Social Equilibrium Existence Theorem Of Nash Equilibrium Existence Theorem And The Relationship Between

Game theory is the rational player of the conflict and cooperation between the mathematical model.Game theory has become mainstream economics.To study the market economy,the rules of market economy-based micro-economics,and to study the whole national or regional economic growth,the unemployment rate and the relationship between inflation and the economic structure adjustment and economic policy and management,economic operation mechanism and the impact on economic development-oriented microeconomics are wider application of game theory;in particular,in building a new industrial organization,regulation, competition policy in areas such as the use of non-cooperative game theory has made a lot of Success.The research and application of equilibrium in game theory promote economic development. Nash equilibrium of modern game theory is the most important solution concepts,Nash equilibrium for the modern game theory to the formation and development has laid a solid theoretical foundation.Nash equilibrium existence theoremâ… ,â…¡andâ…¢is a limited-based strategy game in a row Game different and the results prove that its methods are similar with it.Limited-game strategy to expand the hybrid game in a row is a game that Nash Equilibrium existence theoremâ… ,the strategy is limited in the type of game on the hybrid game for the expansion,that is,expansion of the hybrid game,at least there is a mixed strategy Nash equilibrium;at the same time mixed strategy related to the nature and the nature of the relevant consecutive game is the same,so Nash equilibrium existence theoremâ… andâ…¡Nash equilibrium existence theorem proof is the same as it;On the other hand,limited game-strategy game in a row and there is a mixed strategy Nash equilibrium is,they were mixed to expand its own game of pure strategy Nash equilibrium, the establishment of a mixed strategy of the game in a row and expect to pay in the definition of the functions of both linear,Which makes the player payment function in any other player on the strategy of its own strategy is to be concave,and thus on the Nash equilibrium existence theoremâ…¢and the narrative is also common to prove.How to build the relationship among the integrated Nash equilibrium existence theorem proved? The goal of this paper is trying to set up Nash equilibrium existence theoremâ… ,â…¡andâ…¢to prove their intrinsic link.The paper introduces the concept of game with constraint condition,and illustrates the-consistency of the corresponding and their extended games under games with constraint condition,and indicates that methods of proving Nash equilibrium existence theoremâ… andâ…¡are similar,and presents and proves the social equilibrium and its existence theorem.Using the social equilibrium existence theorem,it gives other proof of Nash equilibrium existence theoremâ… ,â…¡andâ…¢,and thus explains the relation to proofs of three theorems,and it provides one proof of Nash equilibrium existence theoremâ…¢and its corollary.