Dynamics Study Of Bounded Rational Game Model With Time Dela

Bounded rationality is a hot topic in game theory,economics,management and psychology,and it is also a very important research field.It is a concept more in line with reality than complete rationality.Under the condition of bounded rationality,this paper studies the evolutionary game model with time delay.This paper mainly studies the following three problems:The first is the research of the dynamics of the single-population three-strategy game model with discrete distributed time delay.Firstly,two kinds of fixed delay models with off-diagonal delay and full delay are constructed on the basis of the replicator equation,and the replicator equation with multiple discrete distributed delays are obtained.Secondly,we first discuss the case with one fixed delay,and the conditions for the asymptotic stability of the interior equilibrium point are obtained by using the relevant theorem of Hopf bifurcation in dynamics.Thirdly,multiple delay cases are discussed on the basis of one delay.The method can be extended to any multiple delay cases.Finally,rockpaper-scissors game is taken as an example for numerical simulation,and the simulation results are analyzed theoretically.The second is the research of the dynamics of a single-population three-strategy game model with continuous distributed time delay.Firstly,the concept of continuous distributed delay is introduced to obtain the replicator equation with continuous distributed delay.Secondly,considering that the probability density function of delay is kernel function,and the conditions for the asymptotic stability of the interior equilibrium point are obtained by using Routh-Hurwitz stability criterion in dynamics.Finally,the theoretical method is applied to a concrete example,three-strategy snowdrift game,and then using MATLAB to carry out numerical simulation.Third,the dynamics of two-population three-strategy game model with two fixed time delays are discussed.Firstly,a replicator equation with two delays is constructed by introducing delay in population and delay between populations.Secondly,we obtain the conditions for the asymptotic stability of the interior equilibrium point by using the correlation theorem of the existence of Hopf bifurcation in dynamics.Finally,the numerical simulation of rock-paper-scissors game is carried out by using MATLAB to verify the correctness of the theoretical results.