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Open AccessArticle

A Dynamic Duopoly Model: When a Firm Shares the Market with Certain Profit

1
Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
2
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Mathematics 2020, 8(10), 1826; https://doi.org/10.3390/math8101826
Received: 14 September 2020 / Revised: 10 October 2020 / Accepted: 13 October 2020 / Published: 17 October 2020
(This article belongs to the Special Issue Dynamical Systems and Their Applications Methods)
The current paper analyzes a competition of the Cournot duopoly game whose players (firms) are heterogeneous in a market with isoelastic demand functions and linear costs. The first firm adopts a rationally-based gradient mechanism while the second one chooses to share the market with certain profit in order to update its production. It trades off between profit and market share maximization. The equilibrium point of the proposed game is calculated and its stability conditions are investigated. Our studies show that the equilibrium point becomes unstable through period doubling and Neimark–Sacker bifurcation. Furthermore, the map describing the proposed game is nonlinear and noninvertible which lead to several stable attractors. As in literature, we have provided an analytical investigation of the map’s basins of attraction that includes lobes regions. View Full-Text
Keywords: duopoly game; gradient mechanism; stability; bifurcation; basin of attraction; lobes duopoly game; gradient mechanism; stability; bifurcation; basin of attraction; lobes
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Askar, S.S. A Dynamic Duopoly Model: When a Firm Shares the Market with Certain Profit. Mathematics 2020, 8, 1826.

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