City: Me, IQ 300

Chapter 83 I think game theory is controversial (ask for support, fifth change)

Economics teacher, Liu Li, woke up in the morning and received a notice that Chen Fan would go to her class today.

Peking University did not know that Chen Fan’s students might exist, but the teacher did not exist.

“What, economics, didn’t this guy just end the Goldbach conjecture? Haven’t wanted to play for a while? He just made more than 20 million US dollars, don’t he know to enjoy it? ”

“I don’t know, but Chen Fan wants to listen to the game theory of economics.”

“That thing, it has not improved for many years, what is there to hear about this, I really don’t understand, is Chen Fan so boring?”

“I don’t know, you are ready to prepare.”

At this time, Liu Li looked at Chen Fan and said: “The three assumptions you said are official explanations, what are your superfluous ideas?” ”

“Absolute rationality, I think it is unreasonable, people have feelings, because of the existence of feelings, so this article naturally does not hold.”

“Why?”

“I don’t know how to explain it, so let’s start with an economic experiment.”

Economics experiments, also called economics games.

Liu Li came interested and said: “Not bad, not bad, Chen Fan, you have a certain understanding of game theory, you come, come up, you say, I will see.” ”

Chen Fan nodded and walked to the stage.

The ratio of men to women in the audience is five times that of girls as boys.

Everyone looked at this boy, that determined look.

“Would this man like girls?”

“Curious, really curious, very curious.”

“I always think that this person is like a robot.”

Chen Fan came to the stage and said: “There is an interesting game in economics, called Beauty Coin, teacher, I do it with you?” ”

“That I know, you and people who don’t know are more suitable to do this game.”

Chen Fan nodded.

A random girl was ordered to walk onto the stage.

A strange beauty comes up to talk to you and asks to play a game with you. The beauty suggested: “Let’s each show one side of the coin, positive or negative.” If we are all positive, then I give you 3 yuan, if we are all negative, I give you 1 yuan, and in the rest of the case you give me 2 yuan. “Sounds like a good proposition. If I were male, I would play anyway, but economics considerations are another matter, is this game really fair enough?

Chen Fan elaborated on the general idea of the game, and the teacher wrote down on the blackboard.

The girl was stunned for a moment, this game is indeed linked to economics, but where is the connection?

“What is this game?”

Chen Fan said: “This game itself is your absolute victory, I think this algorithm is not difficult.” ”

Countless people in the audience looked at Chen Fan.

Big brother, we have an IQ of three hundred, and we don’t think it’s difficult.

You can be clear.

Chen Fan sighed helplessly and said, “This is a simple probability calculation, why is it difficult?” Mathematical modeling, don’t you know? I remember there was an introduction in advanced mathematics. 、”

Teacher, you kill this Chen Fan, I understand, Chen Fan is here to pretend.

“Yes, it’s definitely to pretend, this guy, how to say it so seriously.”

“This game, we are still thinking about the weight ratio.”

Chen Fan helplessly took the chalk and wrote on the blackboard.

“Let’s say our probability of heads is x and the probability of heads is 1-x. In order to maximize the benefits, we should have equal returns when the opponent is positive or negative, otherwise the opponent can always change the probability of the positive and negative sides to reduce our total income, so the equation is 3x+(-2)*(1-x)=(-2)*x+1*(1-x)

This equation is colloquially said to be that the benefits you get when the opponent keeps coming out of the positive are the same and the greatest benefits that your opponent keeps coming out of the negative. Solving the equation yields x = 3/8, which means that on average 3 heads every eight times, 5 heads is our optimal strategy. By substituting x=3/8 into the income expression 3*x+(-2)*(1-x), you can get the expected income each time, and the calculation result is -1/8 yuan.

Similarly, let the probability of a beauty be y, the probability of a tail be 1-y, and the column equation -3y+2(1-y)=2y+(-1)*(1-y)

Solving y is also equal to 3/8, and the expected return of beauty each time is 2 (1-y)-3y = 1/8 yuan. This tells us that with both sides adopting the optimal strategy, the beauty wins an average of 1/8 yuan each time. In fact, as long as the beauty adopts the (3/8, 5/8) plan, no matter what plan you use, it cannot change the situation. If all positives, the expected return each time is (3+3+3+3-2-2-2-2-2)/8=-1/8 yuan

If all the opposites are true, the expected return each time is also (-2-2-2+1+1+1+1+1)/8=-1/8 yuan. ”

Writing and saliva were used together, and after Chen Fan gave the formula, everyone in the audience could understand it.

It turns out that it is expected to return, this understands, economics is taught.

The teacher said: “This in economics is called pricing weight interests, Chen Fan, where do you see?” ”

“In theory, I have read all the game theory, and I have also read the economics books, but I still don’t understand a single point.”

The teacher picked up the blackboard and began to wipe the blackboard.

“There is a reason why you chose me as your economics teacher, and what you think about is a topic I wrote about five years ago, what is the role of human feelings in economics.”

Chen Fan’s eyes lit up, standing aside, looking at Liu Li, this was the inspiration he needed.

“The prisoner’s dilemma, the students who are doing it know it.”

A student raised his hand and said: “I know, this is very famous, the police put the two in two different rooms for interrogation, for each criminal suspect, the policy given by the police is: if both suspects confess their crimes and hand over the stolen goods, then the evidence is conclusive, both are found guilty, each sentenced to 8 years in prison; If only one suspect confesses and the other does not confess but denies, the sentence for obstruction of official duties (for which there is already evidence of guilt) is increased by two years, while the confessor is commuted by eight years and immediately released. If both deny, the police cannot convict them of theft due to insufficient evidence, but they can each be sentenced to one year in prison for trespassing into a private house. 、”

The teacher nodded and motioned for the student to sit down.

“We need to know that these prisoners confess with feelings and deception, and the police themselves have feelings, and feelings are the core element that affects people’s judgment.”

“The Nash equilibrium indicated gives the theory that people will move in the direction of maximizing their own interests, but don’t forget that Nash has been fighting schizophrenia all his life.”

Everyone has actually understood this.

Liu Li said: “Today I was going to talk about game theory, in fact, I don’t expect you to understand, the historical game theory research is powerful, has won the Nobel Prize, but since Chen Fan talked about this, the following, I speak on behalf of my personal statement, not on behalf of the official answer of game theory.” ”

Everyone nodded, this is the teacher to take out the private goods.

“I did such a survey in the stock market, on the stock exchange side, the personnel in charge of operations, in the morning, the proportion of securities trading money is 28.4 percent, and in the evening, it drops to 28.4 percent; The amount is twenty-six point five, but by eight o’clock in the evening, it is raised to thirty-six point three, and the supplement of Nash equilibrium brings game theory to thirty-two. ”

Chen Fan nodded.

Liu Li continued: “However, this data is unstable, it is difficult to accept, mathematics, there is no such a probability of change, because the change, it means that the data is inaccurate, take the average, in economics is existing, but not desirable.” ”

Liu Li wrote a series of numbers and said: “For example, game theory in everyone’s cognition of the puff girl, there is a saying called wingman, right, in fact, this is also inaccurate, people for mate selection, there are many standards, if you contact girls according to game theory, then the final result is only mechanical communication.” ”

Chen Fan agreed.

Anna’s affairs benefited Chen Fan a lot.

Anna knew herself in advance.

Game theory itself ignores the influence of environmental and other factors, and finally causes the data to reach more than 50%, which is an embarrassing thing.

“Chen Fan, I know your research, you are looking for a coefficient, a coefficient that can be replaced by a group or a value space, to improve game theory, right?”

“Yes, I hope that the accurate value of game theory can be improved to more than fifty percent.”

Liu Li took out the blackboard to wipe, erased the text on the blackboard, and said: “Then I will give you such a one, remember, if you study that the washing reaches fifty percent, or sixty, don’t tell others, just know it.” ”

“Why?”

“Because, in that case, everyone is a stock god, then, in the end, the economy may collapse, you said before, your research may change the world economic pattern, this is right, not game theory can not reach a higher level, but cannot, if achieved, you can not share it, this is the rule, then, when you can’t share it, how do you explain that you have completed such a high numerical study?”

Chen Fan understood, it turned out that the answer was here.

Higher coefficients were discarded by everyone.

Even if you do research it, how do you say it?

You can’t say.

This may have taken into account the altruistic idea of mathematics.

And Chen Fan’s eyes were firm, and said: “I think, I can try, teacher, can you give me your data?” ”

That’s okay, but Chen Fan, I think what you’re dealing with now is the next question, how do you answer when others issue a war book on your math.” ’

ps: Please support, thank you all.