The world's funniest economics stories

Chapter 15 Game Theory Tricks (2)
For example, if someone with a bad temper walks on the street, if they are stepped on by a stranger, they will immediately glare at the other person, but if they are someone they are usually familiar with, they will laugh it off.In fact, getting angry with strangers is because it is a kind of "non-repetition", while smiling at acquaintances is because of the "repetition" of "seeing up but not seeing down".

In repeated games, the conditions, rules and content of each game are the same.However, when it comes to games, due to the existence of a long-term interest, each player must consider in the current stage of the game that it cannot cause confrontation, retaliation or vicious competition from other players in the later stage, that is, it cannot be like in a one-time static game. That does not take into account the interests of other game parties.

Sometimes, one party makes a cooperative gesture, which may make other players adopt a cooperative attitude in the future, so as to realize common long-term interests.

Pareto optimality refers to a state of resource allocation in which it is impossible to make some people better off without making anyone worse off.Pareto optimality is only the "minimum standard" among ideal standards.

That is to say, if a state is not yet Pareto optimal, it must be unsatisfactory, because there is still room for improvement, which can improve the welfare of some people without harming anyone.

4. Three gunmen duel, who is the final winner - Gunners Game
There is such a story in "The Romance of the Three Kingdoms":
After Yuan Shao's army was defeated by Cao Cao, Yuan Shao's sons Yuan Shang and Yuan Xi defected to Wuhuan.In order to eliminate future troubles, Cao Cao decided to attack Wuhuan.Therefore, the desperate Yuan brothers turned to Gongsun Kang, the prefect of Liaodong.Facing the two Yuan brothers who were at the end of the road, all the generals of Cao Jun, who were in high spirits, asked Cao Cao for orders, marched into Liaodong, and captured the two Yuans in one go.However, Cao Cao, who was scheming and calculating, did not listen to the opinions of the generals, and chose to stand still.

A few days later, Gongsun Kang sent people to send the heads of Yuan Shang and Yuan Xi to Cao Cao's tent. This move shocked many people.At this time, Cao Cao took out Guo Jia's suicide note for everyone to pass on.

It turned out that Guo Jia advised Cao Cao not to rush to attack Liaodong, because Gongsun Kang had always been afraid of being annexed by the Yuan family. Now that the Yuan brothers went to him, it would inevitably arouse his suspicion.And if Cao Cao goes to crusade, Yuan and Gongsun Kang will naturally join forces to fight against Cao Jun, and Cao Jun's chances of winning are not high.But if you stand still and wait for the fight between Gongsun Kang and the Yuan family, it will be Cao Jun who will benefit in the end.

Guo Jia's "sitting on the mountain and watching the tiger fight" finally allowed Cao Cao to achieve the result he wanted.

The Gunners game is a behavior in which when facing more than one enemy or opponent, in order to avoid one's own attack and competition, the opponents unite against themselves, and take a stand still and wait for the opportunity.In order to obtain the desired result, in this game, the most important thing is to pay attention not to act too hastily.

Cao Cao followed Guo Jia's advice and chose to wait quietly when facing multiple opponents, "sit on the mountain and watch the tiger fight", and finally let himself lose one competitor who was his enemy without any effort.In fact, Cao Cao's approach is similar to the Gunners Game.

But having said that, Cao Cao and his subordinates are in the position of rulers. Their strategies belong to the emperor's mind or kingly way, and most of them cannot avoid their dark side in the true sense.Then the modern game is about strategy.The purpose of game theory lies in ingenious strategies, and the strategies emphasized here are also more operable.

Knowing the difference between the two, let us take a look at the model of the Gunners game.

One day, three mortal gunmen met on the street. The three of them drew their guns and fired at the same time. Assume that Gunner A has a 90% hit rate, Gunner B has a 60% hit rate, and Gunner C has a 40% hit rate. They are all very rational people.So, who is more likely to survive after the first burst of gunfire?
You need to think carefully before answering such a question.Usually, people think that A's marksmanship is good, and the possibility of surviving will be higher.But after some close reasoning, it was C who had the worst marksmanship and had the best chance of surviving.

In a fierce gun battle, Gunner A will definitely shoot Gunner B first, because B is much more threatening to A than C is to A.A should kill B first, this is A's strategy.

In the same way, the best strategy for gunman B is to shoot at A first.Once A is killed, B and C will have a duel, and B's winning rate will increase a lot.

Gunner C’s best strategy is to shoot at A first. B’s marksmanship is worse than A’s. Kill A first and then fight against B. C’s survival rate is higher.

Through the probability statistics of the survival rate of the three gunmen after making a decision, the survival rate of C with the worst marksmanship is the highest, while the survival probability of the other two is much lower than that of C.

It can be seen that in a multiplayer game with complex relationships, whether a participant can win in the end depends not only on his own strength, but more importantly, the comparison of the strengths of all parties and the strategies of all parties.

Looking at political campaigns in the West, we can see many shadows of the gunman game.In a situation where multiple competitors compete, often the top performers will be defeated in embarrassment under the repeated attacks of less powerful candidates.

"A tree is as beautiful as a forest, but the wind will destroy it." Therefore, for competitors, it is more beneficial for competitors to wait until others are fighting each other and withdrawing from the election to make their debut.In the eyes of other players, a player who does not have any degree of threat, if he adopts the best strategy, is more likely to "stand out" from the mutual killing of stronger opponents.

In a multi-party game, as long as we can adopt our own optimal strategy, no matter what the opponent does, there will be unexpected results favoring us!

The basic components of the game:
[1] Participant: also known as the player in the game, refers to the decision-making subject who chooses his own behavior to maximize utility;
[2] Action: Refers to the decision variable of the participant at a certain point in the game.

[3] Information: The knowledge of the players about the game, especially about the "natural" choices, the characteristics and actions of other players.Information set refers to the participants' knowledge about variable values ​​at a specific moment.

[4] Strategy: Refers to the action rules of the participants in the case of given information, which stipulates when to choose what action.

[5] Payment: Refers to the determined utility level obtained by a participant in a specific strategy set or the expected utility level obtained by a participant.

[6] Results: mainly refers to the equilibrium strategy portfolio, equilibrium action portfolio, equilibrium payment portfolio, etc.

[7] Equilibrium: refers to the optimal strategy set of all participants.

5. Why doesn't quarrel increase one's own income--negotiation game
Here is a story about a pair of brothers hunting.

One day, the two brothers, who really wanted to eat game, came to the mountain to hunt together with shotguns after some careful preparations.On the path leading into the mountains, they encountered a stray goose.So the two set up their arrows at the same time to shoot the wild goose.

The arrow was on the string, and seeing that the two arrows were about to be fired at the same time, the elder brother suddenly said: "After shooting the wild goose, let's cook it and eat it."

"The domestic goose is delicious when boiled, but the roasted wild goose is more delicious. Let's roast the wild goose." Hearing what the elder brother said, the younger brother was a little unconvinced and argued anxiously.

So, the two brothers began to quarrel because of this issue, but their opinions were never unified.At this time, a villager who collected firewood came and heard their quarrel. He said: "Actually, this problem is very easy to solve. Just divide the wild goose into two halves, steam the half and boil the half."

After hearing what the villager said, the two brothers suddenly realized that they stopped their quarrel.But when he drew the bow again, he found that the wild geese in the sky had already disappeared.

In a quarrel, the two brothers let go the wild goose they got, which really echoed the proverb "the cooked duck flew away".In fact, the two brothers can discuss how to deal with the wild geese slowly after the wild geese are shot down.But at the moment when the sword is on the verge of breaking out, seeing the vested interests in front of them, they fall into the trap of "fantasy".In real life, many times our income is not constant.Often when we plan how to distribute the income, our income may continue to shrink.If it is explained by game theory, it involves negotiation game theory.

We can look at the basic model of the game.

Suppose there is a piece of cake on the table, both A and B want to eat the cake right away, but they have a quarrel over the distribution of the cake.And all the while they were arguing, the cake kept melting.Assume that with each round of negotiation, the cake shrinks by the same size.At this time, in the first round of bargaining, A proposes a way to divide the cake, and if B accepts it, the negotiation will succeed, and if B does not accept it, it will enter the second round of negotiation.In the second round, B proposes a way to divide the cake. If A accepts it, the cake will melt completely.

In this process, the method proposed by A at the beginning is very important.If the method B proposed by A is unacceptable, half of the cake will be melted. Even if the second round of negotiation is successful, it may not be as big as the first round.Therefore, after careful consideration, wise A decides to choose a method that must not exceed half of the cake in the initial method of the first stage, and equally wise B will agree to A's request.

In daily economic life, the issue of bargaining not only occurs in daily commodity sales, but also in international trade and even major political negotiations.The story of dividing the cake is widely used in many fields. Whether in daily life, business, or international politics, the parties involved often need to bargain or judge how to distribute the total income. This total income is actually a big "cake".

Of course, in real life, the way returns shrink is very complicated because different situations have different requirements.But one thing is certain, that is, the entire negotiation process of bargaining cannot be extended indefinitely, because the negotiation itself requires costs.If both parties in the negotiation insist on not compromising in order to obtain a result that is more favorable to them, then the benefits they get will often exceed the cost of the negotiation.The longer the negotiation, the more the cake shrinks.For this reason, the real stalemate between the two sides will not be too long.Therefore, the most obvious feature of this kind of cost game is that the negotiators as a whole should try to shorten the negotiation process and reduce the cost.

In commercial negotiations, usually the seller first proposes a price, and then the buyer decides whether he can accept it.If he does not accept it, he can offer a price he can accept, or wait for the seller to adjust the price himself.But if the negotiation is indefinite, sellers lose many opportunities to sell more goods, and buyers lose access to new products.Negotiations cost both buyers and sellers a lot of opportunities, but they are still deadlocked in constant bargaining. This is because the interests of the two parties in the game are opposite, that is, the increase of one party's utility will damage the interests of the other party.In order to avoid losing both sides, they all hope to reach some kind of agreement.In this way, both parties need to weigh the bottom line of reaching an agreement and striving for a better result.

We often see this phenomenon: many people who are eager to buy something will always pay a higher price to buy what they need; while people who are eager to sell their goods are often used to selling their own things at a lower price. out.In view of this, many experienced people often show an unhurried, unhurried attitude when shopping in shopping malls and shopping. Even if they like things in their hearts, they will not show them in front of the seller. .In fact, these practices are closely related to game theory.Because when the multi-stage game of negotiation is an even-numbered stage, the second bidder has a "late-moving advantage".

As opposed to non-zero-sum games, zero-sum games are a concept in game theory and belong to non-cooperative games, which means that under strict competition between the parties participating in the game, one party’s gain will inevitably mean the other party’s loss, and the gains of all parties in the game and The sum of losses is always zero.The result of a zero-sum game is that one party eats the other, and what one party gains is exactly what the other party loses, and the interests of the whole society will not increase by one point.

6. Why can a fortune teller be able to "see the future"-strategic deception
There is a fortune teller in the local area who is regarded as a god by many people because of his good luck and fortune and deduction of cause and effect.In order to get the protection of the gods, many people will pay him a high fortune-telling fee when they come to ask for divination.In a blink of an eye, it was time to go to Beijing for the exam again. On this day, three scholars came to the fortune teller and asked him to help them calculate a divination.

The fortune teller, who had been resting with his eyes closed, understood what they were coming for. He didn't even open his eyes. He just stretched out a finger and waved it in the air, without saying a word.This time, the three scholars were completely dumbfounded.

"Sir, which of the three of us can pass the exam?" After calming down, a scholar asked eagerly.However, the fortune teller still stretched out his finger as before, without saying a word.The three scholars considered that the secret might not be revealed, and it was inconvenient for the fortune-teller to explain, so they left with doubts.

At this time, a little boy who had been following the fortune teller asked him curiously: "Sir, who among the three of them can win?"

"It doesn't matter whether it is successful or not, or how many of them can be successful, I have already mentioned it." The fortune teller said with confidence: "One finger can indicate that one of them is successful, or it can mean that only one of them is not successful. It means that all three people won the election, of course, it can also mean that none of them won the election.”

Xiaotong suddenly realized.

In the above story, the fortune teller summed up the four endings of the exams for the scholars with a gesture.It can be seen from this that it is not that the fortune teller has any magical powers, but the clever application of the strategic deception we talked about in game theory today.

The basis of strategic deception, when the game participants are well aware of their own and the opponent's strengths and weaknesses, they will often find ways to use the information they have, and use their weaknesses as the focus of breaking through the opponent's defense.In this way, the basis for strategic deception is formed.

(End of this chapter)