Asymmetric information on price can affect Bertrand duopoly players with the gradient-based mechanism
type: Item
instance of: scholarly article
title: Asymmetric information on price can affect Bertrand duopoly players with the gradient-based mechanism
zbMATH Open document ID: 1459.91085
DOI: 10.1155/2020/6620570
author: S. S. Askar
published in: Mathematical Problems in Engineering
publication date: 2021-01-04T00:00:00Z
review text: Summary: 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 \(Z_0- Z_2\) or \(Z_1- Z_3\), while the classical model is of type \(Z_0- Z_2\) only. This explains the quite complicated basins of attraction given for the proposed map.
Mathematics Subject Classification ID: 91B55
Mathematics Subject Classification ID: 37N40
Mathematics Subject Classification ID: 91A80
Mathematics Subject Classification ID: 91B54
zbMATH DE Number: 7290067
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/6620570
OpenAlex ID: W3113247132
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description: scientific article; zbMATH DE number 7290067