Book Review "The Trick of Game Theory"
Small coffee/holding a lamp to see the sword on May 7, 2008.
It is a long-cherished wish to study game theory. Game theory is at least the first great economic theory I heard after graduating from college. This is not an economics class, but a beautiful mind displayed in a meditation class. This film, which defeated The Lord of the Rings and defended the Oscar's "conscience", has a great influence on us freshmen in economics. And game theory is an analytical tool that some people are about to and have been keen on.
I have always wanted to know something about Nash and the magical experience of the game itself. However, as a theory proved by rigorous mathematics, it must be difficult to go deep into it. I walked around the library and found traces of game theory in two categories: economic management and mathematics. Either way, it's a bit of a monograph and a bit of a headache. Fortunately, I found a vernacular book "The Trick of Game Theory" in the cracks of mathematics, which is really a good book for a person who only knows the prisoner's dilemma and answers blows with blows.
Summary and thinking of game theory tricks
Prisoner's Dilemma: This simple example is almost synonymous with game theory. From a rational point of view, what will happen to two prisoners based on "confessing leniency and resisting severity"? As a result, if they are rational and pursue the maximization of personal interests, then both of them confess, which is betrayal. This is not dominant among the four strategies. Why not adopt the most collective strategy and cooperate? Very simple collective optimization will inevitably infringe on the maximization of personal interests. Of course, all this presupposes a rational hypothesis, that is, the famous economic man hypothesis: people in economics are "villains" (while people in management are considered "gentlemen", which is an interesting and reasonable metaphor). The solution to this dilemma is to break the information isolation, and the countermeasures of law enforcement are to maintain isolation or strengthen threats. Regardless of betrayal or cooperation, whoever persists in this matter to the end will win.
Repeated game: prisoner's dilemma, which smashed the field of traditional economics. Because the individual's selfish behavior does not necessarily lead to the maximization of collective interests, the "invisible hand" can't help it, and human beings tend to slide into the city of depravity. Is this really sad? Not at all. Let's ignore the rational assumptions of game theory. Game theorists soon found that the prisoner's dilemma is only obvious in the case of a single game. Once the game starts to repeat, cooperation comes. Because future income will affect the current decision.
Answer blows with blows: Repeated games lead to cooperation, but no one can guarantee the continuation of cooperation, because it has been said before that the price of cooperation is based on harming personal interests. If the individual gives up the future income or the current betrayal income is greater than the future income, then the betrayal risk still exists. So what kind of strategy is the best in repeated games? After the PK in the computer, some wise and complicated "answer blows with blows" strategies stand out. Although this strategy is extremely simple, it is so powerful that after a short period of joy, people find Tai 'a's finger sword terrible. Once there is a betrayal (perhaps inadvertently) in the repeated chain, the game based on this principle will never end. At the same time, individual interests will be extremely inflated and collective interests will be infinitely reduced. Fortunately, the world is not a model, nor is it that simple. Many times, we don't have to answer blows with blows. The third party's norm: morality and law are our dentures. They are more in favor, more rational and more restrained.
Hostage dilemma: a humble game. Grab the first bird, the hostage alliance can subdue the gangsters, but who wants to stand up? This gave countless hijackers an opportunity, similar to Qin's long-range attack and divide-and-rule strategy, and finally won a complete victory. Hostages can certainly have countermeasures, but it is extremely difficult. The hostage can choose silence, so that he has a certain survival time; Or unite the hijackers to deal with the hostages, and the outcome depends on the hijacker. What if he burns the bridge? Resist at the same time, the collective will get the left and right strategy, but it takes the courage of a strong man to break his wrist, and someone may get hurt. This is a contest between strength and courage, and strength has prevailed for the time being.
Bar game: If everyone is rational, then the number of people who go to bars every day will be almost the same, but people who are not sages are often limited and rational. There are many people coming to the bar for the first time, so most people think the bar is too crowded. When making the second decision, refer to the previous one instead of going to the bar. Several people who went to the bar found that there were fewer people in the bar the next day, and they felt very cool. They will continue to come back for the third time, bringing back many people ... the cycle begins. On the one hand, bar games show that real game participants are extremely limited and rational, and their rationality is only a short delay. Historical data is only useful for computers, not necessarily for people.
On the other hand, bar games point out that winners are always only a few. Although it is possible to adjust it, such as sending a message to remind you from time to time, the cost is probably too high. On other occasions, a few people may even set up various obstacles to prevent the latecomers from rising. In other words, our world is still manipulated by a few people. However, in the end, the world is not a model, and the path of ethnic minorities is still traceable. Sophisticated generals will still find the only way out in the maze of gossip. You must be a more experienced general if you like.
The shooter's game: the sorrow of the king. Three people are self-determined about guns, and the marksmanship of A, B and C is decreasing. The final helpless and magical ending will not depend on simultaneous shooting or successive shooting. The best shooter has the highest probability of falling. However, the worst gunman has the greatest hope of survival. Because no one will list the gunman with the least threat as the number one clear target. Here, the weak will win. It is by no means a myth to defeat the strong with the weak.
Is the fate of the king really so unbearable? Oh, say goodbye, forget that every theoretical model has a premise. If you break any of them, the king will still come back. This is the first-Mover advantage. Suppose this is a competition similar to CS, and the excellent gunner knocks down the No.2 gunner and immediately gets a reward: shield. Then shooter number three will be desperate. However, in any case, this game mode gives the vulnerable groups a hope. Opportunities always exist.
Deer hunting game: The benefits of two hunters hunting deer together will be far greater than the benefits of hunting rabbits alone, and the strategic alliance will begin. This may be a good thing, but it depends on the allocation of deer as a public resource. If properly distributed, the overall efficiency will be improved. If one side is dominant and the other side suffers, then Pareto improvement cannot be carried out and cooperation may eventually break down.
Another problem, a bigger problem. The demonstration of cooperation will allow more hunters to join, the number of deer hunting will increase greatly, and the interests of human beings will increase geometrically in the short term. But in the end, it was indeed an ecological imbalance, and the deer became extinct. After a short period of prosperity, hunters will return to their original rabbit hunting life again. Although in order to avoid this tragedy, mankind still has the last hope: Coase theorem, the magic weapon of institutional economics, uses the ownership of property rights to solve external economic problems. However, due to the cost and feasibility of negotiations, the tragedy of human society will continue to be staged.
Smart pig game: the last game before chaos. Little pig and big pig live on one side of the pigsty (the trough is here), and turn on the food switch on the other side. Whoever steps on it loses the initiative. What was the result? It is the little pig who chooses to hitchhike, and the big pig who runs diligently. Because no matter whether the pig runs or stops, the best strategy of the big pig is to step on the organ. But in real life. There are still two strategies.
Piggy's "hitchhiking" Sometimes, the big pig consciously or unconsciously calls himself "the great man of chivalry, serving the country and the people", and therefore bears some unbearable burdens. The trick of game theory points out that America behaves like a big pig after the war. After the war, the United States tried its best to publicize its universal values, went deep into overseas affairs, and even spared no expense to help small countries defend themselves. In this way, small countries unconsciously "exploited" big countries.
After breaking a hypothesis of the model, the big pig still has a chance to get the upper hand. Because the big pig and the little pig have different hunger tolerance, so the big pig has the ability to last longer. If the pig doesn't want to starve to death, there is only one way to bet: the tortoise and the rabbit race. I hope the big pig can take a nap and eat a bite or two when he comes back, otherwise he will really lose his wife and lose his soldiers. Accordingly, it is no longer difficult to explain why many people gnash their teeth at Tencent, follow the trend unscrupulously, do QQ whirlwind and clap their hands. Because the unwilling pigs have completed the early stage of new technology research and development, the big pigs only need to follow quietly and kick out a path at an appropriate time.
The backwardness of the big pig here is not in line with the shooter's game. The backwardness of the gunman is based on the fierce struggle of others, and the backwardness of the big pig is entirely based on its own strength. And the big pig doesn't have to take any radical measures at all, just follow. Because the condition for pigs to win is not proximity, but distance.
A depressing game ending. A policeman and a thief each have only one chance to patrol or steal a place or b place. The value of land A is greater than that of land B, so the police should always protect land A in order to protect it. Game theory holds that of course not, and the reasonable strategy of the police should be to tend to patrol randomly with a certain probability. This probability is: the value of p =/the total value of ab. Only in this case can the thief's greatest chance of success be reduced to a minimum. But unfortunately, what the thief is looking for at this time is to maximize the minimum chance of success. In other words, the police's best strategy will improve the thief's worst strategy! This is the "minimum-maximum law" put forward by von Neumann.
We must thank this imperfect world again, because in reality, similar phenomena can still try to find the deadly routine of the opponent (of course, we must consider whether the other party is a more experienced hunter and deliberately release the bait). And maintaining the disorder of one's actions may become a weapon of deception strategy, which is just like what Zhang Sanfeng said: If you have a move, you will win.
Chicken Game: When two cockfights are fighting, it is a difficult problem to choose whether to advance or retreat, because Nash equilibrium has given the best strategy for winning or losing. In many contests, putting all your eggs in one basket will not pay off, because it is likely to give a third party an opportunity. Therefore, the two powerful forces that already exist on the battlefield are likely to consciously follow Nash equilibrium, with one attacking and the other temporarily retreating. Although one side may be temporarily damaged, it is much better than both sides. However, in order to maintain this situation, we must ensure that the next time the earlier damaged party launches an offensive, the other party will also retreat. So such attacks began to become "ritualized" and no one really bled. This is just a game played by two giants. The purpose is to warn the latecomers that they have to play with us if they want to come in, but can you afford it? This is why Pepsi's advertisements, even if they imply provocation, only reach the point of "Dare to be China Red" at most.
Concorde fallacy: European governments can't extricate themselves after investing heavily in Concorde. Even if the prospect is bleak, I will throw it in the past with a face, and I will give up when I have no choice. At this time, the cost of investment is all in vain. If, when you find it impossible to continue, you dare to let go, the loss will be much smaller. But will they? Can they? How heroic it is for a strong man to break his wrist, but how difficult it is!
The sunk cost is likely to continue people's fearless persistence. People who have sunk should have given up, but unfortunately most of them have the psychology of gamblers, believing that Archimedes' lever will eventually start. It's a pity that they suffocated before they reached the fulcrum enough to pry the lever.
Concordia fallacy is actually a reason to give up halfway. Will anyone worry that its origin will affect some goals that should be adhered to? It is indeed possible, but we must believe that people are rational enough to compare the relationship between sunk cost, opportunity cost and future income. If you look at it clearly, you will definitely get out of the Concordia fallacy.
Centipede game: a repeated game. The mechanism of centipede game is to return to the beginning with the final result. This is a wise strategy, karma, grasping karma, has its own good results. Another advantage of it is to make the future planning clear, so that you will no longer hesitate. Unfortunately, many times, we can't see through the eyes of puzzles. Our black eyes are only used to night.
There is also a fatal paradox in the centipede game, which is still the conflict between individual interests and collective interests, because the final betrayal is always superior to cooperation. Sadly, this betrayal will be due to human reasons, and the leap is just to visit and return to the original place: people will refuse to cooperate from the beginning. Let's thank this imperfect world. In fact, people rarely do this. Of course, there is little cooperation in the end, that is to say, the backward method only takes effect suddenly in the intermediate stage, but no one can predict where the intermediate step is. There, we only hope in trust, morality, conscience and so on.
Cake sharing game: how do two children share the cake? Classic story, classic answer: choose one point. In reality, the rational distribution of rights will effectively promote fairness and efficiency. The separation of management rights and ownership rights really makes the economy more dynamic. However, the advanced model of cake sharing emphasizes bargaining strategy. The sharing of cakes is not one-off, but multiple rounds, and there is a cost: the cakes are melting.
The increase of time scale will complicate the distribution. If the two sides can't reach a deal in time, not only the collective income will decrease, but also the personal income will decrease. In this case, it will be extremely beneficial for one party to weigh the cost, threat and commitment with time. The customer may be forced by the situation and must end the negotiation as soon as possible. At this time, the seller is not in a hurry and deliberately delays, and the customer will compromise on the price.
Of course, clients also have policies. Its strategy is to shop around and ask for promises or threats. This premise is the existence of a buyer's market. Customers should also protect their bargaining power, that is, customers have the right to complain about businesses.
Eagle pigeon game: this game is equivalent to eating chicken by many people. But cockfighting is two aggressive individuals, while eagle pigeon is a game between two different groups, one is peaceful and the other is aggressive. In a corn field with only pigeons, the eagle who suddenly joins will benefit a lot and attract his companions to join. But the result is not that the eagles drive the pigeons out of the cornfield, but that there is a certain proportion, because the marginal income of adding an eagle to the eagle group tends to zero (infighting among the eagles), and equilibrium will come.
This leads to the stable strategy of ESS evolution, that is, once the equilibrium is formed, the deviated movement will be hit by natural selection. In other words, after the eagle is full, the eagle trying to join will be squeezed out by the eagle.
The greatest benefit of evolutionary stability and balance is to remain stable. But the problem is to form a strong path dependence, that is, the winner is not necessarily the best. Because the best will be beaten into early birds, this is a personal failure, a group victory, and a collective stagnation.
Dirty face game: Epiphany game. There were three people in the room and they didn't speak. Beauty came in and said, at least one of you has a dirty face. There were three people around, and there was no response. The beauty said again: Do you know? The three of them watched it again and suddenly realized that they were all red in the face. Why? Because of the beauty's nonsense, all three people know about the existence of dirty faces, and they must also know that the other side knows about the existence of dirty faces (because the other two faces are not red, which means they have seen dirty faces), and they know that the other side knows that they have thought of the previous step ... The cycle began, knowledge began to assimilate, and the truth came out: all three people were dirty and blushed.
This is the role of knowledgeable * * *, which is a bit scary and powerful. It's almost a legless trick, killing people without bloodshed. Before the table game, private calculation has killed the opponent. However, it is very likely that the other party also anticipated this, thought of it long ago and killed it at the same time. Finally, a double-death situation was formed.
Of course, although there are similar phenomena in reality, the greater role of knowledge is to reduce transaction costs. Because some rules are well known, both sides just have to act according to them.
Information balance: naturally, information plays a very important role in the game. Restore the game theory to reality, people are no longer completely rational, information is asymmetric, and the game needs to strive to seize the information highland.
Information asymmetry is a big obstacle. The asymmetry of information will cause "adverse selection" and "moral hazard", the former is beforehand and the latter is afterwards. Information asymmetry will benefit one party in the short term, but it will eventually destroy the whole market. So there are two solutions.
Information transmission: a strategy to convey your positive information, that is, to attract customers to your counter. Its main point is to maintain effectiveness and reduce costs.
Information screening: induce opponents to reveal the real information they have in private. Is to give customers a magnifying glass to ensure that customers will not go to other counters. This strategy is obviously more effective, but it is also more risky: what if customers see their defects with a magnifying glass?
Another comment: Wang Chunyong's game theory skills.
Tags: Wang Chunyong's game theory tricks, history and culture.
We live in a game every day, and the game theory only explains our long-term game with mathematical methods. Even so, when we see the conclusion of mathematical deduction, we still can't help but be dumbfounded.
Although the game is played every day, we often can't see the essence clearly because of complicated factors. Playing cards by intuition often falls into the calculation of others. Maybe this book can help us solve some problems. This book covers a wide range, from life choices to three meals a day. It explains all kinds of problems in our life from the perspective of game theory, including career, communication, love, economy, time management and so on. Sometimes it will make you forget that this book is a game theory book and think it is a successful study. But speaking of it, isn't the game for success?
There is a lot of content in this book. The author appropriately links game theory and experimental cases with history, politics, literature, news and stories. These are comprehensive, arbitrary, beautiful and admirable. More interestingly, at the beginning of each article, the author quotes the lyrics of a popular song (most of which I don't know) as an introduction, which has almost the structural significance of classical novels. Under the education system in China, how many people who study mathematics will still pay attention to human history, let alone fashion? The author of this book seems to have rich experience and extensive reading, and many things quoted in it are new things and new sayings in recent years. I think it's all summed up by my own keen discovery and research. Therefore, every time I look at the highlights, I can't help but sigh the author's span of arts and sciences.
Some of the author's ambitions can often be seen in the article. He is very clever, paving some sensitive points clearly, and then passing by, which is self-evident to readers. He often quotes Mr. Wu's works, but he is not as clever as Mr. Wu. I think this is also the result of game training.
The references at the end of the book make people laugh. Perhaps because there are too few references, the author even included Luo Guanzhong's Romance of the Three Kingdoms. If so, it would be too wrong for him to quote Historical Records, Mirror and so on. In fact, this book is very informative. If you list the references one by one, the author will be very tired, so fool around.