The world's funniest economics stories

Chapter 14 Game Theory Tricks (1)——
The economics that must be known in daily games
1. Why both prisoners are willing to go to jail - Prisoner's Dilemma
During the detection of a theft and homicide case, the police arrested two suspects.But seeing the closing time approaching, the two suspects always denied that they had killed anyone.Regarding the property found in the residence of the two, they all confessed that they found that someone had been killed, and then they took the sheep and stole things.In order to prevent the two from reaching a tacit understanding and forming an offensive and defensive alliance, the police decided to interrogate them separately.As long as one of the two confessed to the crime, the charges of the two people were proved.The two suspects were locked in separate cells and awaited arraignment one by one.

In the interrogation room, the police began to mobilize the two suspects to confess their guilt. Before that, the police also helped them clarify their situation and the choices they faced: if one of them pleaded guilty, the confessor would immediately Released, the other will be sentenced to 10 years in prison; if both confess the crime, they will each be sentenced to 5 years in prison; if both refuse to confess, due to the lack of evidence by the police, they will be charged with theft and sentenced to 1 year in prison .

In such a predicament, what choice will the two suspects make?Each of them will inevitably consider how to shorten their sentence to the shortest possible time, but they don't know what the other party will choose.

If you plead guilty and the other party denies it, you will be released; if you plead guilty and the other party also pleads guilty, both parties will receive a lower punishment.Considering this, in the end, both suspects chose to plead guilty.

The above story is about the "Prisoner's Dilemma" in game theory.When two people face the same situation, after rational thinking, both sides will come to the same conclusion, so the two suspects finally chose to plead guilty.

The Prisoner's Dilemma is a representative example of a non-zero-sum game in game theory, reflecting that the individual's best choice is not the group's best choice.Although the predicament itself is only a model, similar situations frequently occur in reality in terms of price competition and environmental protection.

The main idea of ​​the prisoner's dilemma is that although the prisoners cooperate with each other and are firm and honest, they can bring the best interests of all [acquittal], but in the case of unknown information, because betraying their accomplices can bring benefits to themselves [shortened sentence], and because the accomplice recruiting himself can bring him benefits, so betraying each other is contrary to the best common interests, but it is in their own best interests.

In the imperial society in ancient my country, although many officials did not know the theory of the prisoner's dilemma, they followed the wisdom of the prisoner's dilemma when deciding cases.

Li Deyu, who was prime minister twice, was a famous statesman in the late Tang Dynasty in my country.During Tang Jingzong's time, he tried a very difficult frame-up case in Zhejiang.In the process of handling the case, Li Deyu applied the wisdom of the prisoner's dilemma.

In a local temple, the current principal monk sued the former principal to Li Deyu's yamen on the grounds that he embezzled money for temple construction.In the initial simple investigation, Li Deyu and many of his staff knew that the former principal was wronged, but they could not find any clues to clear up their grievances. The evidence provided by the current principal is enough to convict the former principal.

We must seek justice for our ex-principal!Li Deyu, who was in a hurry and wise, finally came up with a good way, that is, to separate the monks who had been summoned with a completely unified caliber, and to ask them one by one.At the same time, during the interrogation process, he also gave each monk a piece of yellow clay and ordered them to squeeze out the appearance of the gold that he said he had seen and embezzled by the former master.

None of the monks who were questioned alone had expected such a hand, and the shapes of the gold they squeezed were naturally strange.As a result, the case of colluding with perjury to frame the former principal was completely clarified.

From the case of Li Deyu, we can also see that when the monks, as a cooperative group, insisted on not speaking up for the best interests of all, they were separated, and when the information was unclear, everyone showed their flaws.It can be seen that the prisoner's dilemma theory is widely used.

However, when applying the Prisoner's Dilemma theory, we must also pay attention to the fact that the results of the repeated Prisoner's Dilemma are different from those of a single occurrence.In an iterated prisoner's dilemma, the game is played repeatedly so that each player has the opportunity to "punish" the previous player for his uncooperative behavior in the previous round.At this point, cooperation may emerge as an equilibrium outcome.

Thus, the incentive to cheat may now be overcome by the threat of punishment, which may lead to a better, cooperative outcome.

Game theory, also known as game theory, originated in modern mathematics and is also an important component of operations research. It has been widely used in economics today.

Game theory is that two people use each other's strategy to change their own confrontation strategy in an equal game to achieve the meaning of winning.According to Professor Robert, who won the Nobel Prize in Economics for his contribution to game theory in 2005, game theory is the theory of studying interaction strategies.

2. Why does the little pig take advantage of it——Smart pig game
There are two pigs, big and small, in the pigsty, and they eat in the same trough.In order to keep the feed fresh, there is a pedal on the other side away from the pig trough. Every time the pedal is pressed, 10 units of food will fall into the trough from the feeding port.

This design makes it possible for the big pig and the little pig, as long as one of them steps on the pedal, the other has a chance to eat the 2 units of food that fell in the trough first.In this way, before the big pig and the little pig eat each time, such a situation is formed:
If the big pig goes to the trough first before each meal, the ratio of the food eaten by the big and small pigs is 9:1; If the pigs go to the trough first, the ratio of big and small pigs eating food is 7:3.In this way, no matter which pig goes to step on the pedal, the little pig will eventually have the upper hand.

Therefore, the little pig prefers to choose to sit comfortably by the trough and wait for the food to fall out, while the big pig can only tirelessly rush between the pedal and the trough.

The story of the big pig and the little pig eating that we have seen is actually a model of the smart pig game that scholars demonstrate through assumptions.The result of this game is used by economists to explain a series of socioeconomic phenomena.Below we can make a specific analysis of this model.

Smart pig game.In fact, the reason why the little pig chooses to wait and let the big pig step on the pedal can be explained as follows:
If when the big pig chooses to act, the little pig also chooses to act, then the little pig can get 1 unit of net income, that is, it will consume 3 units of cost while eating 2 units of food; and if the little pig chooses to wait, then For a net gain of 4 units, waiting is better than acting.

If the big pig chooses to wait and the little pig chooses to act, then the net income of the little pig is -1 unit, and the income will not cover the cost; and if the little pig also chooses to wait, then the cost of the little pig is zero, and the income is also zero.

Why does the piggy act?
The basis of the game between the big pig and the little pig is that both parties are in the same situation, and it is difficult to get rid of it for a while, and one party must pay a price in exchange for the interests of both parties.Once one of the parties has enough ability to break such a situation, for example, if the little pig grows into a big pig, this coexistence will collapse and cease to exist.

In the smart pig game, no matter how you choose, the little pig always takes advantage, while the big pig always suffers from exhaustion.This seemingly unfair situation, viewed from the perspective of economics, can be understood as: Whoever has more resources must assume more obligations.

For this explanation, we can understand it through a classic fragment in "The Romance of the Three Kingdoms".

The Battle of Red Cliff is one of the famous battles in Chinese history in which a lot was won with less.In 208 A.D., facing Cao Cao's 20 troops lying on the north bank of the Yangtze River, Liu Bei and Sun Quan, who had a huge disparity in military strength, formed an anti-Cao alliance in order to jointly fight against Cao's army.At that time, Liu Bei had only ten thousand troops.

In this battle, Huang Gai, Zhou Yu's general, feigned surrender to Cao Cao, and drove 10 warships full of oil-soaked hay into Cao Ying. of chaos.

Cao Jun, who suffered heavy casualties, was pursued by Zhou Yu, and Cao Cao, who had lost his power, finally led his army back.After this battle, Liu Bei, who was the weakest, won the greatest victory.

In this famous Battle of Chibi, we can clearly see that Sun Quan's army played the role of "big pigs", while Liu Bei's army played the role of "little pigs".In a normal battle, it was Sun Quan who was really involved and fighting head-on, so it was Sun Quan who made great efforts, but Liu Bei took the biggest victory.

There is no gain from more effort, and less effort will take advantage of it to a certain extent.It can be seen that the Battle of Chibi is actually a game.

Knowing the game of smart pigs, in real life, we should pay attention to distinguishing the situation when we encounter problems, and strive for the most convenience for ourselves according to the principle of least risk and greatest benefit.

Nash equilibrium, also known as non-cooperative game equilibrium, is an important term in game theory named after John Nash.Assuming that there are n players participating in the game, given the strategy of others, each player chooses his own Nash equilibrium optimal strategy [the individual optimal strategy may or may not depend on others' strategies], thereby maximizing their own interests.All player strategies constitute a strategy portfolio.

Nash equilibrium refers to such a strategic combination, which is composed of the optimal strategies of all participants.That is, given the strategy of others, no one has enough reason to break this equilibrium.Nash equilibrium, in essence, is a non-cooperative game state.

When the Nash equilibrium is reached, it does not mean that both players in the game are in a state of motion. In the maintenance game, this equilibrium is achieved in the continuous actions and reactions of the players.Nash equilibrium does not mean that both sides of the game have reached an overall optimal state. The prisoner's dilemma above is an example.

3. Why does the beggar want $1 instead of $10—repeated game
On the street, there was a beggar who often had nothing to eat and a little boy who looked less than 6 years old.Because there is no one to take care of him, the taciturn little boy is always considered a silly boy by the townspeople.Once, a man joked with him by putting a 1-dollar bill and a 10-dollar bill in front of him and asking him to pick whichever he chose.The little boy looked and picked a $1 bill.This move made people laugh, and they all laughed and called the little boy a "little fool".

This matter spread quickly in the local area, and many people came to see this "silly boy" with great interest, and brought him $1 and $10 banknotes for him to choose.Each time, the little boy would take the $1 instead of the $10.

Once, another person offered money for the little boy to choose. Looking at the others laughing, a woman looked at the little boy very pitifully, so she asked him: "Don't you really know which one is more valuable?" The little boy said : "Rich people, of course I know, but if I take a $10 bill, they will never put money in front of me again, so I won't even get a dollar."

In the story, the seemingly silly and ridiculous little boy is actually "taking advantage of a small loss", isn't he?Although the little boy is still very young, his approach has already applied the theory of repeated games unconsciously.In the final analysis, in fact, the smartest is this child.If a certain cooperation may be a loss from a local perspective, but it has a great effect on the overall development, then this loss is worth it.

Repeated game is a special game in which the game with the same structure is repeated many times, even infinitely.Among them, each game is called "stage game".In each phase of the game, players may or may not act simultaneously.Because the history of past actions of other players is observable, each player in a repeated game can make the strategy he chooses at each stage depend on the past actions of other players.

The definition of the repeated game can be specifically understood in this way.For example, in the story of the little boy, we can see that from the very beginning, the little boy only wanted 1 dollar and was dubbed a little fool. The little boy kept repeating the same pattern.That is to say, as long as the little boy does not tell the truth and let the person concerned understand the purpose of his choice, then the little boy can always rely on his usual method to face many participants who come to see "fools".And every time the little boy faces a participant who comes to see the fool, it can be called a "stage game".

Also, with regard to repeated games, we need to note that repeated games simply mean that the game of the same structure is repeated many times.If, like the little boy, the game is repeated many times, the participants may choose different equilibrium strategies by sacrificing some immediate interests for the sake of long-term interests.And when the game is played only once, each participant only cares about a one-time payment.Therefore, the number of repeated games will affect the result of the game equilibrium.

Regarding the one-time repeated game, here is also an example that can help us understand.

It is recorded in "Xiaoxiaolu" written by the Qing Dynasty that a man went to a barber shop to shave his head, and the lazy barber shaved his head hastily.Although the barber was in a bad mood for this, but after thinking about it again, he paid the barber double the price in the end.

More than a month later, the shaved man came to the barber shop again.It was the same barber who received him last time.In order to earn some extra money, the barber decided to shave the head of this generous guest.This time, he shaved very carefully.Seeing the busyness of the barber through the mirror, the barber was full of pride.

When the head was shaved, the barber got up, but only paid half of the price to the barber.Seeing the angry face of the barber, the barber said, "I paid you the money for today's shaving last time, and the money I give today is the last time's shaving fee." After finishing speaking, he left.

This story shows that when the number of times a game occurs is limited, as long as the end of the game is approaching, the possibility of non-cooperative strategies will increase for the two players in the game.In the story, after seeking justice for himself, the shaved man would naturally never come to this barber shop again, so he chose a non-cooperative strategy.Today, because of the existence of a large number of one-time games, many uncooperative behaviors have been triggered.

(End of this chapter)