Research On Stochastic Evolutionary Game Dynamicsand Its Application

Evolutionary game theory is the combination of classical game theory and evolutionary biology. As one of the most important evolutionary game theory models, Replicator equation is based on deterministic infinite population. Then random evolutionary theory was came up in consideration of the random of the game theory. Random evolutionary game theory has formed a scientific theory system after30years of development. As the very important model in random evolutionary theory, Moran model and Wright-fisher model have been studied widely.This paper made quantitative and qualitative analysis of detailed and thorough by using the method of combining random evolutionary game analysis with simulation analysis. Firstly, considering that all of the studies of traditional Moran model focus on weak selection and non-weak selection is still a blank field which is more realistic compared with weak selection. Therefore based on the three cases of dominance, stability and coexistence, this paper studies on the non-weak selection and obtains a stable solution under non-weak selection conditions through a lot of experiments. Secondly, replicator equation is improved to be more realistic in this paper to eliminate the limitation of infinite population;2×2symmetrical evolutionary game can be used in a finite population. Finally, to analyze and understand the characteristics of the models of stochastic evolutionary game more deeply, Moran model and Wright-fisher model are compared with dynamic replication model in four cases of dominance, stability, coexistence and neutrality. The comparison concludes that the Wright-fisher model is more quickly than the Moran model. Meanwhile this paper uses Moran model, Wright-fisher model and dynamic replication model to analyze and simulate some classical game theory examples.