Global dynamics of an oligopoly competition model with isoelastic demand and strategic delegation

Liu, Yuxia; Zhou, Wei; Wang, Qian

doi:10.1016/j.chaos.2022.112304

Cited by 9 publications

(1 citation statement)

References 28 publications

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“…Zhu and Zhou [29] established a static quantum game model about isoelastic demand, considered quantum entanglement in inter-enterprise decision making, and analyzed the local bifurcation and global dynamics of the system. More literature on isoelastic demand can be found in [30]- [33].…”

Section: Introductionmentioning

confidence: 99%

Global dynamics analysis of a duopoly game model with isoelastic demand and consumer surplus

Liu

Zhou

et al. 2023

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We established a dynamic duopoly game model with consumer surplus and isoelastic demand, and studied the local and global dynamic characteristics of the game model. The local stability of the boundary equilibrium point is examined by way of the stability theory and Jacobian matrix, and through the Jury criterion, the stable region of the Nash equilibrium point is determined. The analysis revealed that the system may lose stability via the Flip bifurcation and the Neimark-Sacker bifurcation. The effect of each parameter on the stability of the system is discussed in virtue of numerical simulations, and it is concluded that when enterprises choose relatively small the speed of adjustment, profit weight coefficient and marginal cost, as well as relatively large price elasticity coefficient, it is more beneficial to the future long-term development of enterprises. With the help of the basin of attraction, the problem of attractor coexistence is studied. Multiple stability always implies path dependence, implying that historical chance has a significant impact on the future behavior of enterprises. In other words, the slight perturbations of the initial conditions will have a significant impact on how the system develops. In addition, we investigate the system’s global dynamical behavior using critical curves, basins of attraction, attracting areas and the noninvertible map, and discover three global bifurcations of the system. The boundary of the chaotic attractor and the region with higher density of points are given by the critical curve.

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Section: Introductionmentioning

confidence: 99%