Profit comparisons between Cournot and Stackelberg duopoly with isoelastic demand function

2019 ◽  
Author(s):  
Adyda Ibrahim
Keyword(s):  
Demand Function ◽  
Isoelastic Demand Function ◽  
Stackelberg Duopoly

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.

scholarly journals Local Stability of Cournot Equilibrium as the Number of Firms Increases

2021 ◽  
pp. 972-980
Author(s):  
Adyda Ibrahim ◽  
Nerda Zura Zaibidi ◽  
Azizan Saaban
Keyword(s):  
Local Stability ◽  
Marginal Cost ◽  
Demand Function ◽  
Cournot Oligopoly ◽  
Cournot Equilibrium ◽  
Adaptive Expectations ◽  
The Third ◽  
Decision Mechanisms ◽  
Isoelastic Demand Function ◽  
Number Of Firms

In this paper, a Cournot oligopoly with isoelastic demand function and constant marginal cost is considered. The local stability conditions of the Cournot equilibrium are determined for four models with different decision mechanisms. In the first model, firms adjust their outputs using the best reply response with naive expectations. The second model is a generalization of the first one, where firms have adaptive expectations. Meanwhile, the third and fourth models adopt the bounded rationality and local monopolistic approximation, respectively. The results show that, in the case of identical firms, the Cournot equilibrium is always stable when the firms adopt the local monopolistic approximation mechanism.

Heterogeneous triopoly game with isoelastic demand function

2011 ◽  
Vol 68 (1-2) ◽  
pp. 187-193 ◽  
Author(s):  
Fabio Tramontana ◽  
Abd Elalim Abdo Elsadany
Keyword(s):  
Demand Function ◽  
Isoelastic Demand Function

scholarly journals Analysis of Triopoly Game with Isoelastic Demand Function and Heterogeneous Players

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Hong-Xing Yao ◽  
Lian Shi ◽  
Hao Xi
Keyword(s):  
Demand Function ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Game Model ◽  
Bifurcation Diagrams ◽  
Heterogeneous Players ◽  
Sensitive Dependence ◽  
Linear Demand ◽  
Isoelastic Demand Function ◽  
Asymptotic Stability Conditions

We analyze a triopoly game model with fully heterogeneous players when the demand function is isoelastic. The three players were considered to be bounded rational, adaptive, and naïve. Existing equilibrium points and their locally asymptotic stability conditions are studied. Complexity of the dynamical system is examined by means of numerical simulations, such as period cycles, bifurcation diagrams, strange attractors and sensitive, dependence on initial conditions. This paper extends the result of Tramontana (2010) who considered a heterogeneous duopoly with isoelastic demand function. Comparisons with respect to the heterogeneous triopoly model of Elabbasy et al. (2009) assuming linear demand function are performed.

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