Abstract
The impact of inaccurate demand beliefs on dynamics of a Triopoly game is studied. We suppose that all the players make their own estimations on possible demand with errors. A dynamic Triopoly game with such demand belief is set up. Based on this model, existence and local stable region of the equilibriums are investigated by 3D stable regions of Nash equilibrium point. The complex dynamics, such as bifurcation scenarios and route to chaos, are displayed in 2D bifurcation diagrams, in which e1 and α are negatively related to each other. Basins of attraction are investigated and we found that the attraction domain becomes smaller with the increase in price modification speed, which indicates that all the players’ output must be kept within a certain range so as to keep the system stable. Feedback control method is used to keep the system at an equilibrium state.
Highlights
A Triopoly is a market structure dominated by three firms in the market
Assuming cost function to be twice differentiable increasing, Elabbasy et al [1] analyzed the dynamics of oligopoly games with three types of players: bounded rational, naive, and adaptive
Ma and Liu [2] studied a generalized nonlinear FokkerPlanck diffusion equation with external force and absorption. They obtained the corresponding exact solution expressed by q-exponential function and the solutions can have a compact behavior or a long tailed behavior
Summary
A Triopoly is a market structure dominated by three firms in the market. The market is known as Cournot game if firms choose quantities as their strategic variables to maximize their profits in an uncertain demand environment. Ma and Wu [7] studied the complexity of a Triopoly price game model and influence of delayed decisions on the stability All those approaches assume that there is one uniform and accurate market demand function available and shared by all player. Wang and Ma [10] considered a Cournot-Bertrand mixed duopoly game model with limited information about the market and opponent They studied the local stability of the game model at the Nash equilibrium point and discussed the influences of the parameters on the system’s performance. Guo and Ma [12] built a collecting price game model for a close-loop supply chain system with a manufacturer and a retailer who have different rationalities They analyzed the influences of parameters on complex dynamic phenomena, such as the bifurcation, chaos, and continuous power spectrum.
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