Based on the study of scholars, supposing that one of the two competitors in the market makes decision only with bounded rationality without delay, and the other competitor makes the delayed decision with one period and two periods, we established the dynamic price game models respectively. In this paper we mainly analyzed the stable points and their stabilities of the dynamic system with two-period delayed decision, and made computer simulations for the system stability under different decision rules and the complexity such as the bifurcations, chaos and so on. The numerical simulation results showed that, the delayed decision can not change the system's Nash equilibrium point, however it can improve the system's stability; the changes of delayed period and weights of delay variables will make the system's stability area change correspondingly; when the company make decision with delay, they should consider the introducing time. Because the proper delayed periods and weights of variables will obviously improve his competition advantages.
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