| Based on participants in Cournot game can whether achieve cooperation according to tit-for-tat mechanism in repeated games,this thesis builds a cooperative model dynamic system with time delay for Couront duopoly game,which aimed at the problem of dynamic output decision-making of players in oligopoly market with incomplete information and time delay structure.What’s more,dynamic features and properties of policymakers’ strategy-making have been analyzed.Firstly,We consider the duopoly game model with players with cooperative intention and a time delay structure.The model assumes that players with cooperative intention consider the dynamical adjustment method according to the tit-for-tat strategy and time delay.We establish the the corresponding dynamic system of cooperative model to analyze whether the participants in the model can achieve cooperation,and consider the effect of time delay on the cooperation of participants.The instability of three boundary equilibrium is shown and the conditions for the local stability of the interior equilibrium which is Pareto optimality are obtained by Schur-Cohn Criterion.Numerical simulations are done for different kinds of dynamical behaviors such as bifurcation diagram,phase portrait,stability region and convergence speed,the complicated dynamical behaviors of system show what influence the model parameters including the delay weight.Numerical simulation shows that delay weight,which reflect the decision-making for participants,have great influence on the stability and complexity of the system.A moderate delay can increase the system’s stability.We can see some complex behaviors such as bifurcation and chaos,when the weight is too low or too high.It also shows that a proper delay weight may make the firms more likely to achieve cooperation.Secondly,in order to control the chaotic behavior generated by the system,we add feedback control to this model and establish a chaotic control system.Numerical analysis shows that the chaotic behaviors of the system can be stabilized by the time-delayed feedback control,but different time delay values play different roles onthe system control ability,the proper delay has more influence on the system control. |
