scholarly journals Complexity of a Duopoly Game in the Electricity Market with Delayed Bounded Rationality

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Junhai Ma ◽  
Hongliang Tu
Keyword(s):  
Nash Equilibrium ◽  
Bounded Rationality ◽  
Electricity Market ◽  
Complex Dynamics ◽  
Fractal Dimensions ◽  
Practical Significance ◽  
Stable Region ◽  
Phase Portraits ◽  
Largest Lyapunov Exponent ◽  
Game Model

According to a triopoly game model in the electricity market with bounded rational players, a new Cournot duopoly game model with delayed bounded rationality is established. The model is closer to the reality of the electricity market and worth spreading in oligopoly. By using the theory of bifurcations of dynamical systems, local stable region of Nash equilibrium point is obtained. Its complex dynamics is demonstrated by means of the largest Lyapunov exponent, bifurcation diagrams, phase portraits, and fractal dimensions. Since the output adjustment speed parameters are varied, the stability of Nash equilibrium gives rise to complex dynamics such as cycles of higher order and chaos. Furthermore, by using the straight-line stabilization method, the chaos can be eliminated. This paper has an important theoretical and practical significance to the electricity market under the background of developing new energy.

scholarly journals Complex Dynamics of an Adnascent-Type Game Model

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Baogui Xin ◽  
Junhai Ma ◽  
Qin Gao
Keyword(s):  
Schwarzian Derivative ◽  
Complex Dynamics ◽  
Fractal Dimensions ◽  
Phase Portraits ◽  
Game Model ◽  
Bifurcation Diagrams ◽  
Bifurcation And Chaos ◽  
Normal Form Theory ◽  
Form Theory ◽  
Largest Lyapunov Exponents

The paper presents a nonlinear discrete game model for two oligopolistic firms whose products are adnascent. (In biology, the term adnascent has only one sense, “growing to or on something else,” e.g., “moss is an adnascent plant.” See Webster's Revised Unabridged Dictionary published in 1913 by C. & G. Merriam Co., edited by Noah Porter.) The bifurcation of its Nash equilibrium is analyzed with Schwarzian derivative and normal form theory. Its complex dynamics is demonstrated by means of the largest Lyapunov exponents, fractal dimensions, bifurcation diagrams, and phase portraits. At last, bifurcation and chaos anticontrol of this system are studied.

BIFURCATIONS AND CHAOS IN FRACTIONAL-ORDER SIMPLIFIED LORENZ SYSTEM

2010 ◽  
Vol 20 (04) ◽  
pp. 1209-1219 ◽  
Author(s):  
KEHUI SUN ◽  
XIA WANG ◽  
J. C. SPROTT
Keyword(s):  
Fractional Order ◽  
Lorenz System ◽  
Complex Dynamics ◽  
Phase Portraits ◽  
Largest Lyapunov Exponent ◽  
Fractional Order Systems ◽  
Wide Range ◽  
The Time Domain ◽  
Fractional Orders ◽  
Simplified Lorenz System

The dynamics of fractional-order systems have attracted increasing attention in recent years. In this paper, we numerically study the bifurcations and chaotic behaviors in the fractional-order simplified Lorenz system using the time-domain scheme. Chaos does exist in this system for a wide range of fractional orders, both less than and greater than three. Complex dynamics with interesting characteristics are presented by means of phase portraits, bifurcation diagrams and the largest Lyapunov exponent. Both the system parameter and the fractional order can be taken as bifurcation parameters, and the range of existing chaos is different for different parameters. The lowest order we found for this system to yield chaos is 2.62.

Towards a Predictive Analysis of UAV-Based Flying Base Station Decisions

2020 ◽  
Vol 16 (2) ◽  
pp. 20-52 ◽  
Author(s):  
Hamid Garmani ◽  
Driss Ait Omar ◽  
Mohamed El Amrani ◽  
Mohamed Baslam ◽  
Mostafa Jourhmane
Keyword(s):  
Nash Equilibrium ◽  
Unmanned Aerial Vehicles ◽  
Base Station ◽  
Base Stations ◽  
Practical Significance ◽  
Game Model ◽  
Activity Scheduling ◽  
Area Of Interest ◽  
Aerial Vehicles ◽  
Fairness Concern

The use of unmanned aerial vehicles (UAVs) as a communication platform is of great practical significance in the wireless communications field. This paper studies the activity scheduling of unmanned aerial vehicles acting as aerial base stations in an area of interest for a specific period. Specifically, competition among multiple UAVs is explored, and a game model for the competition is developed. The Nash equilibrium of the game model is then analyzed. Based on the analysis, an algorithm for Nash equilibrium computation is proposed. Then, a game model with fairness concern is established, and its equilibrium price is also analyzed. In addition, numerical examples are conducted to determine the factors that affect the strategies (price, quality of service, and beaconing duration) of the UAV and to show how the expected profits of UAVs change with that fairness concern point. The authors believe that this research paper will shed light on the application of UAV as a flying base station.

scholarly journals Analysis of Price Stackelberg Duopoly Game with Bounded Rationality

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Lian Shi ◽  
Yun Le ◽  
Zhaohan Sheng
Keyword(s):  
Bounded Rationality ◽  
Stackelberg Game ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Price Adjustment ◽  
Stable Region ◽  
Largest Lyapunov Exponent ◽  
Existence And Stability ◽  
Theoretical And Numerical Analysis ◽  
Stackelberg Duopoly

The classical Stackelberg game is extended to boundedly rational price Stackelberg game, and the dynamic duopoly game model is described in detail. By using the theory of bifurcation of dynamical systems, the existence and stability of the equilibrium points of this model are studied. And some comparisons with Bertrand game with bounded rationality are also performed. Stable region, bifurcation diagram, The Largest Lyapunov exponent, strange attractor, and sensitive dependence on initial conditions are used to show complex dynamic behavior. The results of theoretical and numerical analysis show that the stability of the price Stackelberg duopoly game with boundedly rational players is only relevant to the speed of price adjustment of the leader and not relevant to the follower’s. This is different from the classical Cournot and Bertrand duopoly game with bounded rationality. And the speed of price adjustment of the boundedly rational leader has a destabilizing effect on this model.

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.

scholarly journals Complexity Analysis of a 3-Player Game with Bounded Rationality Participating in Nitrogen Emission Reduction

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Jixiang Zhang ◽  
Xuan Xi
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Bounded Rationality ◽  
Control Method ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Stable Region ◽  
Nitrogen Emissions ◽  
Nash Equilibrium Point ◽  
The Stability

In this paper, a decision-making competition game model concerning governments, agricultural enterprises, and the public, all of which participate in the reduction of nitrogen emissions in the watersheds, is established based on bounded rationality. First, the stability conditions of the equilibrium points in the system are discussed, and the stable region of the Nash equilibrium is determined. Then, the bifurcation diagram, maximal Lyapunov exponent, strange attractor, and sensitive dependence on the initial conditions are shown through numerical simulations. The research shows that the adjustment speed of three players’ decisions may alter the stability of the Nash equilibrium point and lead to chaos in the system. Among these decisions, a government’s decision has the largest effect on the system. In addition, we find that some parameters will affect the stability of the system; when the parameters become beneficial for enterprises to reduce nitrogen emissions, the increase in the parameters can help control the chaotic market. Finally, the delay feedback control method is used to successfully control the chaos in the system and stabilize it at the Nash equilibrium point. The research of this paper is of great significance to the environmental governance decisions and nitrogen reduction management.

scholarly journals Complexity Analysis of a Master-Slave Oligopoly Model and Chaos Control

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Junhai Ma ◽  
Fang Zhang ◽  
Yanyan He
Keyword(s):  
Control Method ◽  
Complexity Analysis ◽  
Dynamic Properties ◽  
Stable Region ◽  
Largest Lyapunov Exponent ◽  
Game Model ◽  
Oligopoly Model ◽  
Long Run ◽  
Feedback Control Method ◽  
Delay Feedback Control

We establish a master-slave oligopoly game model with an upstream monopoly whose output is considered and two downstream oligopolies whose prices are considered. The existence and the local stable region of the Nash equilibrium point are investigated. The complex dynamic properties, such as bifurcation and chaos, are analyzed using bifurcation diagrams, the largest Lyapunov exponent diagrams, and the strange attractor graph. We further analyze the long-run average profit of the three firms and find that they are all optimal in the stable region. In addition, delay feedback control method and limiter control method are used in nondelayed model to control chaos. Furthermore, a delayed master-slave oligopoly game model is considered, and the three firms’ profit in various conditions is analyzed. We find that suitable delayed parameters are important for eliminating chaos and maximizing the profit of the players.

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