| In the study of the traditional Cournot oligopoly game,the supply quantity of products is assumed to be the decision variables for the firms.However in their infant stage of some emerging industries,due to their lack of investment accumulation,therefore they cannot form production competition among them.In this article,under the condition of two players with bounded rationality,we set up two delayed investment game dynamic models based on the producers making investment as decision variables,and then we analyze its dynamic properties.In the first model,one player only adjusts its investment decision based on the marginal profit of the current,while another player takes into consideration the time delay,and its decision is to arrange its investment that depend on averaging the previous and current marginal profit with different weights.Through the analysis of the stability of the system,we show that the boundary equilibrium is unstable and obtain the stability conditions for the interior equilibrium.To show how the stability of this system depend on the model parameters,numerical simulations are used to provide evidence.In the second model,two players have delay decision rationally and also adjust the investment strategy by the delayed marginal profit.To its corresponding discrete dynamic system,the existence and stability condition of equilibrium solutions are also investigated.And by using numerical simulation,it also shows the model parameters have an impact on the system stability.In this paper,the research of the two systems shows: in the process of dynamic adjustment,a higher adjustment speed will lead to the instability of the system and even appear chaotic behavior;an intermediate delay weight played by players can enlarge the stability region of the system;a smaller depreciation rate has a greater impact on the system stability.Numerical simulation also shows the system may lose stability through a period-doubling bifurcation or a Neimark-Sacker bifurcation. |
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