Asymmetric Information on Price Can Affect Bertrand Duopoly Players with the Gradient-Based Mechanism
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 res...
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Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2020/6620570 |
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doaj-a2fe14e0e857402292083a6132dfaec52020-12-21T11:41:32ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472020-01-01202010.1155/2020/66205706620570Asymmetric Information on Price Can Affect Bertrand Duopoly Players with the Gradient-Based MechanismS. S. Askar0Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi ArabiaWe 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 Z0−Z2 or Z1−Z3, while the classical model is of type Z0−Z2 only. This explains the quite complicated basins of attraction given for the proposed map.http://dx.doi.org/10.1155/2020/6620570 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
S. S. Askar |
spellingShingle |
S. S. Askar Asymmetric Information on Price Can Affect Bertrand Duopoly Players with the Gradient-Based Mechanism Mathematical Problems in Engineering |
author_facet |
S. S. Askar |
author_sort |
S. S. Askar |
title |
Asymmetric Information on Price Can Affect Bertrand Duopoly Players with the Gradient-Based Mechanism |
title_short |
Asymmetric Information on Price Can Affect Bertrand Duopoly Players with the Gradient-Based Mechanism |
title_full |
Asymmetric Information on Price Can Affect Bertrand Duopoly Players with the Gradient-Based Mechanism |
title_fullStr |
Asymmetric Information on Price Can Affect Bertrand Duopoly Players with the Gradient-Based Mechanism |
title_full_unstemmed |
Asymmetric Information on Price Can Affect Bertrand Duopoly Players with the Gradient-Based Mechanism |
title_sort |
asymmetric information on price can affect bertrand duopoly players with the gradient-based mechanism |
publisher |
Hindawi Limited |
series |
Mathematical Problems in Engineering |
issn |
1024-123X 1563-5147 |
publishDate |
2020-01-01 |
description |
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 Z0−Z2 or Z1−Z3, while the classical model is of type Z0−Z2 only. This explains the quite complicated basins of attraction given for the proposed map. |
url |
http://dx.doi.org/10.1155/2020/6620570 |
work_keys_str_mv |
AT ssaskar asymmetricinformationonpricecanaffectbertrandduopolyplayerswiththegradientbasedmechanism |
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