Chapter 449: 0-sum game

Chapter 449
Game theory, this term is probably familiar to many people.
Its history cannot be verified, but as a method of mathematical operations research, with the continuous changes of the times, a set of mature rules has been formed and applied to economic and trade wars.
Such as the Nash equilibrium in the non-cooperative game, the Akerov commodity market theory in the incomplete information market game and so on.
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, the game between countries in the futures market is a typical game competition.
In a typical game competition, the necessary participants, the rational assumptions of countries, the optimal choice to ensure the maximization of benefits, the constraints of the game, the importance of the information game, and the optimal choice formed by the parties to a certain compromise are a typical game. Necessary factors of the market.
The main participants in the international futures market are financial venues where countries use information as the axis and form strategies through speculation under the agreement of the international futures market to buy and sell.
Another point, 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 gains of all parties in the transaction add up to zero, that is, the gains of one party equal the losses 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 game market is an information-oriented market. In other words, there is information asymmetry in the futures market.
Knowing these three points, the rest is very simple.
Denton and Qiaoya are still figuring out how to link game theory with the futures market, but Cheng Nuo here has taken pen and draft paper to verify his ideas.
Seeing that Cheng Nuo had begun to write, the two ended their thinking, focusing on the formula in Cheng Nuo's pen.
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-(cost of capital + transaction costs).
Next, calculate the formula based on the differences in the four aspects of funding and credit (credit status), information, and decision-making.
Move your wrists, ponder for a few seconds, lower your head, and Cheng Nuo wrote on the paper:
[Suppose P0 is the buying price, P1 is the selling price, the price P and the circulating 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 amount of speculation in the futures market. Exceeding the critical trading volume, the price rises again is a "bubble price". When there is only one major trading country in the futures market, that country can control the market price, and the maximum profit is solved at this time:
(Q1)=PQ=(Pt(Q1)-P0)Q1
The formula represents income, Pt represents the current futures market price of the big country in the process of reselling, and P0 represents the purchase price of the futures market. 】
…………
Cheng Nuo listed formulas under the adoring eyes of Denton and Joe Ya.
On the other side, the group of bigwigs sitting in the front three rows of the auditorium did not forget the purpose of this trip, and got up and got together in twos and threes and walked towards the back row.
The reason why they came to watch the last game was not to simply come over as a mascot and announce the result after sitting for a few hours.
The more than forty students here are among the top talents in the mathematics circles of the two countries.
The bigwigs also want to know what kind of strength the fresh blood of this group of countries can show.
Hearing is worse than seeing.
So everyone intends to personally observe the process of everyone solving the problem.
Director Alding and the other two old men gathered together and walked back.
It is certainly not an ordinary task to be able to get together with Director Ordin. The other two elderly people, one is the deputy dean of the Mathematics Branch of the Royal Academy of Sciences of England, and the other is the dean of the School of Mathematics of the University of Bonn in Germany.
The two people's status is no weaker than Ording, the director of the Cambridge University Institute of Mathematics and Physics.
At the same time, these three are also the three with the highest status among the guests here tonight.
Among the fifteen teams, the University of Cambridge sits relatively late.
The three old men first walked to a small group of three at the University of Bonn.
The three doctoral students from the University of Berne completed the division of labor after intense discussions. They adopted 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 modeling idea is relatively simple, and it takes half the time compared with the conventional method. It's good, good." Ording first judged.
The deputy dean of the Mathematics Branch of the Royal Academy of Sciences next to him stroked his beard and nodded again and again, "Safe and innovative, Fendi, you have taught a group of good students!"
Fendi, Dean of the School of Mathematics at the University of Bonn, also two old friends spoke highly of their students, and they also felt proud, "Haha, although the three of them were not trained by me, these three The reputation of our school is quite high, and such performance can be considered as not falling into their reputation."
Dean Fendi turned his head to look at Augustin, "Augudin, I heard that the three students from Cambridge University performed very well in this exchange event. Why don't we go and take a look?"
"Of course." Alding looked around in the auditorium, found the position of Cheng Nuo's three, and pointed to the two old people, "It's over there, let's go and take a look."
After speaking, he walked slowly to the three of Cheng Nuo.
Cheng Nuo and others are still writing by Cheng Nuo alone. Denton and Joya are staring at ~EbookFREE.me~ and no one speaks, except for the rustle on the paper.
Seeing the working status at Cambridge University, the three of Alding were a little confused.
However, after seeing Cheng Nuo's formula on the paper, he quickly immersed himself in it.
Cheng Nuo didn't know that there were three big guys staring behind him, still writing at his own pace:
[When there is only one big country in the market, the big congress acquiesces to achieve a reasonable maximum trading volume, and raises the price to a critical price to make the largest 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 return function of the n-th big country is:
R(Qm)=Qa(Pt(Qm)-P)
Pt(Qm) is the price represented by the n-th big country trading in the market, Qm is the sum of all the big country's transaction volume, and the i-th big country's transaction volume is set to Qa when the profit is maximized. According to the maximization condition, there are the following equations:
αRa/αQa=QaPt\'(Qm)+Pt(Qm)-P0=0.】