Evolution Dynamics For One Kind Of Random Game Based On Moran Process

Moran process is a stochastic evolutionary model for studying the selection process of finite population and an important mechanism for individual renewal of strategies in evolutionary game theory.Weak selection is an important concept in biology.Under the premise of weak selection,we can get results that are not available in general situations.Therefore,it is of practical significance to establish a suitable mathematical model based on Moran process and analyze the relevant results under weak selection to explain the phenomena of biological evolution.In the first chapter,we mainly introduce the background,preliminary knowledge and the main work of the article.In the second chapter,we consider a stochastic co-evolution model of n-strategy game of the two populations with both internal and external games.Firstly,we obtain the expected return of individual under parameter control,analyze the evolutionary dynamics of the two populations by mutation-selection Moran process,and obtain the general formula of the equilibrium frequency of the strategy under neutral selection and weak selection.Then,we discuss the joint equilibrium of the strategy combination and analyze the conditions of parameters value that the parameters need to satisfy when the equilibrium frequency of the strategy combination is larger or smaller 1/ N.In the third chapter,we discuss the evolutionary dynamics of the strategy under kin selection,introduce the model of kinship game into the group evolution process,and get the new income matrix of individual game.Based on the Moran process update mechanism,we calculate the fixed probability of the strategy,and discuss the situation that the evolution process of group selection includes individual migration and does not include individual migration,and analyze the conditions to be satisfied of the correlation coefficient when it is conducive to the evolution of a certain strategy.In the fourth chapter,we discuss the strategy limit distribution and properties of discrete stochastic processes.Firstly,we consider the limit distributions of two strategies under small mutations based on Moran process.Then,we give the limit distributions of three strategies by using embedded Markov chain method base on Fermi process.Finally,we study the approximation properties of embedded Markov chains obtained by mutation-selection Moran process to the original Markov chain.The fifth chapter presents the conclusion of the thesis and the topic for further study.