Research On Two Person Game System

Based on the ideas of input-output analysis theory,optimization analysis and game theory,aclass of two person game economic system with payment is introduced in this paper. Lied on theestablishment of input-output equations,two basic issues are proposed,namely,the existence andoptimization. First,appropriate semi-continuous and convex conditions are introduced,secondly,the existence of non-cooperative equilibrium is proved by applying Kakutani's fixed-point theoremand nonlinear analysis. Last but not the least,this paper makes some research on the conditionaloptimal problems with equilibrium of input-output model as a set of constraints. With the help ofnonlinear analysis and mathematical economics methods,relevant theorems and their economicsignificance are obtained.This article is devided into four parts:The first part briefly describes the research background and research status,as the ideologicalbasis of this paper,as well as additional information on the input-output analysis,the optimalapproach and game theory and other related content.In the second part,two person game economic systems with payment are considered,andseveral equilibrium theorems regarding these systems will be shown under some appropriateconditions of semi-continuous and convex,with the use of Kakutani's fixed-point theorem andnonlinear analysis methods.Under the conditions that the equilibria of the economic systems with two players exist, thethird part considers their maximum problems with the mathematical methods of conditionaloptimization in some appropriate assumptions.As a conclusion,the fourth part includs the results of this article,prospect andacknowledgements.