Dynamics Of Trust Game And Cyclic Dominance Game

In recent years,using the theory of dynamics to study the evolution of game models is a hot topic in evolutionary game theory.As two important branches of evolutionary game dynamics,replicator dynamics and imitation dynamics are both effective tools to study the evolution of game models.Finite populations are a common prerequisite in real game problems.Therefore,it is also of great significance to study the evolutionary game dynamics based on finite populations.In this paper,the dynamic behavior of dynamical system corresponding to the trust game and three-strategy cyclic dominance game based on finite populations is investigated respectively.The main work of this paper can be divided into the following three parts.In the first part,the dynamic behavior of imitation dynamical system corresponding to the single community trust game with environmental feedback which is transformed between the truster and trustee is studied.Firstly,a single community trust game mathematical model with environmental feedback is proposed.Secondly,the stability of equilibrium point of the imitation dynamical system corresponding to the model is analyzed by special cases.In the end,the dynamic behavior of the imitation dynamical system corresponding to the single community trust game model is analyzed and the influence of the relationship of parameters on the model results of dynamical system is discussed by numerical simulation.In the second part,the dynamic behavior of imitation dynamical system corresponding to the two-community trust game with environmental feedback without mutual transformation between the truster and trustee is investigated.In the first place,a mathematical model for two-community trust game with environmental feedback is proposed.In the second place,the stability of all equilibrium points of the imitation dynamical system corresponding to the model is analyzed.In the third place,the influence of the relationship of parameters on the model results of dynamical system is discussed by numerical simulation.In the fourth place,the influence of delay on the dynamic behavior of the imitation dynamical system corresponding to the two-community trust game model is analyzed.In the third part,the dynamic behavior of dynamical system corresponding to the three-strategy cyclic dominance game is investigated in finite populations.First of all,a mathematical model for three-strategy cyclic dominance game is proposed.Secondly,the stability of dynamical system corresponding to the three-strategy cyclic dominance game model based on finite populations is compared with that of replicator dynamical system by numerical simulation,it verifies that there is a difference between them.