Complex dynamics and synchronization of a duopoly game with bounded rationality

Agiza, H.N.; Hegazi, A. S.; Elsadany, A. A.

doi:10.1016/s0378-4754(01)00347-0

Cited by 145 publications

(71 citation statements)

References 10 publications

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“…Since the market information is not complete, the duopoly enterprise must adopt bounded rationality for a price decision. The scholars have studied the complexity of the game model with bounded rationality about synchronization, marginal costs, and so on [8][9][10]. The duopoly enterprise makes price decisions not only in reference to the current price but also in reference to historical prices.…”

Section: Introductionmentioning

confidence: 99%

Complex Dynamics of a Continuous Bertrand Duopoly Game Model with Two-Stage Delay

2016

Entropy

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This paper studies a continuous Bertrand duopoly game model with two-stage delay. Our aim is to investigate the influence of delay and weight on the complex dynamic characteristics of the system. We obtain the bifurcation point of the system respect to delay parameter by calculating. In addition, the dynamic properties of the system are simulated by power spectrum, attractor, bifurcation diagram, the largest Lyapunov exponent, 3D surface chart, 4D Cubic Chart, 2D parameter bifurcation diagram, and 3D parameter bifurcation diagram. The results show that the stability of the system depends on the delay and weight, in order to maintain stability of price and ensure the firm profit, the firms must control the parameters in the reasonable region. Otherwise, the system will lose stability, and even into chaos, which will cause fluctuations in prices, the firms cannot be profitable. Finally, the chaos control of the system is carried out by a control strategy of the state variables' feedback and parameter variation, which effectively avoid the damage of chaos to the economic system. Therefore, the results of this study have an important practical significance to make decisions with multi-stage delay for oligopoly firms.

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Section: Introductionmentioning

confidence: 99%

Complex Dynamics of a Continuous Bertrand Duopoly Game Model with Two-Stage Delay

2016

Entropy

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“…And from firm 2's expected price in (7), the market price expression in (11), and the cost function 2 in (12), we obtain firm 2's expected profit as follows:…”

Section: Two Different Delay Structuresmentioning

confidence: 99%

“…Bischi and Naimzada [9] first gave the general formula of bounded rationality in a duopoly game, where each firm uses the local knowledge of its marginal profit to adjust strategy in a new period: increasing its output if it perceives a positive marginal profit and decreasing its production if the perceived marginal profit is negative. A great deal of research work has been done for the dynamical Cournot game played by homogeneous players with such a kind of rationality (e.g., [9][10][11][12]). …”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Duopoly Game with Two Different Delay Structures

Jiang¹,

Xu²,

Ding³

et al. 2017

Discrete Dynamics in Nature and Society

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Two different time delay structures for the dynamical Cournot game with two heterogeneous players are considered in this paper, in which a player is assumed to make decision via his marginal profit with time delay and another is assumed to adjust strategy according to the delayed price. The dynamics of both players output adjustments are analyzed and simulated. The time delay for the marginal profit has more influence on the dynamical behaviors of the system while the market price delay has less effect, and an intermediate level of the delay weight for the marginal profit can expand the stability region and thus promote the system stability. It is also shown that the system may lose stability due to either a period-doubling bifurcation or a Neimark-Sacker bifurcation. Numerical simulations show that the chaotic behaviors can be stabilized by the time-delayed feedback control, and the two different delays play different roles on the system controllability: the delay of the marginal profit has more influence on the system control than the delay of the market price.

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“…Usually the price p is characterized by the nonlinear inverse demand function of p = a − b Q, where a and b are positive constants, a is the maximum price in the market, and Q is the total quantity in the market. This kind of form has been used in other oligopoly models and in the experimental economics dealing with learning and expectations formation (see, e.g., [10][11][12]). The transformation of this formula is as follows: In this case, the land market and housing market are interrelated.…”

Section: Nonlinear Models For Real Estate Marketmentioning

confidence: 99%

Complex Dynamics in a Nonlinear Cobweb Model For Real Estate Market

Ma¹,

Mu²

2011

Models and Applications of Chaos Theory in Modern Sciences

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We establish a nonlinear real estate model based on cobweb theory, where the demand function and supply function are quadratic. The stability conditions of the equilibrium are discussed. We demonstrate that as some parameters varied, the stability of Nash equilibrium is lost through period-doubling bifurcation. The chaotic features are justified numerically via computing maximal Lyapunov exponents and sensitive dependence on initial conditions. The delayed feedback control (DFC) method is applied to control the chaos of system.

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Complex dynamics and synchronization of a duopoly game with bounded rationality

Cited by 145 publications

References 10 publications

Complex Dynamics of a Continuous Bertrand Duopoly Game Model with Two-Stage Delay

Complex Dynamics of a Continuous Bertrand Duopoly Game Model with Two-Stage Delay

Dynamics of a Duopoly Game with Two Different Delay Structures

Complex Dynamics in a Nonlinear Cobweb Model For Real Estate Market

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