scholarly journals Nonlinear Phenomena in Cournot Duopoly Model

Systems ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 30
Author(s):  
Pavel Pražák ◽  
Jaroslav Kovárník
Keyword(s):  
Demand Function ◽  
Deterministic Chaos ◽  
Linear Functions ◽  
Nonlinear Phenomena ◽  
Cournot Duopoly ◽  
Limit Values ◽  
Economic Agents ◽  
Duopoly Model ◽  
Sensitive Dependence ◽  
Stackelberg Duopoly

The economic world is very dynamic, and most phenomena appearing in this world are mutually interconnected. These connections may result in the emergence of nonlinear relationships among economic agents. Research discussions about different markets’ structures cannot be considered as finished yet. Even such a well-known concept as oligopoly can be described with different models applying diverse assumptions and using various values of parameters; for example, the Cournot duopoly game, Bertrand duopoly game or Stackelberg duopoly game can be and are used. These models usually assume linear functions and make analyses of the behavior of the two companies. The aim of this paper is to consider a nonlinear inverse demand function in the Cournot duopoly model. Supposing there is a sufficiently large proportion among the costs of the two companies, we can possibly detect nonlinear phenomena such as bifurcation of limit values of production or deterministic chaos. To prove a sensitive dependence on the initial condition, which accompanies deterministic chaos, the concept of Lyapunov exponents is used. We also point out the fact that even though some particular values of parameters are irrelevant for the above-mentioned nonlinear phenomena, it is worth being aware of their existence.

Fundamental Sources of Economic Complexity

2016 ◽  
Vol 17 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Aleksander Jakimowicz
Keyword(s):  
Deterministic Chaos ◽  
Final State ◽  
Economic Complexity ◽  
Coexistence Of Attractors ◽  
Long Term Effect ◽  
Duopoly Model ◽  
Sensitive Dependence ◽  
Business Cycle Model ◽  
The Business Cycle

AbstractThis article analyses the basic sources and types of economic complexity: chaotic attractors and repellers, complexity catastrophes, coexistence of attractors, sensitive dependence on parameters, final state sensitivity, effects of fractal basin boundaries and chaotic saddles. Four nonlinear classic models have been used for this purpose: virtual duopoly model, model of a centrally planned economy, cobweb model with adaptive expectations and the business cycle model. The issue of economic complexity has not been sufficiently dealt with in the literature. Studies of complexity in economics usually focus on identifying the conditions under which deterministic chaos emerges in models as the main form of complexity, while analyses of other forms of complexity are much less frequent. The article has two objectives: methodological and explicative, which are to shed some new light on the issue. The first objective is to make as comprehensive a catalogue of sources of economic complexity as possible; this is to be achieved by the numerical calculations presented in this article. The issue of accumulation of complexity has been emphasized, which is a type of system dynamics which has its roots in coincidence and overlapping of complexity originating in different sources. The second objective involves an explanation of the role which is played in generating complexity by classic laws of economics. It appears that there is another overarching law, which is independent of the type of system or the level of economic analysis, which states that the long-term effect of conventional economic laws is an inevitable increase in the complexity of markets and economies. Therefore, the sources of complexity discussed in this article are called fundamental ones.

scholarly journals Strategic trade policy with interlocking cross-ownership

2021 ◽  
Author(s):  
Luciano Fanti ◽  
Domenico Buccella
Keyword(s):  
Trade Policy ◽  
Free Trade ◽  
Strategic Trade Policy ◽  
Cournot Duopoly ◽  
Public Intervention ◽  
Tax Subsidy ◽  
Strategic Trade ◽  
Duopoly Model ◽  
Product Competition ◽  
Cross Ownership

AbstractBy analysing interlocking cross-ownership, this work reconsiders the inefficiency of activist governments that set subsidies for their exporters (Brander and Spencer, J Int Econ 18:83–100). Making use of a third-market Cournot duopoly model, we show that the implementation of strategic trade policy in the form of a tax (subsidy) when goods are differentiated (complements) is Pareto-superior to free trade within precise ranges of firms’ cross-ownership, richly depending on the degree of product competition. These results challenge the conventional ones in which public intervention (1) is always the provision of a subsidy and (2) always leads to a Pareto-inferior (resp. Pareto-superior) equilibrium when products are substitutes (resp. complements).

scholarly journals The Chaos Dynamic of Multiproduct Cournot Duopoly Game with Managerial Delegation

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Fang Wu ◽  
Junhai Ma
Keyword(s):  
Flip Bifurcation ◽  
Cournot Duopoly ◽  
Oligopoly Theory ◽  
Output Fluctuations ◽  
Duopoly Model ◽  
High Volatility ◽  
Route To Chaos ◽  
Barrier To Entry ◽  
Intermittent Chaos ◽  
Consumer Tastes

Although oligopoly theory is generally concerned with the single-product firm, what is true in the real word is that most of the firms offer multiproducts rather than single products in order to obtain cost-saving advantages, cater for the diversity of consumer tastes, and provide a barrier to entry. We develop a dynamical multiproduct Cournot duopoly model in discrete time, where each firm has an owner who delegates the output decision to a manager. The principle of decision-making is bounded rational. And each firm has a nonlinear total cost function due to the multiproduct framework. The Cournot Nash equilibrium and the local stability are investigated. The tangential bifurcation and intermittent chaos are reported by numerical simulations. The results show that high output adjustment speed can lead to output fluctuations which are characterized by phases of low volatility with small output changes and phases of high volatility with large output changes. The intermittent route to chaos of Flip bifurcation and another intermittent route of Flip bifurcation which contains Hopf bifurcation can exist in the system. The study can improve our understanding of intermittent chaos frequently observed in oligopoly economy.

Aspiration-Based Learning in a Cournot Duopoly Model

2013 ◽  
Vol 10 (2) ◽  
pp. 295-314 ◽  
Author(s):  
Manahan Siallagan ◽  
Hiroshi Deguchi ◽  
Manabu Ichikawa
Keyword(s):  
Cournot Duopoly ◽  
Duopoly Model

scholarly journals A Dynamic Duopoly Model: When a Firm Shares the Market with Certain Profit

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1826
Author(s):  
Sameh S. Askar
Keyword(s):  
Equilibrium Point ◽  
Market Share ◽  
Period Doubling ◽  
Analytical Investigation ◽  
Basins Of Attraction ◽  
Stability Conditions ◽  
Cournot Duopoly ◽  
Demand Functions ◽  
Duopoly Model ◽  
Dynamic Duopoly

The current paper analyzes a competition of the Cournot duopoly game whose players (firms) are heterogeneous in a market with isoelastic demand functions and linear costs. The first firm adopts a rationally-based gradient mechanism while the second one chooses to share the market with certain profit in order to update its production. It trades off between profit and market share maximization. The equilibrium point of the proposed game is calculated and its stability conditions are investigated. Our studies show that the equilibrium point becomes unstable through period doubling and Neimark–Sacker bifurcation. Furthermore, the map describing the proposed game is nonlinear and noninvertible which lead to several stable attractors. As in literature, we have provided an analytical investigation of the map’s basins of attraction that includes lobes regions.

Simulation and Control of a Duopoly Model

2014 ◽  
Vol 472 ◽  
pp. 146-151
Author(s):  
Ya Li Lu
Keyword(s):  
Nash Equilibrium ◽  
Demand Function ◽  
Delayed Feedback Control ◽  
Control Scheme ◽  
Duopoly Model ◽  
Adjustment Speed ◽  
The Stability ◽  
Boundary Fixed Points ◽  
And Control ◽  
Time Delayed Feedback

This paper studies the dynamics of a duopoly model with bounded rationality and nonlinear demand function. Based on the stability theorem and Jurys criterions, we prove that the model has two unstable boundary fixed points and a local stable Nash equilibrium. Then we depict the stability region of Nash equilibrium, and investigate the effects of output adjustment speed on the players profit respectively. Theoretical analysis and simulations show that higher output adjustment speed can result in chaotic variation of outputs, and that the Nash equilibrium is the optimal result of duopoly game. To improve the profitability of each player and achieve the optimal game result, we put forth a new scheme combined with the time-delayed feedback control and the limiter control to stabilize the output to Nash equilibrium. Finally, the numerical simulation is adopted to verify the effectiveness and feasibility of the above control scheme.

scholarly journals The Impact of Cost Uncertainty on Cournot Duopoly Game with Concave Demand Function

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
S. S. Askar
Keyword(s):  
Optimization Problem ◽  
Demand Function ◽  
Equilibrium Points ◽  
Cournot Duopoly ◽  
Worst Case ◽  
Dynamical Characteristics ◽  
Inflection Points ◽  
The Cost ◽  
The Impact ◽  
Theoretical Results

It is reported in the literature that the most fundamental idea to address uncertainty is to begin by condensing random variables. In this paper, we propose Cournot duopoly game where quantity-setting firms use nonlinear demand function that has no inflection points. A random cost function is introduced in this model. Each firm in the model wants to maximize its expected profit and also wants to minimize its uncertainty by minimizing the cost. To handle this multiobjective optimization problem, the expectation and worst-case approaches are used. A model of two rational firms that are in competition and produce homogenous commodities is introduced using an unknown demand function. The equilibrium points of this model are obtained and their dynamical characteristics such as stability, bifurcation, and chaos are investigated. Complete stability and bifurcation analysis are provided. The obtained theoretical results are verified by numerical simulation.

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