Research On Equilibrium Theory And Its Applications In The Economic Field

Game Theory is an extremely important theoretical subject in the economics and even the entire scientific community, which uses mathematical tools analysis socio-economic phenomenon, has obtained the substantial achievement. The gambling analysis's goal is forecasting a gambling equilibrium result. Therefore the equilibrium theory is the very important content in the game theory.This paper is based on the theory of Nash equilibrium to establish a multi-vendor Cournot model and analysis it, found manufacturers' production changes in this model. Some manufacturer, as they have different initial production, various manufacturers' output will achieve an equilibrium or appear fluctuation between two equilibrium after they adjust their production many times. This kind of fluctuation is called the cycle equilibrium. Because manufacturers' total initial production is different, this kind of cycle fluctuation's scope will also be different. And we have analysed this rule. This has the vital practical significance to each production profession.In this paper, the other elements include:(1) Game Theory is introduced, include the development of game theory, the major achievements in recent years and basic concepts.(2) We go on with the correlative theory in Nash equilibrium, the relation of Nash Equilibrium and General equilibrium, the defects and solutions in Nash equilibrium.(3) Next we study the Nash equilibrium in Cournot model, have analyzed the Nash equilibrium solution of the double Oligarch Cournot model under the different demand function condition and the different cost function.(4) In the last part we mainly introduce other two classical models in the game theory, Betrand and Stackelberg model. And the key point was promotion about Stackelberg model.