The general economic equilibrium theory is the central topic of mathematical economics. The question can be traced back to Adam Smith’s profound formulation of the problem using mathematical axiomatic methods under some assumptions with clear economic significance. By using Brouwer's fixed point theorem and Kakutani's fixed point theorem, the existence and optimality of the general equilibrium of the Walras economy were strictly proved, making the "invisible hand" a rigorous scientific system, and making economics form a Unified methodology and analytical framework. They won the Nobel Prize in Economics in 1972 and 1983 respectively. In recent years, the economic situation has undergone profound changes. The scale of production has expanded, monopoly power has strengthened, and people have to negotiate, cooperate, and bargain. But all of this is based on individual rationality and competition. As this competition intensifies, the confrontation, dependence and constraints of various strategies and interests have made game theory (mainly non-cooperative game (rather than the most important and core concept in cooperative game theory is Nash equilibrium) has reached its heyday. Based on its concepts, content, ideas and methods, it has and will continue to almost comprehensively rewrite economics, and will also be Wider application.

Von Neumann. This model actually assumes:

(1) For every player, all information is public *** , complete and symmetrical;

(2) Each player in the game is completely rational and can choose the most beneficial strategy for themselves in their respective strategy sets.

Yes In terms of application, the above two assumptions are too ideal and too harsh, because they require everyone in the game to be a god - omniscient and omnipotent. Therefore, for quite some time, research on game theory has been It is mainly the "patent" of mathematicians, and a large number of papers are mainly published in mathematics magazines. Economists have not shown much interest and enthusiasm, while mathematicians are always working hard day and night. Various theorems are constantly being improved and promoted.

The work of Harsanyi[7] and Selten[8] respectively proposed new ideas in these two aspects, greatly expanding the application of game theory (both of them Both are economists with mathematical backgrounds). Because of this, together with Nash, they won the Nobel Prize in Economics in 1994. [1] Gao Hongye. Western Economics (Micro Part 4th Edition) [M] . China Renmin University Press, 2007.

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[8] R. Selten. Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games[J]. Inter. J. Game Theory, 1975, (4):25– 55.

[9] Wang Zeke, Zuo Zaisi, Li Zhiqiang. Topological Methods in Economics[M]. Peking University Press, 2002.

[10] Zheng Quan. Economic Balance General theory and method of finding points[J]. Journal of Operations Research, 1986, 6 (5): 9–18.

[11] Zou Huiwen. An application of Kakutani’s fixed point theorem in mathematical economics [J]. 1996, 6, (25): 28–33.

[12] Yu Jian. Fixed point theorem and its application in economic equilibrium [J]. Journal of Guizhou University of Technology ( Natural Science Edition), 1988, S1.

[13] Yu Jian. Game Theory: Nash Equilibrium[J]. Journal of Guizhou University of Technology (Natural Science Edition), 2004, 10, (33): 1 –5, 19.

[14] Shi Shuzhong. Mathematical Problems of General Economic Equilibrium[J]. Practice and Understanding of Mathematics, 1986, (3).

[15] Deng Ying Han. Application of fixed point theory in economic equilibrium[J]. 2006 undergraduate thesis of Southwest University, 2010.