A Kind Of Strategy Dominant Problem Of Stochastic Evolutionary Game

The study of finite population is an important direction of evolutionary game theory.We can study it by many ways,including inclusive fitness,Price equation,fixed probability,Moran process and so on.Different populations have different structures.Some are homogeneous,while the others are heterogeneous.Most of the current studies have focused on homogeneous population structures,and heterogeneous populations have received less attention because of their complexity.In addition,compared with the two-player and two-strategy games,there are relatively fewer models and results for the multi-player games and multi-strategy games.But in real life,these games are more common,so it makes sense to study them.The first chapter introduces the research background,preliminary knowledge,research progress and the structure of this paper.The second chapter discusses the inclusive fitness of the finite heterogeneous metapopulation.Firstly,we present the model of heterogeneous metapopulation.We add the reproductive value to the nodes to get the fitness of each individual and each node.Then,the new Price equation is calculated based on the characteristics of the metapopulation.Also,we obtain the average frequency change of the specific genotype(strategy)and the expression of the inclusive fitness.Finally,through comparison,the conditions conducive to the evolution of the specific genotype are discussed.The third chapter discusses the dominance of the strategy in evolutionary three-player game with multiple strategies in finite population.It is mainly based on Moran updating process and "Coalescence" theory to calculate the frequency change of one of the multiple strategies.Comparing the frequency changes with 1/n,we can get the conditions of strategy dominance.The fourth chapter is to study the evolutionary dynamics of multi-player game with two strategies.Based on the Moran process and the multi-player game model,we calculate the fixed probability and then obtain the dominant condition of the specific strategy.Finally,the results are applied to three different game models,and we discuss the dominant strategy in each game respectively.The fifth chapter summarizes the thesis and points out the direction of further study.