scholarly journals Cournot Duopoly Games: Models and Investigations

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1079 ◽  
Author(s):  
S. S. Askar ◽  
A. Al-khedhairi
Keyword(s):  
Fixed Point ◽  
Bounded Rationality ◽  
Local Stability ◽  
Adjustment Process ◽  
Limited Information ◽  
Cournot Duopoly ◽  
Dynamic Adjustment ◽  
Local Stability Analysis ◽  
Tit For Tat ◽  
Adjustment Parameter

This paper analyzes Cournot duopoly games that are constructed based on Cobb–Douglas preferences. We introduce here two models whose dynamic adjustments depend on bounded rationality, dynamic adjustment, and tit-for-tat mechanism. In the first model, we have two firms with limited information and due to that they adopt the bounded rationality mechanism. They update their productions based on the changing occurred in the marginal profit. For this model, its fixed point is obtained and its stability condition is calculated. In addition, we provide conditions by which this fixed point loses its stability due to flip and Neimark–Sacker bifurcations. Furthermore, numerical simulation shows that this model possesses some chaotic behaviors which are recovered due to corridor stability. In the second model, we handle two different mechanisms of cooperation. These mechanisms are dynamic adjustment process and tit-for-tat strategy. The players who use the dynamic adjustment increase their productions based on the cooperative output while, in tit-for-tat mechanism, they increase the productions based on the cooperative profit. The local stability analysis shows that adopting tit-for-tat makes the model unstable and then the system becomes chaotic for any values of the system’s parameters. The obtained results show that the dynamic adjustment makes the system’s fixed point stable for a certain interval of the adjustment parameter.

scholarly journals Dynamics of a Cournot Duopoly Game with a Generalized Bounded Rationality

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
A. Al-khedhairi
Keyword(s):  
Stability Analysis ◽  
Bounded Rationality ◽  
Numerical Computation ◽  
Local Stability ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Cournot Duopoly ◽  
Local Stability Analysis

In this paper, the dynamics of Cournot duopoly game with a generalized bounded rationality is considered. The fractional bounded rationality of the Cournot duopoly game is introduced. The conditions of local stability analysis of equilibrium points of the game are derived. The effect of fractional marginal profit on the game is investigated. The complex dynamics behaviors of the game are discussed by numerical computation when parameters are varied.

scholarly journals Analysis of a Dynamical Cournot Duopoly Game with Distributed Time Delay

2015 ◽  
Vol 8 (s1) ◽  
pp. 1-13
Author(s):  
Nicoleta SÎrghi ◽  
Mihaela NeamȚu ◽  
Petru Claudiu Străin
Keyword(s):  
Time Delay ◽  
Equilibrium Point ◽  
Bounded Rationality ◽  
Local Stability ◽  
Distributed Delay ◽  
Adjustment Process ◽  
Cournot Duopoly ◽  
Current Time ◽  
Distributed Time Delay ◽  
Delay Differential

Abstract The aim of the paper is to analyze the dynamic model of the Cournot duopoly game with bounded rationality associated to two firms. We consider the cost function of the first firm as nonlinear and for the second firm as linear. The players do not have a complete knowledge of the market and they follow a bounded rationality adjustment process based on the estimation of the marginal profit. Also, the distributed time delay is introduced, because the decisions at the current time depend on the average past decisions. The mathematical model is described by a distributed delay differential system with two nonlinear equations. The study for the local stability of the Nash equilibrium point is carried out in the case of two types of kernels: weak (exponential) and Dirac. A change in local stability of the equilibrium point, from stable to unstable, implies a Hopf bifurcation. The delays are considered as bifurcation parameters. In some conditions of the parameters of the model, we have proved that a family of periodic solutions bifurcates from the equilibrium point when the bifurcation parameter passes through a critical value. Numerical simulations are performed to illustrate the effectiveness of our results. Finally, conclusions and future researches are provided.

scholarly journals Implications for Firms with Limited Information to Take Advantage of Reference Price Effect in Competitive Settings

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Junhai Ma ◽  
Zhanbing Guo
Keyword(s):  
Reference Price ◽  
Partial Information ◽  
Necessary Condition ◽  
Adjustment Process ◽  
Flip Bifurcation ◽  
Limited Information ◽  
Dynamic Adjustment ◽  
Internal Reference ◽  
Special Cases ◽  
Price Effects

This paper studies internal reference price effects when competitive firms face reference price effects and make decisions based on partial information, where their decision-making mechanism is modeled by a dynamic adjustment process. It is shown that the evolution of this dynamic adjustment goes to stabilization if both adjustment speeds are small and the complexity of this evolution increases in adjustment speeds. It is proved that the necessary condition for flip bifurcation or Neimark-Sacker bifurcation will occur with the increase of adjustment speed in two special cases. What is more, numerical simulations show that these bifurcations do occur. Then, the impacts of parameters on stability and profits are investigated and some management insights for firms with limited information to take advantage of reference price effects are provided.

scholarly journals Analysis of Nonlinear Duopoly Game: A Cooperative Case

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
S. S. Askar ◽  
Ahmad M. Alshamrani ◽  
K. Alnowibet
Keyword(s):  
Fixed Point ◽  
Demand Function ◽  
Complex Behavior ◽  
Equilibrium Stability ◽  
Cournot Duopoly ◽  
Dynamic Strategy ◽  
Tit For Tat ◽  
The Stability ◽  
The Impact ◽  
Linear Cost

We make further attempts to investigate equilibrium stability of a nonlinear Cournot duopoly game. Our studies in this paper focus on the cooperation that may be obtained among duopolistic firms. Discrete time scales under the assumption of unknown inverse demand function and linear cost are used to build our models in the proposed games. We introduce and study here an adjustment dynamic strategy beside the so-called tit-for-tat strategy. For each model, the stability analysis of the fixed point is analyzed. Numerical simulations are carried out to show the complex behavior of the proposed models and to point out the impact of the models’ parameters on the cooperation.

The Olympic Games as a News Shock

2017 ◽  
Vol 19 (6) ◽  
pp. 884-906 ◽  
Author(s):  
Viktoria C. E. Langer ◽  
Wolfgang Maennig ◽  
Felix Richter
Keyword(s):  
Steady State ◽  
Olympic Games ◽  
Structural Models ◽  
Adjustment Process ◽  
Dynamic Adjustment ◽  
Economic Variables ◽  
Long Run ◽  
News Shock ◽  
Steady State Levels ◽  
The Olympic Games

The awarding of the Olympic Games to a certain city or the announcement of a city’s Olympic bid may be considered as a news shock that affects agents’ market expectations. A news shock implies potential impacts on the dynamic adjustment process that change not only the volatility but also the long-run steady-state levels of endogenous economic variables. In this study, we contribute to and extend previous researchers’ attempts to empirically test for the Olympic Games as a news shock by implementing full structural models and by matching Olympic hosts and bidders to structurally similar countries.

Dynamic Analysis of Mechanical Systems With Time-Varying Topologies: Part 1 — Dynamic Model and Stability Analysis

1990 ◽  
Author(s):  
Yu Wang
Keyword(s):  
Stability Analysis ◽  
Dynamic Model ◽  
Local Stability ◽  
Global Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Time Varying ◽  
Discrete Equations ◽  
Local Stability Analysis ◽  
Multiple Collisions

Abstract A model is developed for analyzing mechanical systems with a pair of bodies with topological changes in their kinematic constraints. It is built upon the concept of Poincaré map rather than following the traditional methods of differential equations. The model provides a set of well-defined and naturally-discrete equations of motion and is capable of giving physical insights of dynamic characteristics of deadbeat convergence of multiple collisions and periodic or chaotic responses. The development of dynamic model and a local stability analysis are presented in Part 1, and the global analysis and numerical simulation are discussed in Part 2.

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