Evolutionary Game Theory And The Analysis Of Asymptotical Stablity For Investors In Security Market

Now,there are many irrational investors filled with the security market, which makes"the bound rationality"more realistic than"the complete rationality"of the classical finance theory. The noise theory broke away from restrict of idealized market state which had been the complete competition in the assumption of the efficient market. And studying the process of the investors'decision with the noise theory will let us know more about the rules of the market and it will be practiseful for not only the government and also the investors.It is well known that the shortcoming of the classical game theory is the requisition of the plays'rationality and as the development of the evolutionary game theory, the problem had been solved. The evolutionary game theory which gave up the assumption of the complete rationality reserched the process of the investors'decision on the premise of the bound rationality. But not all of the Nash Equilibriums are asymptotically stable. And the article will give the sufficiency-requirement factor of that the Nash Equilibrium is the asymptotically stable strategy of the evolutionary game theory by using the famous Lyapunov theory [19] in the differential equation, which will construct the basement of the theory for the followed model.The article will apply the the evolutionary game theory and build the single-population model with the rational and irrational investors in our security market being the players. Pursuiting the asymptotically stable strategy of the model, we obtain the asymptotically stable ratio of the rational and irrational investors and acquire the conclusion that the rational and irrational strategies should be compatible and the moderate noise is beneficial for the flowability of the market, by which we can give suggestions about policy to the market and government .