Analysis of nonlinear triopoly game with heterogeneous players

Elabbasy, Elmetwally M.; Agiza, H.N.; Elsadany, A. A.

doi:10.1016/j.camwa.2008.09.046

Cited by 86 publications

(76 citation statements)

References 14 publications

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“…The effect of two-stage delay on the complexity of the system is studied in [11,12], and the stability region of the system is given. The nonlinear dynamic behavior of the triopoly game model is studied from heterogeneous and delayed bounded rationality, respectively, in [13,14]. The research conclusions are the same as that of a two-dimensional game model, but the research process is more complex.…”

Section: Introductionsupporting

confidence: 48%

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: Introductionsupporting

confidence: 48%

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

2016

Entropy

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“…In this section, we show that the usually used method of time-delayed feedback control (e.g., [32,[36][37][38]) can also be used to control the chaos in our model.…”

Section: Chaos Controlmentioning

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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“…In such studies, the main concern is to study the complex dynamic characteristics of the game. For example, some complex dynamics of duopoly game were studied in [8,[21][22][23][24][25]. In practice, such game is close to the economic reality and it is widely deployed in oligopoly.…”

Section: Introductionmentioning

confidence: 99%

“…Such model was later investigated by Ji [30] considering heterogeneous players. Elabbasy et al [25] have proposed a triopoly game with heterogeneous players in order to study its dynamical behaviors with linear cost function. Another model of a nonlinear triopoly game was proposed by Elabbasy et al [31] using three heterogeneous players, namely, naïve, bounded rational, and adaptive players.…”

Section: Introductionmentioning

confidence: 99%

“…Elabbasy et al [25] have proposed a triopoly game with heterogeneous players in order to study its dynamical behaviors with linear cost function. Another model of a nonlinear triopoly game was proposed by Elabbasy et al [31] using three heterogeneous players, namely, naïve, bounded rational, and adaptive players. Askar and Alshamrani [32] have studied four different models, namely, cooperative Cournot triopoly, rational Bertrand triopoly, rational Cournot triopoly, and Puu triopoly, based on a quantity competition.…”

Section: Introductionmentioning

confidence: 99%

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Exploration of Complex Dynamics for Cournot Oligopoly Game with Differentiated Products

2018

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This paper proposes a Cournot game organized by three competing firms adopting bounded rationality. According to the marginal profit in the past time step, each firm tries to update its production using local knowledge. In this game, a firm's preference is represented by a utility function that is derived from a constant elasticity of substitution (CES) production function. The game is modeled by a 3-dimensional discrete dynamical system. The equilibria of the system are numerically studied to detect their complex characteristics due to difficulty to get an explicit form for those equilibria. For the proposed utility function, some cases with different value parameters are considered. Numerical simulations are used to provide an experimental evidence for the complex behavior of the evolution of the system. The obtained results show that the system loses its stability due to different types of bifurcations.

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Analysis of nonlinear triopoly game with heterogeneous players

Cited by 86 publications

References 14 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

Exploration of Complex Dynamics for Cournot Oligopoly Game with Differentiated Products

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