Chapter 449

Game theory, I'm afraid many people are familiar with this term.

Its history is no longer verifiable, but as a kind of mathematical operations research method, it has formed a mature set of laws that have been applied to economic and trade wars with the continuous changes of the times.

For example, the Nash equilibrium in the non-cooperative game, the Akerov commodity market theory in the incomplete information market game, etc.

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

Therefore, after thinking about it for a long time, Cheng Nuo decided to use the method of game theory to solve this problem.

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

In a typical game competition, the necessary factors of a typical game market are the necessary factors for the necessary participants, the rational assumptions of various countries, the optimal choice to ensure the maximization of benefits, the constraints of the game, the importance of the information-based game, and the optimal choice to form a strategy set under certain compromises by all parties.

The main participants in the international futures market are financial institutions that buy and sell through strategies formed through speculation under the agreement of the international futures market with information as the axis of information.

On the other hand, the futures market is a typical "zero-sum game".

What is a zero-sum game?

As you can see from the name, a zero-sum game is a zero-sum game in which the gains of all parties add up to zero, i.e., the gain of one party is equal to the loss of the other. A typical futures market is generally a "zero-sum game", where when the price of futures rises, when the price rises, the long side will make a profit, and the short side will suffer a loss, and vice versa.

Finally, the gaming market is an information-oriented market. In other words, there is information asymmetry in the futures market.

Knowing these three points, the rest of the stuff is simple.

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

When the two saw that Cheng Nuo had already started writing, they stopped thinking and their eyes fell on the formula written by Cheng Nuo.

Cheng Nuo's method of operation is very simple.

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

Next, the formula is calculated according to the difference between the four aspects of capital and credit degree (credit status), information and decision-making.

Moving his wrist, muttering for a few seconds, lowering his head, Cheng Nuo wrote on the paper:

[Let P0 be the buy price and P1 be the sell price, and the price P and the circulating quantity are generally monotonically increasing but concave functions, that is, P'(Q)>0, P''(Q)1) in the futures market, the return function of the nth large country is:

R(Qm)=Qa(Pt(Qm)-P)

Pt (Qm) is the price represented by the nth large country in the market, Qm is the sum of the trading volume of all large countries, and the trading volume is set to Qa when the ith large trader's profit is maximized. According to the maximization condition, there is the following equation:

αRa/αQa=Qa*Pt'(Qm*)+Pt(Qm*)-P0=0.】