universal data

Chapter 446 Zero Sum Game
449 chapter

Game theory, this term is probably familiar to many people.

Its history cannot be verified, but as a kind of mathematical operations research method, with the continuous changes of the times, a set of mature rules has been formed, which is applied to economic and trade wars.

Such as Nash equilibrium in non-cooperative games, Akerrov commodity market theory in market games with incomplete information, etc.

Similarly, for the international futures market, game theory can still exert its powerful capabilities.

Therefore, after a long time of thinking, Cheng Nuo decided to use game theory to solve this problem.

First of all, the game among countries in the futures market is a typical game competition.

In a typical game competition, the necessary participants, the rational assumptions of each country, the optimal choice to ensure the maximum benefit, the constraints of the game, the importance of the information game, and the formation of a strategy set by the optimal choice under certain compromises by all parties are typical games. Necessary factors of the market.

The participants in the international futures market are the financial venues where various countries take information as the axis and form strategies through speculation under the agreement of the international futures market to buy and sell.

Another point is that the futures market is a typical "zero-sum game".

What is a zero-sum game?

As can be seen from the name, a zero-sum game means that the sum of the gains of all parties is zero during the transaction process, that is, the gain of one party is equal to the loss of the other party.A typical futures market is generally a "zero-sum game". When the futures price rises, when the price rises, the long side will make a profit, and the short side will suffer losses, and vice versa.

Finally, the gaming market is an information-oriented market.That is to say, there is information asymmetry in the futures market.

Knowing these three points, the rest is very simple.

Denton and Joya are still thinking about how to connect game theory with the futures market, but Cheng Nuo here has already taken a pen and scratch paper to verify his ideas on it.

Seeing that Cheng Nuo had started to write, the two stopped thinking, and their eyes fell on the formula written by Cheng Nuo.

Cheng Nuo's calculation method is very simple.

Now that we know that the futures market is a zero-sum game, the income function can be simplified as: profit = income - cost = spread cost - (capital cost + transaction cost).

Next, calculate the formula based on the differences in the four aspects of funds and credit (credit status), information, and decision-making.

Stretching his wrists, pondering for a few seconds, then lowering his head, Cheng Nuo wrote on the paper:

[Assume that P0 is the buying price and P1 is the selling price. The price P and the circulation quantity generally present a monotonically increasing but concave function, that is, P'(Q)>0, P''(Q)<0. 】

[Assuming that Qmax is the maximum trading volume in the market, it represents the price corresponding to the maximum speculation volume in the futures market.The price increase beyond the critical trading volume is a "bubble price".When there is only one major trading country in the futures market, the country can control the market price, and at this time, the maximum return is solved:
R1(Q1)=P*Q=(Pt(Q1)-P0)*Q1
In the formula, R1 represents the income, Pt represents the current futures market price in the reselling process of a big country, and P0 represents the purchase price in the futures market. 】

…………

Under the adoring eyes of Denton and Qiao Ya, Cheng Nuo listed the formulas smoothly.

On the other side, the group of big guys sitting in the first three rows of the auditorium did not forget the purpose of their trip. After getting up, they gathered together in twos and threes and walked to the back row.

The reason why they came to observe the last competition was not simply to be a mascot and announce the result after sitting for a few hours.

The more than 40 students here are all the top talents in the mathematics field of the two countries.

The bosses also want to know what kind of strength this group of fresh blood from the country can show.

Seeing is worse than hearing.

So everyone planned to observe the process of solving the problem for themselves.

Director Aldin and the other two old people laughed and walked back together.

It is definitely not an ordinary task to be able to get together with Director Ordin. The other two old people are the deputy dean of the Mathematics Branch of the Royal Academy of Sciences in Yingguo, and the other is the dean of the Mathematics Faculty of the University of Bonn in Germany.

The status of the two is not weaker than Alding, the director of the Institute of Mathematics and Physics at the University of Cambridge.

At the same time, these three are also the three with the highest status among the guests who came to watch the game tonight.

Among the [-] teams, Cambridge University sits in a relatively late position.

The three old people first walked to the small group of three at the University of Bonn.

The three doctoral students of the University of Bern completed the division of labor after intense discussions. They used the method of mathematical modeling to further analyze and solve the problem by constructing a mathematical model of the international futures market.

The three of them stopped and watched for a few minutes, then walked back.

"Although the problem-solving method is conventional, the idea of ​​modeling is relatively clear, and it takes half the time compared with the conventional method. Not bad, not bad." Aldin was the first to judge.

The deputy dean of the Mathematics Branch of the Royal Academy of Sciences next to him stroked his beard and nodded again and again, "Sureness and innovation, Fendi, you have taught a group of good students!"

Fendi, Dean of the Faculty of Mathematics at the University of Bonn, also had two old friends who spoke highly of their students and felt proud, "Haha, although I did not train them, these three They are quite well-known in our school, so their performance can be regarded as not falling into their reputation."

Dean Fendi turned to look at Augustin, "Augustine, I heard that the three students from Cambridge University performed very well in this exchange activity, why don't we go and have a look?"

"Of course." Ordin looked around the auditorium, found the location of Cheng Nuo and the three, and pointed to the two old people, "It's over there, let's go and have a look."

After finishing speaking, he walked slowly to Cheng Nuo and the other three.

Cheng Nuo and the others were still writing by Cheng Nuo alone, while Denton and Qiao Ya were watching.No one spoke, and there was no other sound except the rustling of paper.

Seeing the working status of Cambridge University, the three of Ordin were a little puzzled.

But when he saw Cheng Nuo's formula on the paper, he quickly immersed himself in it.

Cheng Nuo didn't know that there were three big bosses staring behind him, and he still wrote at his own pace:

[When there is only one big country in the market, the big country will default to a reasonable maximum trading volume and raise the price to the critical price to earn the biggest price difference.When there are multiple big countries in the futures market, assuming that there are m big countries (m>1) in the futures market, the income function of the nth big country is:

R(Qm)=Qa(Pt(Qm)-P)
Pt(Qm) is the price represented by the nth big country in the market, Qm is the sum of the trading volume of all big countries, and the trading volume of the i-th big country is set to Qa when the profit is maximized.According to the maximization condition, there is the following equation:
αRa/αQa=Qa*Pt'(Qm*)+Pt(Qm*)-P0=0.】

(End of this chapter)