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© 2020 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.

Abstract

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.

Details

Title
A Dynamic Duopoly Model: When a Firm Shares the Market with Certain Profit
Author
Askar, Sameh S 1 

 Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia; [email protected]; Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt 
First page
1826
Publication year
2020
Publication date
2020
Publisher
MDPI AG
e-ISSN
22277390
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2548819905
Copyright
© 2020 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.