Hotelling-Bertrand duopoly competition under firm-specific network effects

Tolotti, Marco; Yepez, Jorge

doi:10.1016/j.jebo.2020.05.004

Cited by 4 publications

(2 citation statements)

References 52 publications

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“…According to Lemma 2, we obtain q 1 (t + ) = 0. In view of (8), it is a contradiction. So, q 1 (t) ≥ 0, ∀ t ≥ t 0 .…”

Section: Dynamics Exploration Of the Solutionmentioning

confidence: 99%

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Exploring Dynamics and Hopf Bifurcation of a Fractional-Order Bertrand Duopoly Game Model Incorporating Both Nonidentical Time Delays

et al. 2023

Fractal Fract

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In order to maximize benefits, oligopolistic competition often occurs in contemporary society. Establishing the mathematical models to reveal the law of market competition has become a vital topic. In the current study, on the basis of the earlier publications, we propose a new fractional-order Bertrand duopoly game model incorporating both nonidentical time delays. The dynamics involving existence and uniqueness, non-negativeness, and boundedness of solution to the considered fractional-order Bertrand duopoly game model are systematacially analyzed via the Banach fixed point theorem, mathematical analysis technique, and construction of an appropriate function. Making use of different delays as bifurcation parameters, several sets of new stability and bifurcation conditions ensuring the stability and the creation of Hopf bifurcation of the established fractional-order Bertrand duopoly game model are acquired. By virtue of a proper definite function, we set up a new sufficient condition that ensures globally asymptotically stability of the considered fractional-order Bertrand duopoly game model. The work reveals the impact of different types of delays on the stability and Hopf bifurcation of the proposed fractional-order Bertrand duopoly game model. The study shows that we can adjust the delay to achieve price balance of different products. To confirm the validity of the derived criteria, we put computer simulation into effect. The derived conclusions in this article are wholly new and have great theoretical value in administering companies.

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“…According to Lemma 2, we obtain q 1 (t + ) = 0. In view of (8), it is a contradiction. So, q 1 (t) ≥ 0, ∀ t ≥ t 0 .…”

Section: Dynamics Exploration Of the Solutionmentioning

confidence: 99%

“…Askar and Al-khedhairi [6] implemented concrete discussion on local and global stability of the equilibrium points for a duopoly game concerning price competition. For more detailed works on this aspect, one can see the literature [7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%