有限理性下序贯价格竞争的动态演化

Dynamics of Sequential Pricing Game Model with Bounded Rationality

本文建立了两个企业的序贯价格竞争模型,基于有限理性预期调整,研究了企业博弈的动态演化特征,分析了模型的均衡解及其稳定性条件。研究发现,边界解和纳什均衡解是一定参数条件下的局部稳定均衡。基于有限理性的动态博弈能够实现基于完全信息的纳什均衡。单纯跟随策略是一定条件下的均衡策略,并能使跟随企业获得更高的销售价格。企业之间报价的相互跟随程度和企业预期的调整速度将会影响均衡点的稳定性。本文对模型进行了数值模拟分析,当参数不满足稳定性条件时会出现分岔、奇异吸引子等混沌现象。本文的主要研究结果对相关行业的企业竞争和稳定市场有启发意义。

There is a type of oligopolistic market between the Bertrand model and the price leadership model in the real economy.There are large firms and small firms in the market,as well as different quotation methods,which form a sequential price competition.The study of the equilibrium solutions,the stability of equilibrium points,and the complex phenomena in the dynamic evolution plays great significance for enterprise competition and market regulation.In order to depict the real business,it is supposed that the firms are boundedly rationaland adjust the price according to the marginal profit.In the paper,a basic model based on complete information is established firstly.The Nash equilibria of the model are solved,which are also the Pareto optimal solutions.Then,the expectation adjustment with the bounded rationality is considered and the dynamic market model is established.The four equilibria of the model are solved,and the stability of the equilibrium solutions are discussed.It is found that the boundary solution and the Nash equilibrium solution are local stable equilibrium under certain parameters.The dynamic game based on bounded rationality can achieve the Nash equilibrium based on complete information.The pure following strategy could be equilibrium strategy.Furthermore,the fast adjustment speed of firm expectation and the low following level of pricing can result in chaos,which is bad for market performance.Numerical simulations of the model are provided.As it is shown,the chaotic phenomena such as bifurcations and singular attractors may occur when thestability conditions are violated.According to the results of the study,firms can optimize the competition strategy by adjusting the following level.Regulators can enhance the stability of the market by coordinating the following strategy of firms and building the market price index.