| 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. |
