Abstract: 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.

Key words: bounded rationality, sequential pricing game, dynamic game, stability