Study On Finite Population Evolutionary Game Theory

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. In this paper, considering the infinite hypotheses is inconsistent with the actual situation, we change the population size from infinity to finite; at the same time, because previous study of asymmetric game ignored same-type competition, this paper increases same-type competition.This paper uses the method of theoretical derivation and the MATLAB simulation based on 2×2 symmetric game,2×2 asymmetric game,3×3 symmetric game and 3×3 asymmetric game of the finite groups, and have done the research in four aspects. Firstly, we set finite population quantity as N and establish the replicated dynamic equation using evolutionary game; Secondly, we adopt mathematical analysis method of nonlinear differential equations and get the singularity, the stability and the necessary and sufficient condition of the replicated dynamic equation. Thirdly, we make the phase plane using MATLAB software. We verify the conclusion of theoretical derivation. The simulation results and theoretical derivation is consistent which proves the accuracy of the theoretical derivation. Fourthly, we compare finite population evolution and infinite population evolution. For the symmetric game, when the number of finite groups (N) tends to infinity, finite group can draw the same conclusion as infinite population. However, for asymmetric game, because of the addition of same-type competition, there are obvious differences between the stability condition of finite population and infinite population.