Analysis Of The Dynamical Duopoly Game With Heterogeneous Players And Time Delay

In this thesis, two kinds of models for the duopoly games with heterogeneous players and time delay are discussed. One considers the duopoly game with heterogeneous players and a kind delay structure. Another one considers two different time delay structures for the duopoly game with heterogeneous players.Firstly, we consider the duopoly game with heterogeneous players and a kind delay structure. It is assumed that one player adopts adaptive adjustment method and another one considers the dynamic adjustment method which according to the delayed structure on marginal profit. A nonlinear dynamics system is built for the models, and theoretic and numerical stability analysis is done for it. It is demonstrated that time delay play an important role in the system stability, the intermediate delayed rationality can delay the occurrence of complicated behaviors and promote the system stability. The numerical simulations also show that the system may lose stability through a period-doubling bifurcation or a Neimark-Sacker bifurcation.This thesis also consider heterogeneous players and two different time delay structures for the duopoly game model. In this model, it is assumed the heterogeneous players make their adjustment strategies by the different delayed structures and delayed information. One player makes decision via the delayed structure of the marginal profit. another one is assumed to adjust strategy according to the delayed structure of the price. A nonlinear dynamics system is built for the model, theoretical and numerical analysis are done for the dynamics of the system. We show that the time delay for the marginal profit has more influence on the dynamical behaviors of the system while the market price delay has less effect, and an intermediate level of the delay weight for the marginal profit can expand the stability region and promote the system stability. Numerical simulations show that the system may lose stability due to either a period-doubling bifurcation or a Neimark-Sacker bifurcation. It is also shown that the chaotic behaviors of the system can be stabilized by the time-delayed feedback control, and the two different delays play different roles on the systemcontrollability: the delay of the marginal profit has more influence on the system control than the delay of the market price.The analysis results of the thesis show that the time delay for the market price has less effect on the system. A similar conclusion about the time delay for the marginal profit and the system loss stability can be found in the analysis results of the two different models. It is shown that time delay play an important role in the system stability, an intermediate delay weight for the marginal profit can delay the occurrence of complicated behaviors and promote the system stability. It is also shown the two systems may both lose the stability through a period-doubling bifurcation or a Neimark-Sacker bifurcation.