多个企业同时博弈的动态古诺模型的长期产量解研究

A Study on the Long-Term Produce Solutions of Dynamical Cournot Model with Multi-Firms Simultaneous-Move Game

考虑到多阶段的博弈过程需要涉及长期利润的特点,建立了两个以长期利润为目标的多个耐用品企业同时博弈的动态古诺模型(长期非合作模型和长期竞争均衡模型)。通过对多个模型求解结果的比较与分析可知,长期竞争均衡模型下的市场竞争最为激烈,但还是优于短期竞争均衡模型;当然,它依旧劣于非完全竞争情形下的长期非合作模型和长期合作模型。

The Cournot model is one of basic economic models. After years of continuous development and improvement, the model has become one of the most widely applied models used to analyze the behavior of every production enterprise in the oligopoly market. The Cournot model is also named dynamical Cournot model because it can be used to study the output games among monopolists over a period of time. In the market of special ~turable goods, the implicit assumption of the unchanged market capacity in traditional, dynamical Cournot model has not been established. This paper supposes that capacity in a new stage could be calculated by first deducting the sales amounts of products sokJ in the previous stage, and then adding the newly increased market derived from the waste of sold products because of technological change, lifestyle changes, etc. By applying the dynamic Cournot model to analyze the durable goods market, this paper assumes that all companies primarily pursue immediate self-interest in the production process. However, this model also suggests that an effective production strategy should not only involve immediate profit, hut also consider profit in other stages or the overall profit of the whole game in the multiple-stage game process. This paper applies the dynamiealCournot model in analyzing several durable goods＇ enterprises in the same game, and builds two new models to maximize the long-term profit. These two models are long-term no cooperation model and long-term competitive equilibrium model. The goal of the former model is to maximize profit for an enterprise, and that of the latter model is to achieve the same objective by considering the constraint of inverse inference. The latter model has the advantage of obtaining the Nash equilibrium result. This paper compares and analyzes the production solutions among these models, including the proposed long-term no cooperation model, long-term competitive equilibrium model, short-term competition equilibrium model, short-term cooperation model, and long- term cooperation model. Six findings are derived from the comparison and analysis process： 1. Short-term profit declines monotonously with the gradual deep game. The production solution in long-term cooperation model increases monotonously with gaming. 2. The non-cooperative competition among companies is fiercer than the cooperative cooperation. Fierce competition erodes profit margin and decreases surplus market capacity. 3. The long-term competitive equilibrium model is more intense than the short-term competition equilibrium model. 4. The little profit margin and profit are gained from production under short-term competition equilibrium model in the early gain. More profit margin, profits, surplus market capacity are acquired in the late game according to the long-term competitive equilibrium model. 5. More profit can be achieved in the long-term competitive equilibrium model than the short-term competition equilibrium model. 6. More profit can be achieved in the model pursuing long-term profit than short-term profit. The completely competitive situation is inferior to the imperfect competition condition. Both of these conditions are inferior to cooperation. Long-term cooperation model is superior to imperfect competition model, followed by completely competition model.