Evolutionary Dynamics Analysis Of Three-strategy Game Models

The field of evolutionary game dynamics combines game theory with differential e-quations to simulate Darwin's evolutionary theory of "natural selection,survival of the fittest”through the competition between strategies.This article focuses on the evolu-tionary dynamics of several types of three-strategy game models,where three-strategy refers to each player having three strategies,or a species has three phenotypes.The rock-paper-scissors(RPS)game,as a classic model of the three-strategy cycle-dominated game,widely exists in biological systems.Based on this game,this paper first establishes a Logit equation with a reverse-cycle-mutation,analyzes the stability of the system,and obtains the critical value of Hopf bifurcation.Then,a dynamic model with global mutation and Logistic growth function is constructed.According to the bifurcation theory,the conditions and direction of Hopf bifurcation are obtained.The study find that under different parameter conditions,the three strategies of R,P,and S have two evolutionary results:periodic oscillation and stable coexistence.Secondly,a model of trust game with punishment and mutation is established,the equilibrium of the system is determined,and the impact of punishment and mutation on the game are analyzed.The results show that appropriate punishments and mutations enable the trustworthy people to survive and help to get out of crisis.Finally,the strategy of bully is introduced in snowdrift game.A three-strategy snow-drift game model is established,and the evolution process of the model is analyzed using imitation equations.The complex cost divides the system into three states,namely coex-istence of defection and bully,coexistence of cooperation,bully and defectors,coexistence of cooperation and defection.