Research Of Equilibrium For Noncooperative Games On The Idea Of Behavioral Economics

After the development of Von Neumann, Morgenstern, Nash, game theory hasbecome a very mature and still potential research field, and play an important role ineconomics and social science. The equilibrium has been the focus of the game theory,but some definitions of equilibrium points were not very perfect in these model. Thereare development place according to the reality and the new development of thediscipline. Therefore, in this paper, the author focuses on the existence of equilibriumfor game theory. According to the new development of the discipline and reality, Iimprove and generalize several types of game theory model, define new equilibriumpoint, and prove the existence of equilibrium by mean of methods of mathematicaleconomics.This article mainly has several parts as following:The first chapter: In the actual problem, because of incomplete information, theperfectly rational or the uncertainty of the environment, there are uncertain parametersin the game model, and these players only know the variation scope of these parameters.Under the assumption that these players only know the variation scope of theseparameters， Combined the concept of Nash equilibrium of the classical pareto efficientsolution concept, Zhukovskii introduced NS—equilibrium for noncooperative underuncertainty. In this paper, the author continued to study the existence of equilibrium fornoncooperative under uncertainty. In this part, there are mainly the existence of weaklyPareto-NS equilibrium for multi-objective game under uncertainty, the existence ofequilibrium for multi-leader-follwer game under uncertainty, the existence ofNS—equilibrium for generalized games under generalized uncertainty, abstractrepresentations of games under uncertainty and the existence of Nash equilibrium fornoncooperative games under uncertain sets.The second chapter: Altruistic game has been the hot point of game theory.Altruism is put forward by by the great social scientists kong DE, who illustrate thealtruistic behavior by it. Therefore, altruism behavior is put forward as the opposite ofindividualism, and is the center of modern social psychology. In this section, I study theexistence of equilibrium for these games under the altruism. There are the existence ofslightly altruistic weakly Pareto—Nash equilibrium, the existence of altruistic stableequilibrium and the altruistic analysis on leader-follower games. The third chapter: Psychological guess and regret concept is the important contentof psychology. In the actual decision making problems, people often decide according topsychological guess and regret. Therefore, the author introduced the concept of regret tononcooperative games, and proved the existence of minimax regret equilibria.The fourth chapter: There is n person in the traditional non-cooperative gamemodel. Therefore, in this section, the author considered the existence of equilibriumpoints for infinite person noncooperative game. I prove the existence of weaklyPareto—Nash equilibrium and weakly Pareto—Berge equilibrium for infinite personmulti-objective game.The five chapter: Some applications are given according to above researchs.