Complex Dynamics in a Mixed Duopoly Game Based on Relative Profit Maximization

2021 ◽  
Vol 10 (02) ◽  
pp. 444-452
Author(s):  
星雨 刘
Keyword(s):  
Complex Dynamics ◽  
Profit Maximization ◽  
Mixed Duopoly ◽  
Relative Profit

scholarly journals Complex Dynamics in a Mixed Duopoly Game Based on Relative Profit Maximization

2021 ◽  
pp. 47-57
Author(s):  
Yuqi Dou ◽  
Xingyu Liu
Keyword(s):  
Nash Equilibrium ◽  
Dynamic Systems ◽  
Complex Dynamics ◽  
Rational Expectation ◽  
Profit Maximization ◽  
Mixed Duopoly ◽  
Complex Dynamic ◽  
Discrete Dynamic Systems ◽  
The Stability ◽  
Relative Profit

In this paper, the complex dynamic behavior of a mixed duopoly game model is studied. Based on the principle of relative profit maximization and bounded rational expectation, the corresponding discrete dynamic systems are constructed in the case of nonlinear cost function. In theory, the conditions for the local stability of Nash equilibrium are given. In terms of numerical experiments, bifurcation diagrams are used to depict the effects of product differences, adjustment speed, and other parameters on the stability of Nash equilibrium.

scholarly journals Local and Global Dynamics of a Constraint Profit Maximization for Bischi–Naimzada Competition Duopoly Game

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1458 ◽  
Author(s):  
Sameh S Askar ◽  
Abdulrahman Al-Khedhairi
Keyword(s):  
Complex Dynamics ◽  
Market Competition ◽  
Equilibrium Points ◽  
Profit Maximization ◽  
Stable Complex ◽  
Global Dynamics ◽  
Limited Information ◽  
Critical Curves ◽  
Local And Global Dynamics ◽  
Realistic Situation

The Bischi–Naimzada game is a market competition between two firms with the objective of maximizing profits under limited information. In this article, we study a more generalized and realistic situation that takes into account the sales constraints. we generalize the economic model suggested by Bischi–Naimzada by introducing and studying the maximization of profits based on sales constraints. Our motivation in this paper is the studying of profit and sales constraints maximization and their influences on the game’s dynamics. The local stability of the equilibrium points of the proposed model is discussed. It examines how the dynamics of the proposed two-dimensional competition game model focusing on changes in both the speed of the adjustment and the sales constraint parameters. The map describing the game is proven to be noninvertible and yields many multi-stable, complex dynamics and the coexistence chaotic attractors may arise. The global behavior of the map is achieved by studying the critical curves. The numerical simulations demonstrate the coexistence of two attractors and complex structures of the attraction basins. Several examples are discussed in order to confirm all the analytical results obtained.

scholarly journals Complex Dynamics Analysis for a Cournot-Bertrand Mixed Game Model with Delayed Bounded Rationality

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Junhai Ma ◽  
Hongwu Wang
Keyword(s):  
Mixed Model ◽  
Historical Data ◽  
Complex Dynamics ◽  
Dynamic Properties ◽  
Stable Region ◽  
Mixed Duopoly ◽  
Game Model ◽  
Complex Dynamic ◽  
Delayed System ◽  
Route To Chaos

A Cournot-Bertrand mixed duopoly game model is constructed. The existence and local stable region of the Nash equilibria point are investigated. Complex dynamic properties such as bifurcation and route to chaos are analyzed using parameter basin plots. The strange attractors are also studied when the system is in chaotic states. Furthermore, considering the memory of the market, a delayed Cournot-Bertrand mixed model is considered and the results show that the delayed system has the same Nash equilibrium and has a higher chance of reaching steady states or cycles than the model without delay. So making full use of the historical data can improve the system’s stability.

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