On Study Of Strategy Dominance In Evolutionary Games Under The Weak Selection And Mutation With Moran Process

In this thesis, based on evolutionary game theory, we study some evolutionary games in finite mixing populations by applying the method of stochastic process. Firstly, under strategy mutations, a weak choice rule and Moran process, the dominance of strategies in a finite population game is considered. We mainly discuss some evolutionary outcomes in a game of two strategies (A, B) under two learning mechanisms, i.e., innovative learning mechanism and imitative learning mechanism. Then, by applying an embedded chain approximation method and by introducing a total variation measurement, we study the approximation of invariant distribution in a finite population game with strategy mutations.This thesis includes three chapters. Its main contents and results are summarized as follows.Chapter1gives introduction.In Chapter2, we study the dominance of strategies in a finite pop ulation game under strategy mutations, a weak choice rule and Moran p rocess. It shows that the strategy dominance is related to the game pay off matrix and the number N of population:In creative learning model, the strategy A dominates B if and only if and when N>>0, A is adventure dominant if and only ifa+b> c+d.In the i mitation learning model, strategy A dominates B when and N>=6.In Chapter3, by the use of perturbation theory, we study how small mutation rates can ensure embedded chain good approximation to the original Markov chain. It shows that a given error μ, there is a critical value of mutation rateε/(IC1+C2I+C1)such that dTV(φ(ε)φ(0))≤μ.