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Copyright © 2020 S. S. Askar. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0/

Abstract

We study a Bertrand duopoly game in which firms adopt a gradient-based mechanism to update their prices. In this competition, one of the firms knows somehow the price adopted by the other firm next time step. Such asymmetric information of the market price possessed by one firm gives interesting results about its stability in the market. Under such information, we use the bounded rationality mechanism to build the model describing the game at hand. We calculate the equilibrium points of the game and study their stabilities. Using different sets of parameter values, we show that the interior equilibrium point can be destabilized through flip and Neimark–Sacker bifurcations. We compare the region of stability of the proposed model with a classical Bertrand model without asymmetric information. The results show that the proposed game’s map is noninvertible with type Z0Z2 or Z1Z3, while the classical model is of type Z0Z2 only. This explains the quite complicated basins of attraction given for the proposed map.

Details

Title
Asymmetric Information on Price Can Affect Bertrand Duopoly Players with the Gradient-Based Mechanism
Author
Askar, S S 1   VIAFID ORCID Logo 

 Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia; Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt 
Editor
Adel Ouannas
Publication year
2020
Publication date
2020
Publisher
John Wiley & Sons, Inc.
ISSN
1024123X
e-ISSN
15635147
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2474858324
Copyright
Copyright © 2020 S. S. Askar. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0/