "limited number of repetitions", it is actually beneficial to be a good person.

If the number of people participating in the game is relatively small and the benefits of cooperation are relatively large, the parties will form collusion and "collusion", although doing so may not necessarily be beneficial to society.

Sometimes voluntarily giving up some freedom and letting a third party "supervise" can promote freedom, and regulators should also regard themselves as a party to the game.

If you can quickly occupy a certain resource or create a fait accompli, then "strike first to gain the upper hand"; if the party that strikes first cannot defend it, then the "latecomer" will gain the key information. and the right to take action to gain an advantage.

The best way to get someone to do what you want is to give them a "credible threat or promise."

Some games only have "mixed strategy Nash equilibrium". The most advanced gameplay is not to deceive the opponent, but to randomly select strategies.

If there is information asymmetry between the two parties, the best way to convey information is to "send signals", which means you have to use actions to prove yourself.

Nash equilibrium is the ending of the game, but there is never an ending in the real world - this is because the game situation is always changing, and we can even actively change the game.

The most advanced application of game theory is "designing a game", such as formulating the rules of an auction, but this is not easy.

The highest perspective of game theory is to observe the evolution of different game strategies in the population. What we see is that the game never ends.

Additional reading: Player style

The primary spirit of gaming is to be a "player".

Player self-cultivation: A qualified player should have four styles - limited, pragmatic, prudent and objective.

Limited: Player identity is just one of our many identities, and gaming is not everything in life. Only those who can accept failure are qualified to win. When you win, you forget about everything, and when you lose, you cry all over the place. That is the most stupid behavior.

Pragmatic: Game theory is not about making the impossible possible, but about how to make it most possible. "Dimensionality reduction attack" is a fantasy. Any mature field will not give you the opportunity to reduce dimensionality attack at all. If you think you know something that Wall Street doesn't know, then it's most likely that you don't know that you don't know it.

Caution: In any argument, the intensity of emotion is inversely proportional to the value of the interests involved. As a player, you cannot easily provoke disputes, express your stance, or reveal relevant information easily. If you have an impact, you have to pay attention to the impact.

Objective: Participating in the game is actually to consider these factors honestly - 1. What is this game and what do I want; 2. What do I have now and what can I give up; 3. The opponent's Condition. You enter relevant conditions and seek an optimal solution under constraints. Effective public relations must speak from the perspective of the other person and be in sync before you can lead.

A person who is good at being a soldier will not use force, a person who is good at fighting will not be angry, a person who is good at defeating the enemy will not fight against him, and a person who is good at using people will be subordinate. Player, that has temperament.